// Copyright 2015-2023 The Khronos Group Inc. // // SPDX-License-Identifier: CC-BY-4.0 [[textures]] = Image Operations == Image Operations Overview Vulkan Image Operations are operations performed by those SPIR-V Image Instructions which take an code:OpTypeImage (representing a sname:VkImageView) or code:OpTypeSampledImage (representing a (sname:VkImageView, sname:VkSampler) pair). Read, write, and atomic operations also take texel coordinates as operands, and return a value based on a neighborhood of texture elements (_texels_) within the image. Query operations return properties of the bound image or of the lookup itself. The "`Depth`" operand of code:OpTypeImage is ignored. [NOTE] .Note ==== Texel is a term which is a combination of the words texture and element. Early interactive computer graphics supported texture operations on textures, a small subset of the image operations on images described here. The discrete samples remain essentially equivalent, however, so we retain the historical term texel to refer to them. ==== Image Operations include the functionality of the following SPIR-V Image Instructions: * code:OpImageSample* and code:OpImageSparseSample* read one or more neighboring texels of the image, and <> the texel values based on the state of the sampler. ** Instructions with code:ImplicitLod in the name <> the LOD used in the sampling operation based on the coordinates used in neighboring fragments. ** Instructions with code:ExplicitLod in the name <> the LOD used in the sampling operation based on additional coordinates. ** Instructions with code:Proj in the name apply homogeneous <> to the coordinates. * code:OpImageFetch and code:OpImageSparseFetch return a single texel of the image. No sampler is used. * code:OpImage*Gather and code:OpImageSparse*Gather read neighboring texels and <> of each. * code:OpImageRead (and code:OpImageSparseRead) and code:OpImageWrite read and write, respectively, a texel in the image. No sampler is used. ifdef::VK_NV_shader_image_footprint[] * code:OpImageSampleFootprintNV identifies and returns information about the set of texels in the image that would be accessed by an equivalent code:OpImageSample* instruction. endif::VK_NV_shader_image_footprint[] * code:OpImage*Dref* instructions apply <> on the texel values. * code:OpImageSparse* instructions additionally return a <> code. * code:OpImageQuerySize, code:OpImageQuerySizeLod, code:OpImageQueryLevels, and code:OpImageQuerySamples return properties of the image descriptor that would be accessed. The image itself is not accessed. * code:OpImageQueryLod returns the LOD parameters that would be used in a sample operation. The actual operation is not performed. ifdef::VK_QCOM_image_processing[] * code:OpImageWeightedSampleQCOM reads a 2D neighborhood of texels and computes a weighted average using weight values from a separate weight texture. * code:opImageBlockMatchSADQCOM and code:opTextureBlockMatchSSD compare 2D neighborhoods of texels from two textures. * code:OpImageBoxFilterQCOM reads a 2D neighborhood of texels and computes a weighted average of the texels. endif::VK_QCOM_image_processing[] ifdef::VK_QCOM_image_processing2[] * code:opImageBlockMatchWindowSADQCOM and code:opImageBlockMatchWindowSSDQCOM compare 2D neighborhoods of texels from two textures with the comparison repeated across a window region in the target texture. * code:opImageBlockMatchGatherSADQCOM and code:opImageBlockMatchWindowSSDQCOM compares four 2D neighborhoods of texels from a target texture with a single 2D neighborhood in the reference texture. The R component of each comparison is gathered and returned in the output. endif::VK_QCOM_image_processing2[] [[textures-texel-coordinate-systems]] === Texel Coordinate Systems Images are addressed by _texel coordinates_. There are three _texel coordinate systems_: * normalized texel coordinates [eq]#[0.0, 1.0]# * unnormalized texel coordinates [eq]#[0.0, width / height / depth)# * integer texel coordinates [eq]#[0, width / height / depth)# SPIR-V code:OpImageFetch, code:OpImageSparseFetch, code:OpImageRead, code:OpImageSparseRead, ifdef::VK_QCOM_image_processing[] code:opImageBlockMatchSADQCOM, code:opImageBlockMatchSSDQCOM, endif::VK_QCOM_image_processing[] ifdef::VK_QCOM_image_processing2[] code:opImageBlockMatchWindowSADQCOM, code:opImageBlockMatchWindowSSDQCOM, endif::VK_QCOM_image_processing2[] and code:OpImageWrite instructions use integer texel coordinates. Other image instructions can: use either normalized or unnormalized texel coordinates (selected by the pname:unnormalizedCoordinates state of the sampler used in the instruction), but there are <> on what operations, image state, and sampler state is supported. Normalized coordinates are logically <> to unnormalized as part of image operations, and <> are only performed on normalized coordinates. The array layer coordinate is always treated as unnormalized even when other coordinates are normalized. Normalized texel coordinates are referred to as [eq]#(s,t,r,q,a)#, with the coordinates having the following meanings: * [eq]#s#: Coordinate in the first dimension of an image. * [eq]#t#: Coordinate in the second dimension of an image. * [eq]#r#: Coordinate in the third dimension of an image. ** [eq]#(s,t,r)# are interpreted as a direction vector for Cube images. * [eq]#q#: Fourth coordinate, for homogeneous (projective) coordinates. * [eq]#a#: Coordinate for array layer. The coordinates are extracted from the SPIR-V operand based on the dimensionality of the image variable and type of instruction. For code:Proj instructions, the components are in order [eq]#(s, [t,] [r,] q)#, with [eq]#t# and [eq]#r# being conditionally present based on the code:Dim of the image. For non-code:Proj instructions, the coordinates are [eq]#(s [,t] [,r] [,a])#, with [eq]#t# and [eq]#r# being conditionally present based on the code:Dim of the image and [eq]#a# being conditionally present based on the code:Arrayed property of the image. Projective image instructions are not supported on code:Arrayed images. Unnormalized texel coordinates are referred to as [eq]#(u,v,w,a)#, with the coordinates having the following meanings: * [eq]#u#: Coordinate in the first dimension of an image. * [eq]#v#: Coordinate in the second dimension of an image. * [eq]#w#: Coordinate in the third dimension of an image. * [eq]#a#: Coordinate for array layer. Only the [eq]#u# and [eq]#v# coordinates are directly extracted from the SPIR-V operand, because only 1D and 2D (non-code:Arrayed) dimensionalities support unnormalized coordinates. The components are in order [eq]#(u [,v])#, with [eq]#v# being conditionally present when the dimensionality is 2D. When normalized coordinates are converted to unnormalized coordinates, all four coordinates are used. Integer texel coordinates are referred to as [eq]#(i,j,k,l,n)#, with the coordinates having the following meanings: * [eq]#i#: Coordinate in the first dimension of an image. * [eq]#j#: Coordinate in the second dimension of an image. * [eq]#k#: Coordinate in the third dimension of an image. * [eq]#l#: Coordinate for array layer. * [eq]#n#: Index of the sample within the texel. They are extracted from the SPIR-V operand in order [eq]#(i [,j] [,k] [,l] [,n])#, with [eq]#j# and [eq]#k# conditionally present based on the code:Dim of the image, and [eq]#l# conditionally present based on the code:Arrayed property of the image. [eq]#n# is conditionally present and is taken from the code:Sample image operand. ifdef::VK_EXT_image_sliced_view_of_3d[] If an accessed image was created from a view using slink:VkImageViewSlicedCreateInfoEXT and accessed through a ename:VK_DESCRIPTOR_TYPE_STORAGE_IMAGE descriptor, then the value of [eq]#k# is incremented by slink:VkImageViewSlicedCreateInfoEXT::pname:sliceOffset, giving [eq]#k <- sliceOffset {plus} k#. The image's accessible range in the third dimension is [eq]#k < sliceOffset + sliceCount#. If slink:VkImageViewSlicedCreateInfoEXT::pname:sliceCount is ename:VK_REMAINING_3D_SLICES_EXT, the range is inherited from the image's depth extent as specified by <>. endif::VK_EXT_image_sliced_view_of_3d[] For all coordinate types, unused coordinates are assigned a value of zero. [[textures-texel-coordinate-systems-diagrams]] image::{images}/vulkantexture0-ll.svg[align="center",title="Texel Coordinate Systems, Linear Filtering",opts="{imageopts}"] The Texel Coordinate Systems - For the example shown of an 8{times}4 texel two dimensional image. * Normalized texel coordinates: ** The [eq]#s# coordinate goes from 0.0 to 1.0. ** The [eq]#t# coordinate goes from 0.0 to 1.0. * Unnormalized texel coordinates: ** The [eq]#u# coordinate within the range 0.0 to 8.0 is within the image, otherwise it is outside the image. ** The [eq]#v# coordinate within the range 0.0 to 4.0 is within the image, otherwise it is outside the image. * Integer texel coordinates: ** The [eq]#i# coordinate within the range 0 to 7 addresses texels within the image, otherwise it is outside the image. ** The [eq]#j# coordinate within the range 0 to 3 addresses texels within the image, otherwise it is outside the image. * Also shown for linear filtering: ** Given the unnormalized coordinates [eq]#(u,v)#, the four texels selected are [eq]#i~0~j~0~#, [eq]#i~1~j~0~#, [eq]#i~0~j~1~#, and [eq]#i~1~j~1~#. ** The fractions [eq]#{alpha}# and [eq]#{beta}#. ** Given the offset [eq]#{DeltaUpper}~i~# and [eq]#{DeltaUpper}~j~#, the four texels selected by the offset are [eq]#i~0~j'~0~#, [eq]#i~1~j'~0~#, [eq]#i~0~j'~1~#, and [eq]#i~1~j'~1~#. ifdef::VK_VERSION_1_1,VK_KHR_sampler_ycbcr_conversion[] [NOTE] .Note ==== For formats with reduced-resolution components, [eq]#{DeltaUpper}~i~# and [eq]#{DeltaUpper}~j~# are relative to the resolution of the highest-resolution component, and therefore may be divided by two relative to the unnormalized coordinate space of the lower-resolution components. ==== endif::VK_VERSION_1_1,VK_KHR_sampler_ycbcr_conversion[] image::{images}/vulkantexture1-ll.svg[align="center",title="Texel Coordinate Systems, Nearest Filtering",opts="{imageopts}"] The Texel Coordinate Systems - For the example shown of an 8{times}4 texel two dimensional image. * Texel coordinates as above. Also shown for nearest filtering: ** Given the unnormalized coordinates [eq]#(u,v)#, the texel selected is [eq]#ij#. ** Given the offset [eq]#{DeltaUpper}~i~# and [eq]#{DeltaUpper}~j~#, the texel selected by the offset is [eq]#ij'#. ifdef::VK_NV_corner_sampled_image[] For corner-sampled images, the texel samples are located at the grid intersections instead of the texel centers. image::{images}/vulkantexture0-corner-alternative-a-ll.svg[align="center",title="Texel Coordinate Systems, Corner Sampling",opts="{imageopts}"] endif::VK_NV_corner_sampled_image[] == Conversion Formulas ifdef::editing-notes[] [NOTE] .editing-note ==== (Bill) These Conversion Formulas will likely move to Section 2.7 Fixed-Point Data Conversions (RGB to sRGB and sRGB to RGB) and section 2.6 Numeric Representation and Computation (RGB to Shared Exponent and Shared Exponent to RGB) ==== endif::editing-notes[] [[textures-RGB-sexp]] === RGB to Shared Exponent Conversion An RGB color [eq]#(red, green, blue)# is transformed to a shared exponent color [eq]#(red~shared~, green~shared~, blue~shared~, exp~shared~)# as follows: First, the components [eq]#(red, green, blue)# are clamped to [eq]#(red~clamped~, green~clamped~, blue~clamped~)# as: {empty}:: [eq]#red~clamped~ = max(0, min(sharedexp~max~, red))# {empty}:: [eq]#green~clamped~ = max(0, min(sharedexp~max~, green))# {empty}:: [eq]#blue~clamped~ = max(0, min(sharedexp~max~, blue))# where: [latexmath] +++++++++++++++++++ \begin{aligned} N & = 9 & \text{number of mantissa bits per component} \\ B & = 15 & \text{exponent bias} \\ E_{max} & = 31 & \text{maximum possible biased exponent value} \\ sharedexp_{max} & = \frac{(2^N-1)}{2^N} \times 2^{(E_{max}-B)} \end{aligned} +++++++++++++++++++ [NOTE] .Note ==== // The trailing + is to avoid the asciidoc parser treating the custom role // as a block attribute in some cases. [eq]#NaN#, if supported, is handled as in + <> `minNum()` and `maxNum()`. This results in any [eq]#NaN# being mapped to zero. ==== The largest clamped component, [eq]#max~clamped~# is determined: {empty}:: [eq]#max~clamped~ = max(red~clamped~, green~clamped~, blue~clamped~)# A preliminary shared exponent [eq]#exp'# is computed: [latexmath] +++++++++++++++++++ \begin{aligned} exp' = \begin{cases} \left \lfloor \log_2(max_{clamped}) \right \rfloor + (B+1) & \text{for}\ max_{clamped} > 2^{-(B+1)} \\ 0 & \text{for}\ max_{clamped} \leq 2^{-(B+1)} \end{cases} \end{aligned} +++++++++++++++++++ The shared exponent [eq]#exp~shared~# is computed: [latexmath] +++++++++++++++++++ \begin{aligned} max_{shared} = \left \lfloor { \frac{max_{clamped}}{2^{(exp'-B-N)}} + \frac{1}{2} } \right \rfloor \end{aligned} +++++++++++++++++++ [latexmath] +++++++++++++++++++ \begin{aligned} exp_{shared} = \begin{cases} exp' & \text{for}\ 0 \leq max_{shared} < 2^N \\ exp'+1 & \text{for}\ max_{shared} = 2^N \end{cases} \end{aligned} +++++++++++++++++++ Finally, three integer values in the range [eq]#0# to [eq]#2^N^# are computed: [latexmath] +++++++++++++++++++ \begin{aligned} red_{shared} & = \left \lfloor { \frac{red_{clamped}}{2^{(exp_{shared}-B-N)}}+ \frac{1}{2} } \right \rfloor \\ green_{shared} & = \left \lfloor { \frac{green_{clamped}}{2^{(exp_{shared}-B-N)}}+ \frac{1}{2} } \right \rfloor \\ blue_{shared} & = \left \lfloor { \frac{blue_{clamped}}{2^{(exp_{shared}-B-N)}}+ \frac{1}{2} } \right \rfloor \end{aligned} +++++++++++++++++++ [[textures-sexp-RGB]] === Shared Exponent to RGB A shared exponent color [eq]#(red~shared~, green~shared~, blue~shared~, exp~shared~)# is transformed to an RGB color [eq]#(red, green, blue)# as follows: {empty}:: latexmath:[red = red_{shared} \times {2^{(exp_{shared}-B-N)}}] {empty}:: latexmath:[green = green_{shared} \times {2^{(exp_{shared}-B-N)}}] {empty}:: latexmath:[blue = blue_{shared} \times {2^{(exp_{shared}-B-N)}}] where: {empty}:: [eq]#N = 9# (number of mantissa bits per component) {empty}:: [eq]#B = 15# (exponent bias) == Texel Input Operations _Texel input instructions_ are SPIR-V image instructions that read from an image. _Texel input operations_ are a set of steps that are performed on state, coordinates, and texel values while processing a texel input instruction, and which are common to some or all texel input instructions. They include the following steps, which are performed in the listed order: * <> ** <> ** <> ** <> ifdef::VK_VERSION_1_1,VK_KHR_sampler_ycbcr_conversion[] ** <> endif::VK_VERSION_1_1,VK_KHR_sampler_ycbcr_conversion[] * <> * <> * <> * <> * <> ifdef::VK_VERSION_1_1,VK_KHR_sampler_ycbcr_conversion[] * <> * <> endif::VK_VERSION_1_1,VK_KHR_sampler_ycbcr_conversion[] For texel input instructions involving multiple texels (for sampling or gathering), these steps are applied for each texel that is used in the instruction. Depending on the type of image instruction, other steps are conditionally performed between these steps or involving multiple coordinate or texel values. ifdef::VK_VERSION_1_1,VK_KHR_sampler_ycbcr_conversion[] If <> is implicit, <> instead takes place during chroma reconstruction, before <> occurs. endif::VK_VERSION_1_1,VK_KHR_sampler_ycbcr_conversion[] ifdef::VK_QCOM_image_processing[] The operations described in <> and <> are performed before <> and <>. endif::VK_QCOM_image_processing[] [[textures-input-validation]] === Texel Input Validation Operations _Texel input validation operations_ inspect instruction/image/sampler state or coordinates, and in certain circumstances cause the texel value to be replaced or become undefined:. There are a series of validations that the texel undergoes. [[textures-operation-validation]] ==== Instruction/Sampler/Image View Validation There are a number of cases where a SPIR-V instruction can: mismatch with the sampler, the image view, or both, and a number of further cases where the sampler can: mismatch with the image view. In such cases the value of the texel returned is undefined:. These cases include: * The sampler pname:borderColor is an integer type and the image view pname:format is not one of the elink:VkFormat integer types or a stencil component of a depth/stencil format. * The sampler pname:borderColor is a float type and the image view pname:format is not one of the elink:VkFormat float types or a depth component of a depth/stencil format. ifndef::VK_EXT_border_color_swizzle[] * The sampler pname:borderColor is one of the opaque black colors (ename:VK_BORDER_COLOR_FLOAT_OPAQUE_BLACK or ename:VK_BORDER_COLOR_INT_OPAQUE_BLACK) and the image view elink:VkComponentSwizzle for any of the slink:VkComponentMapping components is not the <>. endif::VK_EXT_border_color_swizzle[] ifdef::VK_EXT_border_color_swizzle[] * The sampler pname:borderColor is one of the opaque black colors (ename:VK_BORDER_COLOR_FLOAT_OPAQUE_BLACK or ename:VK_BORDER_COLOR_INT_OPAQUE_BLACK) and the image view elink:VkComponentSwizzle for any of the slink:VkComponentMapping components is not the <>, and slink:VkPhysicalDeviceBorderColorSwizzleFeaturesEXT::pname:borderColorSwizzleFromImage feature is not enabled, and slink:VkSamplerBorderColorComponentMappingCreateInfoEXT is not specified. * slink:VkSamplerBorderColorComponentMappingCreateInfoEXT::pname:components, if specified, has a component swizzle that does not match the component swizzle of the image view, and either component swizzle is not a form of identity swizzle. * slink:VkSamplerBorderColorComponentMappingCreateInfoEXT::pname:srgb, if specified, does not match the sRGB encoding of the image view. endif::VK_EXT_border_color_swizzle[] ifdef::VK_EXT_custom_border_color[] * The sampler pname:borderColor is a custom color (ename:VK_BORDER_COLOR_FLOAT_CUSTOM_EXT or ename:VK_BORDER_COLOR_INT_CUSTOM_EXT) and the supplied slink:VkSamplerCustomBorderColorCreateInfoEXT::pname:customBorderColor is outside the bounds of the values representable in the image view's pname:format. ifndef::VK_EXT_border_color_swizzle[] * The sampler pname:borderColor is a custom color (ename:VK_BORDER_COLOR_FLOAT_CUSTOM_EXT or ename:VK_BORDER_COLOR_INT_CUSTOM_EXT) and the image view elink:VkComponentSwizzle for any of the slink:VkComponentMapping components is not the <>. endif::VK_EXT_border_color_swizzle[] ifdef::VK_EXT_border_color_swizzle[] * The sampler pname:borderColor is a custom color (ename:VK_BORDER_COLOR_FLOAT_CUSTOM_EXT or ename:VK_BORDER_COLOR_INT_CUSTOM_EXT) and the image view elink:VkComponentSwizzle for any of the slink:VkComponentMapping components is not the <>, and slink:VkPhysicalDeviceBorderColorSwizzleFeaturesEXT::pname:borderColorSwizzleFromImage feature is not enabled, and slink:VkSamplerBorderColorComponentMappingCreateInfoEXT is not specified. endif::VK_EXT_border_color_swizzle[] endif::VK_EXT_custom_border_color[] * The elink:VkImageLayout of any subresource in the image view does not match the slink:VkDescriptorImageInfo::pname:imageLayout used to write the image descriptor. * The SPIR-V Image Format is not <> with the image view's pname:format. * The sampler pname:unnormalizedCoordinates is ename:VK_TRUE and any of the <> are violated. ifdef::VK_EXT_fragment_density_map[] * The sampler was created with pname:flags containing ename:VK_SAMPLER_CREATE_SUBSAMPLED_BIT_EXT and the image was not created with pname:flags containing ename:VK_IMAGE_CREATE_SUBSAMPLED_BIT_EXT. * The sampler was not created with pname:flags containing ename:VK_SAMPLER_CREATE_SUBSAMPLED_BIT_EXT and the image was created with pname:flags containing ename:VK_IMAGE_CREATE_SUBSAMPLED_BIT_EXT. * The sampler was created with pname:flags containing ename:VK_SAMPLER_CREATE_SUBSAMPLED_BIT_EXT and is used with a function that is not code:OpImageSampleImplicitLod or code:OpImageSampleExplicitLod, or is used with operands code:Offset or code:ConstOffsets. endif::VK_EXT_fragment_density_map[] * The SPIR-V instruction is one of the code:OpImage*Dref* instructions and the sampler pname:compareEnable is ename:VK_FALSE * The SPIR-V instruction is not one of the code:OpImage*Dref* instructions and the sampler pname:compareEnable is ename:VK_TRUE ifndef::VK_VERSION_1_3,VK_KHR_format_feature_flags2[] * The SPIR-V instruction is one of the code:OpImage*Dref* instructions and the image view pname:format is not one of the depth/stencil formats with a depth component, or the image view aspect is not ename:VK_IMAGE_ASPECT_DEPTH_BIT. endif::VK_VERSION_1_3,VK_KHR_format_feature_flags2[] ifdef::VK_VERSION_1_3,VK_KHR_format_feature_flags2[] * The SPIR-V instruction is one of the code:OpImage*Dref* instructions, the image view pname:format is one of the depth/stencil formats, and the image view aspect is not ename:VK_IMAGE_ASPECT_DEPTH_BIT. endif::VK_VERSION_1_3,VK_KHR_format_feature_flags2[] * The SPIR-V instruction's image variable's properties are not compatible with the image view: ** Rules for pname:viewType: *** ename:VK_IMAGE_VIEW_TYPE_1D must: have code:Dim = 1D, code:Arrayed = 0, code:MS = 0. *** ename:VK_IMAGE_VIEW_TYPE_2D must: have code:Dim = 2D, code:Arrayed = 0. *** ename:VK_IMAGE_VIEW_TYPE_3D must: have code:Dim = 3D, code:Arrayed = 0, code:MS = 0. *** ename:VK_IMAGE_VIEW_TYPE_CUBE must: have code:Dim = Cube, code:Arrayed = 0, code:MS = 0. *** ename:VK_IMAGE_VIEW_TYPE_1D_ARRAY must: have code:Dim = 1D, code:Arrayed = 1, code:MS = 0. *** ename:VK_IMAGE_VIEW_TYPE_2D_ARRAY must: have code:Dim = 2D, code:Arrayed = 1. *** ename:VK_IMAGE_VIEW_TYPE_CUBE_ARRAY must: have code:Dim = Cube, code:Arrayed = 1, code:MS = 0. ** If the image was created with slink:VkImageCreateInfo::pname:samples equal to ename:VK_SAMPLE_COUNT_1_BIT, the instruction must: have code:MS = 0. ** If the image was created with slink:VkImageCreateInfo::pname:samples not equal to ename:VK_SAMPLE_COUNT_1_BIT, the instruction must: have code:MS = 1. ** If the code:Sampled code:Type of the code:OpTypeImage does not match the <>. ** If the <> does not match the signedness of the image's format. ifdef::VK_NV_corner_sampled_image[] * If the image was created with slink:VkImageCreateInfo::pname:flags containing ename:VK_IMAGE_CREATE_CORNER_SAMPLED_BIT_NV, the sampler addressing modes must: only use a elink:VkSamplerAddressMode of ename:VK_SAMPLER_ADDRESS_MODE_CLAMP_TO_EDGE. endif::VK_NV_corner_sampled_image[] ifdef::VK_NV_shader_image_footprint[] * The SPIR-V instruction is code:OpImageSampleFootprintNV with code:Dim = 2D and pname:addressModeU or pname:addressModeV in the sampler is not ename:VK_SAMPLER_ADDRESS_MODE_CLAMP_TO_EDGE. * The SPIR-V instruction is code:OpImageSampleFootprintNV with code:Dim = 3D and pname:addressModeU, pname:addressModeV, or pname:addressModeW in the sampler is not ename:VK_SAMPLER_ADDRESS_MODE_CLAMP_TO_EDGE. endif::VK_NV_shader_image_footprint[] ifdef::VK_EXT_custom_border_color[] * The sampler was created with a specified slink:VkSamplerCustomBorderColorCreateInfoEXT::pname:format which does not match the elink:VkFormat of the image view(s) it is sampling. * The sampler is sampling an image view of ename:VK_FORMAT_B4G4R4A4_UNORM_PACK16, ename:VK_FORMAT_B5G6R5_UNORM_PACK16, or ename:VK_FORMAT_B5G5R5A1_UNORM_PACK16 format without a specified slink:VkSamplerCustomBorderColorCreateInfoEXT::pname:format. endif::VK_EXT_custom_border_color[] ifdef::VK_VERSION_1_1,VK_KHR_sampler_ycbcr_conversion[] Only code:OpImageSample* and code:OpImageSparseSample* can: be used with a sampler or image view that enables <>. code:OpImageFetch, code:OpImageSparseFetch, code:OpImage*Gather, and code:OpImageSparse*Gather must: not be used with a sampler or image view that enables <>. The code:ConstOffset and code:Offset operands must: not be used with a sampler or image view that enables <>. endif::VK_VERSION_1_1,VK_KHR_sampler_ycbcr_conversion[] [[textures-integer-coordinate-validation]] ==== Integer Texel Coordinate Validation Integer texel coordinates are validated against the size of the image level, and the number of layers and number of samples in the image. For SPIR-V instructions that use integer texel coordinates, this is performed directly on the integer coordinates. For instructions that use normalized or unnormalized texel coordinates, this is performed on the coordinates that result after <> to integer texel coordinates. If the integer texel coordinates do not satisfy all of the conditions {empty}:: [eq]#0 {leq} i < w~s~# {empty}:: [eq]#0 {leq} j < h~s~# {empty}:: [eq]#0 {leq} k < d~s~# {empty}:: [eq]#0 {leq} l < layers# {empty}:: [eq]#0 {leq} n < samples# where: {empty}:: [eq]#w~s~ =# width of the image level {empty}:: [eq]#h~s~ =# height of the image level {empty}:: [eq]#d~s~ =# depth of the image level {empty}:: [eq]#layers =# number of layers in the image {empty}:: [eq]#samples =# number of samples per texel in the image then the texel fails integer texel coordinate validation. There are four cases to consider: . Valid Texel Coordinates + * If the texel coordinates pass validation (that is, the coordinates lie within the image), + then the texel value comes from the value in image memory. . Border Texel + * If the texel coordinates fail validation, and * If the read is the result of an image sample instruction or image gather instruction, and * If the image is not a cube image, ifdef::VK_EXT_non_seamless_cube_map[] or if a sampler created with ename:VK_SAMPLER_CREATE_NON_SEAMLESS_CUBE_MAP_BIT_EXT is used, endif::VK_EXT_non_seamless_cube_map[] + then the texel is a border texel and <> is performed. . Invalid Texel + * If the texel coordinates fail validation, and * If the read is the result of an image fetch instruction, image read instruction, or atomic instruction, + then the texel is an invalid texel and <> is performed. . Cube Map Edge or Corner + Otherwise the texel coordinates lie beyond the edges or corners of the selected cube map face, and <> is performed. [[textures-cubemapedge]] ==== Cube Map Edge Handling If the texel coordinates lie beyond the edges or corners of the selected cube map face (as described in the prior section), the following steps are performed. Note that this does not occur when using ename:VK_FILTER_NEAREST filtering within a mip level, since ename:VK_FILTER_NEAREST is treated as using ename:VK_SAMPLER_ADDRESS_MODE_CLAMP_TO_EDGE. * Cube Map Edge Texel + ** If the texel lies beyond the selected cube map face in either only [eq]#i# or only [eq]#j#, then the coordinates [eq]#(i,j)# and the array layer [eq]#l# are transformed to select the adjacent texel from the appropriate neighboring face. * Cube Map Corner Texel + ** If the texel lies beyond the selected cube map face in both [eq]#i# and [eq]#j#, then there is no unique neighboring face from which to read that texel. The texel should: be replaced by the average of the three values of the adjacent texels in each incident face. However, implementations may: replace the cube map corner texel by other methods. ifndef::VK_EXT_filter_cubic[] The methods are subject to the constraint that if the three available texels have the same value, the resulting filtered texel must: have that value. endif::VK_EXT_filter_cubic[] ifdef::VK_EXT_filter_cubic[] The methods are subject to the constraint that for linear filtering if the three available texels have the same value, the resulting filtered texel must: have that value, and for cubic filtering if the twelve available samples have the same value, the resulting filtered texel must: have that value. endif::VK_EXT_filter_cubic[] [[textures-sparse-validation]] ==== Sparse Validation If the texel reads from an unbound region of a sparse image, the texel is a _sparse unbound texel_, and processing continues with <>. ifdef::VK_VERSION_1_1,VK_KHR_sampler_ycbcr_conversion[] [[textures-layout-validation]] ==== Layout Validation If all planes of a _disjoint_ _multi-planar_ image are not in the same <>, the image must: not be sampled with <> enabled. endif::VK_VERSION_1_1,VK_KHR_sampler_ycbcr_conversion[] [[textures-format-conversion]] === Format Conversion Texels undergo a format conversion from the elink:VkFormat of the image view to a vector of either floating point or signed or unsigned integer components, with the number of components based on the number of components present in the format. * Color formats have one, two, three, or four components, according to the format. * Depth/stencil formats are one component. The depth or stencil component is selected by the pname:aspectMask of the image view. Each component is converted based on its type and size (as defined in the <> section for each elink:VkFormat), using the appropriate equations in <>, <>, <>, <>, and <>. Signed integer components smaller than 32 bits are sign-extended. If the image view format is sRGB, the color components are first converted as if they are UNORM, and then sRGB to linear conversion is applied to the R, G, and B components as described in the "`sRGB EOTF`" section of the <>. The A component, if present, is unchanged. ifdef::VK_QCOM_ycbcr_degamma[] [[textures-ycbcr-degamma]] If slink:VkSamplerYcbcrConversionYcbcrDegammaCreateInfoQCOM::pname:enableYDegamma is equal to ename:VK_TRUE, then sRGB to linear conversion is applied to the G component as described in the "`sRGB EOTF`" section of the <>. If slink:VkSamplerYcbcrConversionYcbcrDegammaCreateInfoQCOM::pname:enableCbCrDegamma is equal to ename:VK_TRUE, then sRGB to linear conversion is applied to the R and B components as described in the "`sRGB EOTF`" section of the <>. The A component, if present, is unchanged. endif::VK_QCOM_ycbcr_degamma[] If the image view format is block-compressed, then the texel value is first decoded, then converted based on the type and number of components defined by the compressed format. [[textures-texel-replacement]] === Texel Replacement A texel is replaced if it is one (and only one) of: * a border texel, * an invalid texel, or * a sparse unbound texel. Border texels are replaced with a value based on the image format and the pname:borderColor of the sampler. The border color is: [[textures-border-replacement-color]] ifdef::VK_EXT_custom_border_color[] .Border Color [eq]#B#, Custom Border Color slink:VkSamplerCustomBorderColorCreateInfoEXT::pname:customBorderColor [eq]#U# endif::VK_EXT_custom_border_color[] ifndef::VK_EXT_custom_border_color[] .Border Color [eq]#B# endif::VK_EXT_custom_border_color[] [options="header",cols="60%,40%"] |==== | Sampler pname:borderColor | Corresponding Border Color | ename:VK_BORDER_COLOR_FLOAT_TRANSPARENT_BLACK | [eq]#[B~r~, B~g~, B~b~, B~a~] = [0.0, 0.0, 0.0, 0.0]# | ename:VK_BORDER_COLOR_FLOAT_OPAQUE_BLACK | [eq]#[B~r~, B~g~, B~b~, B~a~] = [0.0, 0.0, 0.0, 1.0]# | ename:VK_BORDER_COLOR_FLOAT_OPAQUE_WHITE | [eq]#[B~r~, B~g~, B~b~, B~a~] = [1.0, 1.0, 1.0, 1.0]# | ename:VK_BORDER_COLOR_INT_TRANSPARENT_BLACK | [eq]#[B~r~, B~g~, B~b~, B~a~] = [0, 0, 0, 0]# | ename:VK_BORDER_COLOR_INT_OPAQUE_BLACK | [eq]#[B~r~, B~g~, B~b~, B~a~] = [0, 0, 0, 1]# | ename:VK_BORDER_COLOR_INT_OPAQUE_WHITE | [eq]#[B~r~, B~g~, B~b~, B~a~] = [1, 1, 1, 1]# ifdef::VK_EXT_custom_border_color[] | ename:VK_BORDER_COLOR_FLOAT_CUSTOM_EXT | [eq]#[B~r~, B~g~, B~b~, B~a~] = [U~r~, U~g~, U~b~, U~a~]# | ename:VK_BORDER_COLOR_INT_CUSTOM_EXT | [eq]#[B~r~, B~g~, B~b~, B~a~] = [U~r~, U~g~, U~b~, U~a~]# endif::VK_EXT_custom_border_color[] |==== ifdef::VK_EXT_custom_border_color[] The custom border color ([eq]#U#) may: be rounded by implementations prior to texel replacement, but the error introduced by such a rounding must: not exceed one ULP of the image's pname:format. endif::VK_EXT_custom_border_color[] [NOTE] .Note ==== The names etext:VK_BORDER_COLOR_*\_TRANSPARENT_BLACK, etext:VK_BORDER_COLOR_*\_OPAQUE_BLACK, and etext:VK_BORDER_COLOR_*_OPAQUE_WHITE are meant to describe which components are zeros and ones in the vocabulary of compositing, and are not meant to imply that the numerical value of ename:VK_BORDER_COLOR_INT_OPAQUE_WHITE is a saturating value for integers. ==== This is substituted for the texel value by replacing the number of components in the image format [[textures-border-replacement-table]] .Border Texel Components After Replacement [width="100%",options="header"] |==== | Texel Aspect or Format | Component Assignment | Depth aspect | [eq]#D = B~r~# ifdef::VK_EXT_custom_border_color[] | Stencil aspect | [eq]#S = B~r~#{sym2} endif::VK_EXT_custom_border_color[] ifndef::VK_EXT_custom_border_color[] | Stencil aspect | [eq]#S = B~r~# endif::VK_EXT_custom_border_color[] | One component color format | [eq]#Color~r~ = B~r~# | Two component color format | [eq]#[Color~r~,Color~g~] = [B~r~,B~g~]# | Three component color format| [eq]#[Color~r~,Color~g~,Color~b~] = [B~r~,B~g~,B~b~]# | Four component color format | [eq]#[Color~r~,Color~g~,Color~b~,Color~a~] = [B~r~,B~g~,B~b~,B~a~]# ifdef::VK_KHR_maintenance5[] | Single component alpha format | [eq]#[Color~r~,Color~g~,Color~b~, Color~a~] = [0,0,0,B~a~]# endif::VK_KHR_maintenance5[] |==== ifdef::VK_EXT_custom_border_color[] {sym2} [eq]#S = B~g~# may: be substituted as the replacement method by the implementation when slink:VkSamplerCreateInfo::pname:borderColor is ename:VK_BORDER_COLOR_INT_CUSTOM_EXT and slink:VkSamplerCustomBorderColorCreateInfoEXT::pname:format is ename:VK_FORMAT_UNDEFINED. Implementations should: use [eq]#S = B~r~# as the replacement method. endif::VK_EXT_custom_border_color[] The value returned by a read of an invalid texel is undefined:, unless that read operation is from a buffer resource and the pname:robustBufferAccess feature is enabled. In that case, an invalid texel is replaced as described by the <> feature. ifdef::VK_VERSION_1_3,VK_EXT_image_robustness,VK_EXT_robustness2[] If the access is to an image resource and the x, y, z, or layer coordinate validation fails and ifdef::VK_VERSION_1_3,VK_EXT_image_robustness[] the <> feature is enabled, then zero must: be returned for the R, G, and B components, if present. Either zero or one must: be returned for the A component, if present. ifdef::VK_EXT_robustness2[If] endif::VK_VERSION_1_3,VK_EXT_image_robustness[] ifdef::VK_EXT_robustness2[] If the <> feature is enabled, zero values must: be returned. endif::VK_EXT_robustness2[] If only the sample index was invalid, the values returned are undefined:. endif::VK_VERSION_1_3,VK_EXT_image_robustness,VK_EXT_robustness2[] ifdef::VK_VERSION_1_3,VK_EXT_image_robustness[] Additionally, if the <> feature is enabled, ifdef::VK_EXT_robustness2[] but the <> feature is not, endif::VK_EXT_robustness2[] any invalid texels may: be expanded to four components prior to texel replacement. This means that components not present in the image format may be replaced with 0 or may undergo <> as normal. endif::VK_VERSION_1_3,VK_EXT_image_robustness[] ifdef::VK_EXT_robustness2[] Loads from a null descriptor return a four component color value of all zeros. However, for storage images and storage texel buffers using an explicit SPIR-V Image Format, loads from a null descriptor may: return an alpha value of 1 (float or integer, depending on format) if the format does not include alpha. endif::VK_EXT_robustness2[] If the slink:VkPhysicalDeviceSparseProperties::pname:residencyNonResidentStrict property is ename:VK_TRUE, a sparse unbound texel is replaced with 0 or 0.0 values for integer and floating-point components of the image format, respectively. If pname:residencyNonResidentStrict is ename:VK_FALSE, the value of the sparse unbound texel is undefined:. [[textures-depth-compare-operation]] === Depth Compare Operation If the image view has a depth/stencil format, the depth component is selected by the pname:aspectMask, and the operation is an code:OpImage*Dref* instruction, a depth comparison is performed. The result is [eq]#1.0# if the comparison evaluates to [eq]#true#, and [eq]#0.0# otherwise. This value replaces the depth component [eq]#D#. The compare operation is selected by the elink:VkCompareOp value set by slink:VkSamplerCreateInfo::pname:compareOp. The reference value from the SPIR-V operand [eq]#D~ref~# and the texel depth value [eq]#D~tex~# are used as the _reference_ and _test_ values, respectively, in that operation. If the image being sampled has an unsigned normalized fixed-point format, then [eq]#D~ref~# is clamped to [eq]#[0,1]# before the compare operation. [[textures-conversion-to-rgba]] === Conversion to RGBA The texel is expanded from one, two, or three components to four components based on the image base color: [[textures-texel-color-rgba-conversion-table]] .Texel Color After Conversion To RGBA [width="100%", options="header", cols="<4,<6"] |==== | Texel Aspect or Format | RGBA Color | Depth aspect | [eq]#[Color~r~,Color~g~,Color~b~, Color~a~] = [D,0,0,one]# | Stencil aspect | [eq]#[Color~r~,Color~g~,Color~b~, Color~a~] = [S,0,0,one]# | One component color format | [eq]#[Color~r~,Color~g~,Color~b~, Color~a~] = [Color~r~,0,0,one]# | Two component color format | [eq]#[Color~r~,Color~g~,Color~b~, Color~a~] = [Color~r~,Color~g~,0,one]# | Three component color format| [eq]#[Color~r~,Color~g~,Color~b~, Color~a~] = [Color~r~,Color~g~,Color~b~,one]# | Four component color format | [eq]#[Color~r~,Color~g~,Color~b~, Color~a~] = [Color~r~,Color~g~,Color~b~,Color~a~]# ifdef::VK_KHR_maintenance5[] | One alpha component color format | [eq]#[Color~r~,Color~g~,Color~b~, Color~a~] = [0,0,0,Color~a~]# endif::VK_KHR_maintenance5[] |==== where [eq]#one = 1.0f# for floating-point formats and depth aspects, and [eq]#one = 1# for integer formats and stencil aspects. [[textures-component-swizzle]] === Component Swizzle ifndef::VK_VERSION_1_1,VK_KHR_sampler_ycbcr_conversion[] All texel input instructions apply a _swizzle_ based on the elink:VkComponentSwizzle enums in the pname:components member of the slink:VkImageViewCreateInfo structure for the image being read. endif::VK_VERSION_1_1,VK_KHR_sampler_ycbcr_conversion[] ifdef::VK_VERSION_1_1,VK_KHR_sampler_ycbcr_conversion[] All texel input instructions apply a _swizzle_ based on: * the elink:VkComponentSwizzle enums in the pname:components member of the slink:VkImageViewCreateInfo structure for the image being read if <> is not enabled, and * the elink:VkComponentSwizzle enums in the pname:components member of the slink:VkSamplerYcbcrConversionCreateInfo structure for the <> if sampler {YCbCr} conversion is enabled. endif::VK_VERSION_1_1,VK_KHR_sampler_ycbcr_conversion[] The swizzle can: rearrange the components of the texel, or substitute zero or one for any components. It is defined as follows for each color [eq]#component#: [latexmath] +++++++++++++++++++ \begin{aligned} Color'_{component} & = \begin{cases} Color_r & \text{for RED swizzle} \\ Color_g & \text{for GREEN swizzle} \\ Color_b & \text{for BLUE swizzle} \\ Color_a & \text{for ALPHA swizzle} \\ 0 & \text{for ZERO swizzle} \\ one & \text{for ONE swizzle} \\ identity & \text{for IDENTITY swizzle} \end{cases} \end{aligned} +++++++++++++++++++ where: [latexmath] +++++++++++++++++++ \begin{aligned} one & = \begin{cases} & 1.0\text{f} & \text{for floating point components} \\ & 1 & \text{for integer components} \\ \end{cases} \\ identity & = \begin{cases} & Color_r & \text{for}\ component = r \\ & Color_g & \text{for}\ component = g \\ & Color_b & \text{for}\ component = b \\ & Color_a & \text{for}\ component = a \\ \end{cases} \end{aligned} +++++++++++++++++++ If the border color is one of the etext:VK_BORDER_COLOR_*_OPAQUE_BLACK enums and the elink:VkComponentSwizzle is not the <> for all components, the value of the texel after swizzle is undefined:. ifndef::VK_KHR_maintenance5[] If the image view has a depth/stencil format and the elink:VkComponentSwizzle is ename:VK_COMPONENT_SWIZZLE_ONE, the value of the texel after swizzle is undefined:. endif::VK_KHR_maintenance5[] ifdef::VK_KHR_maintenance5[] If the image view has a depth/stencil format and the elink:VkComponentSwizzle is ename:VK_COMPONENT_SWIZZLE_ONE, and sname:VkPhysicalDeviceMaintenance5PropertiesKHR::pname:depthStencilSwizzleOneSupport is not set to ename:VK_TRUE, the value of the texel after swizzle is undefined:. endif::VK_KHR_maintenance5[] [[textures-sparse-residency]] === Sparse Residency code:OpImageSparse* instructions return a structure which includes a _residency code_ indicating whether any texels accessed by the instruction are sparse unbound texels. This code can: be interpreted by the code:OpImageSparseTexelsResident instruction which converts the residency code to a boolean value. ifdef::VK_VERSION_1_1,VK_KHR_sampler_ycbcr_conversion[] [[textures-chroma-reconstruction]] === Chroma Reconstruction In some color models, the color representation is defined in terms of monochromatic light intensity (often called "`luma`") and color differences relative to this intensity, often called "`chroma`". It is common for color models other than RGB to represent the chroma components at lower spatial resolution than the luma component. This approach is used to take advantage of the eye's lower spatial sensitivity to color compared with its sensitivity to brightness. Less commonly, the same approach is used with additive color, since the green component dominates the eye's sensitivity to light intensity and the spatial sensitivity to color introduced by red and blue is lower. Lower-resolution components are "`downsampled`" by resizing them to a lower spatial resolution than the component representing luminance. This process is also commonly known as "`chroma subsampling`". There is one luminance sample in each texture texel, but each chrominance sample may be shared among several texels in one or both texture dimensions. * "`etext:_444`" formats do not spatially downsample chroma values compared with luma: there are unique chroma samples for each texel. * "`etext:_422`" formats have downsampling in the x dimension (corresponding to _u_ or _s_ coordinates): they are sampled at half the resolution of luma in that dimension. * "`etext:_420`" formats have downsampling in the x dimension (corresponding to _u_ or _s_ coordinates) and the y dimension (corresponding to _v_ or _t_ coordinates): they are sampled at half the resolution of luma in both dimensions. The process of reconstructing a full color value for texture access involves accessing both chroma and luma values at the same location. To generate the color accurately, the values of the lower-resolution components at the location of the luma samples must be reconstructed from the lower-resolution sample locations, an operation known here as "`chroma reconstruction`" irrespective of the actual color model. The location of the chroma samples relative to the luma coordinates is determined by the pname:xChromaOffset and pname:yChromaOffset members of the slink:VkSamplerYcbcrConversionCreateInfo structure used to create the sampler {YCbCr} conversion. The following diagrams show the relationship between unnormalized (_u_,_v_) coordinates and (_i_,_j_) integer texel positions in the luma component (shown in black, with circles showing integer sample positions) and the texel coordinates of reduced-resolution chroma components, shown as crosses in red. [NOTE] .Note ==== If the chroma values are reconstructed at the locations of the luma samples by means of interpolation, chroma samples from outside the image bounds are needed; these are determined according to <>. These diagrams represent this by showing the bounds of the "`chroma texel`" extending beyond the image bounds, and including additional chroma sample positions where required for interpolation. The limits of a sample for etext:NEAREST sampling is shown as a grid. ==== image::{images}/chromasamples_422_cosited.svg[align="center",title="422 downsampling, xChromaOffset=COSITED_EVEN",opts="{imageopts}"] image::{images}/chromasamples_422_midpoint.svg[align="center",title="422 downsampling, xChromaOffset=MIDPOINT",opts="{imageopts}"] image::{images}/chromasamples_420_xcosited_ycosited.svg[align="center",title="420 downsampling, xChromaOffset=COSITED_EVEN, yChromaOffset=COSITED_EVEN",opts="{imageopts}"] image::{images}/chromasamples_420_xmidpoint_ycosited.svg[align="center",title="420 downsampling, xChromaOffset=MIDPOINT, yChromaOffset=COSITED_EVEN",opts="{imageopts}"] image::{images}/chromasamples_420_xcosited_ymidpoint.svg[align="center",title="420 downsampling, xChromaOffset=COSITED_EVEN, yChromaOffset=MIDPOINT",opts="{imageopts}"] image::{images}/chromasamples_420_xmidpoint_ymidpoint.svg[align="center",title="420 downsampling, xChromaOffset=MIDPOINT, yChromaOffset=MIDPOINT",opts="{imageopts}"] Reconstruction is implemented in one of two ways: If the format of the image that is to be sampled sets ename:VK_FORMAT_FEATURE_SAMPLED_IMAGE_YCBCR_CONVERSION_CHROMA_RECONSTRUCTION_EXPLICIT_BIT, or the slink:VkSamplerYcbcrConversionCreateInfo's pname:forceExplicitReconstruction is set to ename:VK_TRUE, reconstruction is performed as an explicit step independent of filtering, described in the <> section. If the format of the image that is to be sampled does not set ename:VK_FORMAT_FEATURE_SAMPLED_IMAGE_YCBCR_CONVERSION_CHROMA_RECONSTRUCTION_EXPLICIT_BIT and if the slink:VkSamplerYcbcrConversionCreateInfo's pname:forceExplicitReconstruction is set to ename:VK_FALSE, reconstruction is performed as an implicit part of filtering prior to color model conversion, with no separate post-conversion texel filtering step, as described in the <> section. [[textures-explicit-reconstruction]] ==== Explicit Reconstruction * If the pname:chromaFilter member of the slink:VkSamplerYcbcrConversionCreateInfo structure is ename:VK_FILTER_NEAREST: ** If the format's R and B components are reduced in resolution in just width by a factor of two relative to the G component (i.e. this is a "`etext:_422`" format), the latexmath:[\tau_{ijk}[level\]] values accessed by <> are reconstructed as follows: + [latexmath] ++++++++++++++ \begin{aligned} \tau_R'(i, j) & = \tau_R(\left\lfloor{i\times 0.5}\right\rfloor, j)[level] \\ \tau_B'(i, j) & = \tau_B(\left\lfloor{i\times 0.5}\right\rfloor, j)[level] \end{aligned} ++++++++++++++ ** If the format's R and B components are reduced in resolution in width and height by a factor of two relative to the G component (i.e. this is a "`etext:_420`" format), the latexmath:[\tau_{ijk}[level\]] values accessed by <> are reconstructed as follows: + [latexmath] ++++++++++++++ \begin{aligned} \tau_R'(i, j) & = \tau_R(\left\lfloor{i\times 0.5}\right\rfloor, \left\lfloor{j\times 0.5}\right\rfloor)[level] \\ \tau_B'(i, j) & = \tau_B(\left\lfloor{i\times 0.5}\right\rfloor, \left\lfloor{j\times 0.5}\right\rfloor)[level] \end{aligned} ++++++++++++++ + [NOTE] .Note ==== pname:xChromaOffset and pname:yChromaOffset have no effect if pname:chromaFilter is ename:VK_FILTER_NEAREST for explicit reconstruction. ==== * If the pname:chromaFilter member of the slink:VkSamplerYcbcrConversionCreateInfo structure is ename:VK_FILTER_LINEAR: ** If the format's R and B components are reduced in resolution in just width by a factor of two relative to the G component (i.e. this is a "`etext:_422`" format): *** If pname:xChromaOffset is ename:VK_CHROMA_LOCATION_COSITED_EVEN: + [latexmath] +++++ \tau_{RB}'(i,j) = \begin{cases} \tau_{RB}(\left\lfloor{i\times 0.5}\right\rfloor,j)[level], & 0.5 \times i = \left\lfloor{0.5 \times i}\right\rfloor\\ 0.5\times\tau_{RB}(\left\lfloor{i\times 0.5}\right\rfloor,j)[level] + \\ 0.5\times\tau_{RB}(\left\lfloor{i\times 0.5}\right\rfloor + 1,j)[level], & 0.5 \times i \neq \left\lfloor{0.5 \times i}\right\rfloor \end{cases} +++++ + *** If pname:xChromaOffset is ename:VK_CHROMA_LOCATION_MIDPOINT: + [latexmath] +++++ \tau_{RB}'(i,j) = \begin{cases} 0.25 \times \tau_{RB}(\left\lfloor{i\times 0.5}\right\rfloor - 1,j)[level] + \\ 0.75 \times \tau_{RB}(\left\lfloor{i\times 0.5}\right\rfloor,j)[level], & 0.5 \times i = \left\lfloor{0.5 \times i}\right\rfloor\\ 0.75 \times \tau_{RB}(\left\lfloor{i\times 0.5}\right\rfloor,j)[level] + \\ 0.25 \times \tau_{RB}(\left\lfloor{i\times 0.5}\right\rfloor + 1,j)[level], & 0.5 \times i \neq \left\lfloor{0.5 \times i}\right\rfloor \end{cases} +++++ ** If the format's R and B components are reduced in resolution in width and height by a factor of two relative to the G component (i.e. this is a "`etext:_420`" format), a similar relationship applies. Due to the number of options, these formulae are expressed more concisely as follows: + [latexmath] +++++ \begin{aligned} i_{RB} & = \begin{cases} 0.5 \times (i) & \textrm{xChromaOffset = COSITED}\_\textrm{EVEN} \\ 0.5 \times (i - 0.5) & \textrm{xChromaOffset = MIDPOINT} \end{cases}\\ j_{RB} & = \begin{cases} 0.5 \times (j) & \textrm{yChromaOffset = COSITED}\_\textrm{EVEN} \\ 0.5 \times (j - 0.5) & \textrm{yChromaOffset = MIDPOINT} \end{cases}\\ \\ i_{floor} & = \left\lfloor i_{RB} \right\rfloor \\ j_{floor} & = \left\lfloor j_{RB} \right\rfloor \\ \\ i_{frac} & = i_{RB} - i_{floor} \\ j_{frac} & = j_{RB} - j_{floor} \end{aligned} +++++ + [latexmath] +++++ \begin{aligned} \tau_{RB}'(i,j) = & \tau_{RB}( i_{floor}, j_{floor})[level] & \times & ( 1 - i_{frac} ) & & \times & ( 1 - j_{frac} ) & + \\ & \tau_{RB}( 1 + i_{floor}, j_{floor})[level] & \times & ( i_{frac} ) & & \times & ( 1 - j_{frac} ) & + \\ & \tau_{RB}( i_{floor}, 1 + j_{floor})[level] & \times & ( 1 - i_{frac} ) & & \times & ( j_{frac} ) & + \\ & \tau_{RB}( 1 + i_{floor}, 1 + j_{floor})[level] & \times & ( i_{frac} ) & & \times & ( j_{frac} ) & \end{aligned} +++++ [NOTE] .Note ==== In the case where the texture itself is bilinearly interpolated as described in <>, thus requiring four full-color samples for the filtering operation, and where the reconstruction of these samples uses bilinear interpolation in the chroma components due to pname:chromaFilter=ename:VK_FILTER_LINEAR, up to nine chroma samples may be required, depending on the sample location. ==== [[textures-implict-reconstruction]] ==== Implicit Reconstruction Implicit reconstruction takes place by the samples being interpolated, as required by the filter settings of the sampler, except that pname:chromaFilter takes precedence for the chroma samples. If pname:chromaFilter is ename:VK_FILTER_NEAREST, an implementation may: behave as if pname:xChromaOffset and pname:yChromaOffset were both ename:VK_CHROMA_LOCATION_MIDPOINT, irrespective of the values set. [NOTE] .Note ==== This will not have any visible effect if the locations of the luma samples coincide with the location of the samples used for rasterization. ==== The sample coordinates are adjusted by the downsample factor of the component (such that, for example, the sample coordinates are divided by two if the component has a downsample factor of two relative to the luma component): [latexmath] ++++++ \begin{aligned} u_{RB}' (422/420) &= \begin{cases} 0.5\times (u + 0.5), & \textrm{xChromaOffset = COSITED}\_\textrm{EVEN} \\ 0.5\times u, & \textrm{xChromaOffset = MIDPOINT} \end{cases} \\ v_{RB}' (420) &= \begin{cases} 0.5\times (v + 0.5), & \textrm{yChromaOffset = COSITED}\_\textrm{EVEN} \\ 0.5\times v, & \textrm{yChromaOffset = MIDPOINT} \end{cases} \end{aligned} ++++++ [[textures-sampler-YCbCr-conversion]] === Sampler {YCbCr} Conversion Sampler {YCbCr} conversion performs the following operations, which an implementation may: combine into a single mathematical operation: * <> * <> [[textures-sampler-YCbCr-conversion-rangeexpand]] ==== Sampler {YCbCr} Range Expansion Sampler {YCbCr} range expansion is applied to color component values after all texel input operations which are not specific to sampler {YCbCr} conversion. For example, the input values to this stage have been converted using the normal <> rules. ifdef::VK_QCOM_ycbcr_degamma[] The input values to this stage may have been converted using sRGB to linear conversion if <> is enabled. endif::VK_QCOM_ycbcr_degamma[] Sampler {YCbCr} range expansion is not applied if pname:ycbcrModel is ename:VK_SAMPLER_YCBCR_MODEL_CONVERSION_RGB_IDENTITY. That is, the shader receives the vector C'~rgba~ as output by the Component Swizzle stage without further modification. For other values of pname:ycbcrModel, range expansion is applied to the texel component values output by the <> defined by the pname:components member of slink:VkSamplerYcbcrConversionCreateInfo. Range expansion applies independently to each component of the image. For the purposes of range expansion and {YCbCr} model conversion, the R and B components contain color difference (chroma) values and the G component contains luma. The A component is not modified by sampler {YCbCr} range expansion. The range expansion to be applied is defined by the pname:ycbcrRange member of the slink:VkSamplerYcbcrConversionCreateInfo structure: * If pname:ycbcrRange is ename:VK_SAMPLER_YCBCR_RANGE_ITU_FULL, the following transformations are applied: + [latexmath] +++++++++++++++++++ \begin{aligned} Y' &= C'_{rgba}[G] \\ C_B &= C'_{rgba}[B] - {{2^{(n-1)}}\over{(2^n) - 1}} \\ C_R &= C'_{rgba}[R] - {{2^{(n-1)}}\over{(2^n) - 1}} \end{aligned} +++++++++++++++++++ + [NOTE] .Note ==== These formulae correspond to the "`full range`" encoding in the "`Quantization schemes`" chapter of the <>. Should any future amendments be made to the ITU specifications from which these equations are derived, the formulae used by Vulkan may: also be updated to maintain parity. ==== * If pname:ycbcrRange is ename:VK_SAMPLER_YCBCR_RANGE_ITU_NARROW, the following transformations are applied: + [latexmath] +++++++++++++++++++ \begin{aligned} Y' &= {{C'_{rgba}[G] \times (2^n-1) - 16\times 2^{n-8}}\over{219\times 2^{n-8}}} \\ C_B &= {{C'_{rgba}[B] \times \left(2^n-1\right) - 128\times 2^{n-8}}\over{224\times 2^{n-8}}} \\ C_R &= {{C'_{rgba}[R] \times \left(2^n-1\right) - 128\times 2^{n-8}}\over{224\times 2^{n-8}}} \end{aligned} +++++++++++++++++++ + [NOTE] .Note ==== These formulae correspond to the "`narrow range`" encoding in the "`Quantization schemes`" chapter of the <>. ==== * _n_ is the bit-depth of the components in the format. The precision of the operations performed during range expansion must: be at least that of the source format. An implementation may: clamp the results of these range expansion operations such that Y{prime} falls in the range [0,1], and/or such that C~B~ and C~R~ fall in the range [-0.5,0.5]. [[textures-sampler-YCbCr-conversion-modelconversion]] ==== Sampler {YCbCr} Model Conversion The range-expanded values are converted between color models, according to the color model conversion specified in the pname:ycbcrModel member: ename:VK_SAMPLER_YCBCR_MODEL_CONVERSION_RGB_IDENTITY:: The color components are not modified by the color model conversion since they are assumed already to represent the desired color model in which the shader is operating; {YCbCr} range expansion is also ignored. ename:VK_SAMPLER_YCBCR_MODEL_CONVERSION_YCBCR_IDENTITY:: The color components are not modified by the color model conversion and are assumed to be treated as though in {YCbCr} form both in memory and in the shader; {YCbCr} range expansion is applied to the components as for other {YCbCr} models, with the vector (C~R~,Y{prime},C~B~,A) provided to the shader. ename:VK_SAMPLER_YCBCR_MODEL_CONVERSION_YCBCR_709:: The color components are transformed from a {YCbCr} representation to an {RGBprime} representation as described in the "`BT.709 {YCbCr} conversion`" section of the <>. ename:VK_SAMPLER_YCBCR_MODEL_CONVERSION_YCBCR_601:: The color components are transformed from a {YCbCr} representation to an {RGBprime} representation as described in the "`BT.601 {YCbCr} conversion`" section of the <>. ename:VK_SAMPLER_YCBCR_MODEL_CONVERSION_YCBCR_2020:: The color components are transformed from a {YCbCr} representation to an {RGBprime} representation as described in the "`BT.2020 {YCbCr} conversion`" section of the <>. In this operation, each output component is dependent on each input component. An implementation may: clamp the {RGBprime} results of these conversions to the range [0,1]. The precision of the operations performed during model conversion must: be at least that of the source format. The alpha component is not modified by these model conversions. [NOTE] .Note ==== Sampling operations in a non-linear color space can introduce color and intensity shifts at sharp transition boundaries. To avoid this issue, the technically precise color correction sequence described in the "`Introduction to Color Conversions`" chapter of the <> may be performed as follows: * Calculate the <> corresponding to the desired sample position. * For a pname:minFilter or pname:magFilter of ename:VK_FILTER_NEAREST: . Calculate (_i_,_j_) for the sample location as described under the "`nearest filtering`" formulae in <> . Calculate the normalized texel coordinates corresponding to these integer coordinates. . Sample using <> at this location. * For a pname:minFilter or pname:magFilter of ename:VK_FILTER_LINEAR: . Calculate (_i~[0,1]~_,_j~[0,1]~_) for the sample location as described under the "`linear filtering`" formulae in <> . Calculate the normalized texel coordinates corresponding to these integer coordinates. . Sample using <> at each of these locations. . Convert the non-linear A{prime}{RGBprime} outputs of the {YCbCr} conversions to linear ARGB values as described in the "`Transfer Functions`" chapter of the <>. . Interpolate the linear ARGB values using the [eq]#{alpha}# and [eq]#{beta}# values described in the "`linear filtering`" section of <> and the equations in <>. The additional calculations and, especially, additional number of sampling operations in the ename:VK_FILTER_LINEAR case can be expected to have a performance impact compared with using the outputs directly. Since the variations from "`correct`" results are subtle for most content, the application author should determine whether a more costly implementation is strictly necessary. If pname:chromaFilter, and pname:minFilter or pname:magFilter are both ename:VK_FILTER_NEAREST, these operations are redundant and sampling using <> at the desired sample coordinates will produce the "`correct`" results without further processing. ==== endif::VK_VERSION_1_1,VK_KHR_sampler_ycbcr_conversion[] == Texel Output Operations _Texel output instructions_ are SPIR-V image instructions that write to an image. _Texel output operations_ are a set of steps that are performed on state, coordinates, and texel values while processing a texel output instruction, and which are common to some or all texel output instructions. They include the following steps, which are performed in the listed order: * <> ** <> ** <> ** <> ** <> * <> [[textures-output-validation]] === Texel Output Validation Operations _Texel output validation operations_ inspect instruction/image state or coordinates, and in certain circumstances cause the write to have no effect. There are a series of validations that the texel undergoes. [[textures-format-validation]] ==== Texel Format Validation If the image format of the code:OpTypeImage is not <> with the sname:VkImageView's pname:format, the write causes the contents of the image's memory to become undefined:. [[textures-type-validation]] ==== Texel Type Validation If the code:Sampled code:Type of the code:OpTypeImage does not match the <>, the write causes the value of the texel to become undefined:. For integer types, if the <> does not match the signedness of the accessed resource, the write causes the value of the texel to become undefined:. [[textures-output-coordinate-validation]] === Integer Texel Coordinate Validation The integer texel coordinates are validated according to the same rules as for texel input <>. If the texel fails integer texel coordinate validation, then the write has no effect. [[textures-output-sparse-validation]] === Sparse Texel Operation If the texel attempts to write to an unbound region of a sparse image, the texel is a sparse unbound texel. In such a case, if the slink:VkPhysicalDeviceSparseProperties::pname:residencyNonResidentStrict property is ename:VK_TRUE, the sparse unbound texel write has no effect. If pname:residencyNonResidentStrict is ename:VK_FALSE, the write may: have a side effect that becomes visible to other accesses to unbound texels in any resource, but will not be visible to any device memory allocated by the application. [[textures-output-format-conversion]] === Texel Output Format Conversion If the image format is sRGB, a linear to sRGB conversion is applied to the R, G, and B components as described in the "`sRGB EOTF`" section of the <>. The A component, if present, is unchanged. Texels then undergo a format conversion from the floating point, signed, or unsigned integer type of the texel data to the elink:VkFormat of the image view. If the number of components in the texel data is larger than the number of components in the format, additional components are discarded. Each component is converted based on its type and size (as defined in the <> section for each elink:VkFormat). Floating-point outputs are converted as described in <> and <>. Integer outputs are converted such that their value is preserved. The converted value of any integer that cannot be represented in the target format is undefined:. [[textures-normalized-operations]] == Normalized Texel Coordinate Operations If the image sampler instruction provides normalized texel coordinates, some of the following operations are performed. [[textures-projection]] === Projection Operation For code:Proj image operations, the normalized texel coordinates [eq]#(s,t,r,q,a)# and (if present) the [eq]#D~ref~# coordinate are transformed as follows: [latexmath] +++++++++++++++++++ \begin{aligned} s & = \frac{s}{q}, & \text{for 1D, 2D, or 3D image} \\ \\ t & = \frac{t}{q}, & \text{for 2D or 3D image} \\ \\ r & = \frac{r}{q}, & \text{for 3D image} \\ \\ D_{\textit{ref}} & = \frac{D_{\textit{ref}}}{q}, & \text{if provided} \end{aligned} +++++++++++++++++++ [[textures-derivative-image-operations]] === Derivative Image Operations Derivatives are used for LOD selection. These derivatives are either implicit (in an code:ImplicitLod image instruction in a fragment shader) or explicit (provided explicitly by shader to the image instruction in any shader). For implicit derivatives image instructions, the derivatives of texel coordinates are calculated in the same manner as <>. That is: [latexmath] +++++++++++++++++++ \begin{aligned} \partial{s}/\partial{x} & = dPdx(s), & \partial{s}/\partial{y} & = dPdy(s), & \text{for 1D, 2D, Cube, or 3D image} \\ \partial{t}/\partial{x} & = dPdx(t), & \partial{t}/\partial{y} & = dPdy(t), & \text{for 2D, Cube, or 3D image} \\ \partial{r}/\partial{x} & = dPdx(r), & \partial{r}/\partial{y} & = dPdy(r), & \text{for Cube or 3D image} \end{aligned} +++++++++++++++++++ Partial derivatives not defined above for certain image dimensionalities are set to zero. For explicit LOD image instructions, if the optional: SPIR-V operand code:Grad is provided, then the operand values are used for the derivatives. The number of components present in each derivative for a given image dimensionality matches the number of partial derivatives computed above. If the optional: SPIR-V operand code:Lod is provided, then derivatives are set to zero, the cube map derivative transformation is skipped, and the scale factor operation is skipped. Instead, the floating point scalar coordinate is directly assigned to [eq]#{lambda}~base~# as described in <>. ifdef::VK_VERSION_1_2,VK_EXT_descriptor_indexing[] If the image or sampler object used by an implicit derivative image instruction is not uniform across the quad and <> is not supported, then the derivative and LOD values are undefined:. Implicit derivatives are well-defined when the image and sampler and control flow are uniform across the quad, even if they diverge between different quads. If <> is supported, then derivatives and implicit LOD values are well-defined even if the image or sampler object are not uniform within a quad. The derivatives are computed as specified above, and the implicit LOD calculation proceeds for each shader invocation using its respective image and sampler object. endif::VK_VERSION_1_2,VK_EXT_descriptor_indexing[] === Cube Map Face Selection and Transformations For cube map image instructions, the [eq]#(s,t,r)# coordinates are treated as a direction vector [eq]#(r~x~,r~y~,r~z~)#. The direction vector is used to select a cube map face. The direction vector is transformed to a per-face texel coordinate system [eq]#(s~face~,t~face~)#, The direction vector is also used to transform the derivatives to per-face derivatives. === Cube Map Face Selection The direction vector selects one of the cube map's faces based on the largest magnitude coordinate direction (the major axis direction). Since two or more coordinates can: have identical magnitude, the implementation must: have rules to disambiguate this situation. The rules should: have as the first rule that [eq]#r~z~# wins over [eq]#r~y~# and [eq]#r~x~#, and the second rule that [eq]#r~y~# wins over [eq]#r~x~#. An implementation may: choose other rules, but the rules must: be deterministic and depend only on [eq]#(r~x~,r~y~,r~z~)#. The layer number (corresponding to a cube map face), the coordinate selections for [eq]#s~c~#, [eq]#t~c~#, [eq]#r~c~#, and the selection of derivatives, are determined by the major axis direction as specified in the following two tables. .Cube map face and coordinate selection [width="75%",frame="all",options="header"] |==== | Major Axis Direction | Layer Number | Cube Map Face | [eq]#s~c~# | [eq]#t~c~# | [eq]#r~c~# | [eq]#+r~x~# | [eq]#0# | Positive X | [eq]#-r~z~# | [eq]#-r~y~# | [eq]#r~x~# | [eq]#-r~x~# | [eq]#1# | Negative X | [eq]#+r~z~# | [eq]#-r~y~# | [eq]#r~x~# | [eq]#+r~y~# | [eq]#2# | Positive Y | [eq]#+r~x~# | [eq]#+r~z~# | [eq]#r~y~# | [eq]#-r~y~# | [eq]#3# | Negative Y | [eq]#+r~x~# | [eq]#-r~z~# | [eq]#r~y~# | [eq]#+r~z~# | [eq]#4# | Positive Z | [eq]#+r~x~# | [eq]#-r~y~# | [eq]#r~z~# | [eq]#-r~z~# | [eq]#5# | Negative Z | [eq]#-r~x~# | [eq]#-r~y~# | [eq]#r~z~# |==== .Cube map derivative selection [width="75%",frame="all",options="header"] |==== | Major Axis Direction | [eq]#{partial}s~c~ / {partial}x# | [eq]#{partial}s~c~ / {partial}y# | [eq]#{partial}t~c~ / {partial}x# | [eq]#{partial}t~c~ / {partial}y# | [eq]#{partial}r~c~ / {partial}x# | [eq]#{partial}r~c~ / {partial}y# | [eq]#+r~x~# | [eq]#-{partial}r~z~ / {partial}x# | [eq]#-{partial}r~z~ / {partial}y# | [eq]#-{partial}r~y~ / {partial}x# | [eq]#-{partial}r~y~ / {partial}y# | [eq]#+{partial}r~x~ / {partial}x# | [eq]#+{partial}r~x~ / {partial}y# | [eq]#-r~x~# | [eq]#+{partial}r~z~ / {partial}x# | [eq]#+{partial}r~z~ / {partial}y# | [eq]#-{partial}r~y~ / {partial}x# | [eq]#-{partial}r~y~ / {partial}y# | [eq]#-{partial}r~x~ / {partial}x# | [eq]#-{partial}r~x~ / {partial}y# | [eq]#+r~y~# | [eq]#+{partial}r~x~ / {partial}x# | [eq]#+{partial}r~x~ / {partial}y# | [eq]#+{partial}r~z~ / {partial}x# | [eq]#+{partial}r~z~ / {partial}y# | [eq]#+{partial}r~y~ / {partial}x# | [eq]#+{partial}r~y~ / {partial}y# | [eq]#-r~y~# | [eq]#+{partial}r~x~ / {partial}x# | [eq]#+{partial}r~x~ / {partial}y# | [eq]#-{partial}r~z~ / {partial}x# | [eq]#-{partial}r~z~ / {partial}y# | [eq]#-{partial}r~y~ / {partial}x# | [eq]#-{partial}r~y~ / {partial}y# | [eq]#+r~z~# | [eq]#+{partial}r~x~ / {partial}x# | [eq]#+{partial}r~x~ / {partial}y# | [eq]#-{partial}r~y~ / {partial}x# | [eq]#-{partial}r~y~ / {partial}y# | [eq]#+{partial}r~z~ / {partial}x# | [eq]#+{partial}r~z~ / {partial}y# | [eq]#-r~z~# | [eq]#-{partial}r~x~ / {partial}x# | [eq]#-{partial}r~x~ / {partial}y# | [eq]#-{partial}r~y~ / {partial}x# | [eq]#-{partial}r~y~ / {partial}y# | [eq]#-{partial}r~z~ / {partial}x# | [eq]#-{partial}r~z~ / {partial}y# |==== === Cube Map Coordinate Transformation [latexmath] ++++++++++++++++++++++++ \begin{aligned} s_{\textit{face}} & = \frac{1}{2} \times \frac{s_c}{|r_c|} + \frac{1}{2} \\ t_{\textit{face}} & = \frac{1}{2} \times \frac{t_c}{|r_c|} + \frac{1}{2} \\ \end{aligned} ++++++++++++++++++++++++ === Cube Map Derivative Transformation [latexmath] ++++++++++++++++++++++++ \begin{aligned} \frac{\partial{s_{\textit{face}}}}{\partial{x}} &= \frac{\partial}{\partial{x}} \left ( \frac{1}{2} \times \frac{s_{c}}{|r_{c}|} + \frac{1}{2}\right ) \\ \frac{\partial{s_{\textit{face}}}}{\partial{x}} &= \frac{1}{2} \times \frac{\partial}{\partial{x}} \left ( \frac{s_{c}}{|r_{c}|} \right ) \\ \frac{\partial{s_{\textit{face}}}}{\partial{x}} &= \frac{1}{2} \times \left ( \frac{ |r_{c}| \times \partial{s_c}/\partial{x} -s_c \times {\partial{r_{c}}}/{\partial{x}}} {\left ( r_{c} \right )^2} \right ) \end{aligned} ++++++++++++++++++++++++ [latexmath] ++++++++++++++++++++++++ \begin{aligned} \frac{\partial{s_{\textit{face}}}}{\partial{y}} &= \frac{1}{2} \times \left ( \frac{ |r_{c}| \times \partial{s_c}/\partial{y} -s_c \times {\partial{r_{c}}}/{\partial{y}}} {\left ( r_{c} \right )^2} \right )\\ \frac{\partial{t_{\textit{face}}}}{\partial{x}} &= \frac{1}{2} \times \left ( \frac{ |r_{c}| \times \partial{t_c}/\partial{x} -t_c \times {\partial{r_{c}}}/{\partial{x}}} {\left ( r_{c} \right )^2} \right ) \\ \frac{\partial{t_{\textit{face}}}}{\partial{y}} &= \frac{1}{2} \times \left ( \frac{ |r_{c}| \times \partial{t_c}/\partial{y} -t_c \times {\partial{r_{c}}}/{\partial{y}}} {\left ( r_{c} \right )^2} \right ) \end{aligned} ++++++++++++++++++++++++ ifdef::editing-notes[] [NOTE] .editing-note ==== (Bill) Note that we never revisited ARB_texture_cubemap after we introduced dependent texture fetches (ARB_fragment_program and ARB_fragment_shader). The derivatives of [eq]#s~face~# and [eq]#t~face~# are only valid for non-dependent texture fetches (pre OpenGL 2.0). ==== endif::editing-notes[] [[textures-lod-and-scale-factor]] === Scale Factor Operation, LOD Operation and Image Level(s) Selection LOD selection can: be either explicit (provided explicitly by the image instruction) or implicit (determined from a scale factor calculated from the derivatives). The LOD must: be computed with pname:mipmapPrecisionBits of accuracy. [[textures-scale-factor]] ==== Scale Factor Operation The magnitude of the derivatives are calculated by: {empty}:: [eq]#m~ux~ = {vert}{partial}s/{partial}x{vert} {times} w~base~# {empty}:: [eq]#m~vx~ = {vert}{partial}t/{partial}x{vert} {times} h~base~# {empty}:: [eq]#m~wx~ = {vert}{partial}r/{partial}x{vert} {times} d~base~# {empty}:: [eq]#m~uy~ = {vert}{partial}s/{partial}y{vert} {times} w~base~# {empty}:: [eq]#m~vy~ = {vert}{partial}t/{partial}y{vert} {times} h~base~# {empty}:: [eq]#m~wy~ = {vert}{partial}r/{partial}y{vert} {times} d~base~# where: {empty}:: [eq]#{partial}t/{partial}x = {partial}t/{partial}y = 0# (for 1D images) {empty}:: [eq]#{partial}r/{partial}x = {partial}r/{partial}y = 0# (for 1D, 2D or Cube images) and: {empty}:: [eq]#w~base~ = image.w# {empty}:: [eq]#h~base~ = image.h# {empty}:: [eq]#d~base~ = image.d# (for the pname:baseMipLevel, from the image descriptor). ifdef::VK_NV_corner_sampled_image[] For corner-sampled images, the [eq]#w~base~#, [eq]#h~base~#, and [eq]#d~base~# are instead: {empty}:: [eq]#w~base~ = image.w - 1# {empty}:: [eq]#h~base~ = image.h - 1# {empty}:: [eq]#d~base~ = image.d - 1# endif::VK_NV_corner_sampled_image[] A point sampled in screen space has an elliptical footprint in texture space. The minimum and maximum scale factors [eq]#({rho}~min~, {rho}~max~)# should: be the minor and major axes of this ellipse. The _scale factors_ [eq]#{rho}~x~# and [eq]#{rho}~y~#, calculated from the magnitude of the derivatives in x and y, are used to compute the minimum and maximum scale factors. [eq]#{rho}~x~# and [eq]#{rho}~y~# may: be approximated with functions [eq]#f~x~# and [eq]#f~y~#, subject to the following constraints: [latexmath] ++++++++++++++++++++++++ \begin{aligned} & f_x \text{\ is\ continuous\ and\ monotonically\ increasing\ in\ each\ of\ } m_{ux}, m_{vx}, \text{\ and\ } m_{wx} \\ & f_y \text{\ is\ continuous\ and\ monotonically\ increasing\ in\ each\ of\ } m_{uy}, m_{vy}, \text{\ and\ } m_{wy} \end{aligned} ++++++++++++++++++++++++ [latexmath] ++++++++++++++++++++++++ \begin{aligned} \max(|m_{ux}|, |m_{vx}|, |m_{wx}|) \leq f_{x} \leq \sqrt{2} (|m_{ux}| + |m_{vx}| + |m_{wx}|) \\ \max(|m_{uy}|, |m_{vy}|, |m_{wy}|) \leq f_{y} \leq \sqrt{2} (|m_{uy}| + |m_{vy}| + |m_{wy}|) \end{aligned} ++++++++++++++++++++++++ ifdef::editing-notes[] [NOTE] .editing-note ==== (Bill) For reviewers only - anticipating questions. We only support implicit derivatives for normalized texel coordinates. So we are documenting the derivatives in s,t,r (normalized texel coordinates) rather than u,v,w (unnormalized texel coordinates) as in OpenGL and OpenGL ES specifications. (I know, u,v,w is the way it has been documented since OpenGL V1.0.) Also there is no reason to have conditional application of [eq]#w~base~, h~base~, d~base~# for rectangle textures either, since they do not support implicit derivatives. ==== endif::editing-notes[] The minimum and maximum scale factors [eq]#({rho}~min~,{rho}~max~)# are determined by: {empty}:: [eq]#{rho}~max~ = max({rho}~x~, {rho}~y~)# {empty}:: [eq]#{rho}~min~ = min({rho}~x~, {rho}~y~)# The ratio of anisotropy is determined by: {empty}:: [eq]#{eta} = min({rho}~max~/{rho}~min~, max~Aniso~)# where: {empty}:: [eq]#sampler.max~Aniso~ = pname:maxAnisotropy# (from sampler descriptor) {empty}:: [eq]#limits.max~Aniso~ = pname:maxSamplerAnisotropy# (from physical device limits) {empty}:: [eq]#max~Aniso~ = min(sampler.max~Aniso~, limits.max~Aniso~)# If [eq]#{rho}~max~ = {rho}~min~ = 0#, then all the partial derivatives are zero, the fragment's footprint in texel space is a point, and [eq]#{eta}# should: be treated as 1. If [eq]#{rho}~max~ {neq} 0# and [eq]#{rho}~min~ = 0# then all partial derivatives along one axis are zero, the fragment's footprint in texel space is a line segment, and [eq]#{eta}# should: be treated as [eq]#max~Aniso~#. However, anytime the footprint is small in texel space the implementation may: use a smaller value of [eq]#{eta}#, even when [eq]#{rho}~min~# is zero or close to zero. If either slink:VkPhysicalDeviceFeatures::pname:samplerAnisotropy or slink:VkSamplerCreateInfo::pname:anisotropyEnable are ename:VK_FALSE, [eq]#max~Aniso~# is set to 1. If [eq]#{eta} = 1#, sampling is isotropic. If [eq]#{eta} > 1#, sampling is anisotropic. The sampling rate ([eq]#N#) is derived as: {empty}:: [eq]#N = {lceil}{eta}{rceil}# An implementation may: round [eq]#N# up to the nearest supported sampling rate. An implementation may: use the value of [eq]#N# as an approximation of [eq]#{eta}#. [[textures-level-of-detail-operation]] ==== LOD Operation The LOD parameter [eq]#{lambda}# is computed as follows: [latexmath] ++++++++++++++++++++++++ \begin{aligned} \lambda_{base}(x,y) & = \begin{cases} shaderOp.Lod & \text{(from optional SPIR-V operand)} \\ \log_2 \left ( \frac{\rho_{max}}{\eta} \right ) & \text{otherwise} \end{cases} \\ \lambda'(x,y) & = \lambda_{base} + \mathbin{clamp}(sampler.bias + shaderOp.bias,-maxSamplerLodBias,maxSamplerLodBias) \\ \lambda & = \begin{cases} lod_{max}, & \lambda' > lod_{max} \\ \lambda', & lod_{min} \leq \lambda' \leq lod_{max} \\ lod_{min}, & \lambda' < lod_{min} \\ \textit{undefined}, & lod_{min} > lod_{max} \end{cases} \end{aligned} ++++++++++++++++++++++++ where: [latexmath] ++++++++++++++++++++++++ \begin{aligned} sampler.bias & = mipLodBias & \text{(from sampler descriptor)} \\ shaderOp.bias & = \begin{cases} Bias & \text{(from optional SPIR-V operand)} \\ 0 & \text{otherwise} \end{cases} \\ sampler.lod_{min} & = minLod & \text{(from sampler descriptor)} \\ shaderOp.lod_{min} & = \begin{cases} MinLod & \text{(from optional SPIR-V operand)} \\ 0 & \text{otherwise} \end{cases} \\ \\ lod_{min} & = \max(sampler.lod_{min}, shaderOp.lod_{min}) \\ lod_{max} & = maxLod & \text{(from sampler descriptor)} \end{aligned} ++++++++++++++++++++++++ and [eq]#maxSamplerLodBias# is the value of the slink:VkPhysicalDeviceLimits feature <>. [[textures-image-level-selection]] ==== Image Level(s) Selection The image level(s) [eq]#d#, [eq]#d~hi~#, and [eq]#d~lo~# which texels are read from are determined by an image-level parameter [eq]#d~l~#, which is computed based on the LOD parameter, as follows: [latexmath] ++++++++++++++++++++++++ \begin{aligned} d_{l} = \begin{cases} nearest(d'), & \text{mipmapMode is VK\_SAMPLER\_MIPMAP\_MODE\_NEAREST} \\ d', & \text{otherwise} \end{cases} \end{aligned} ++++++++++++++++++++++++ where: [latexmath] ++++++++++++++++++++++++ \begin{aligned} ifdef::VK_EXT_image_view_min_lod[] d' = max(level_{base} + \text{clamp}(\lambda, 0, q), minLod_{imageView}) endif::VK_EXT_image_view_min_lod[] ifndef::VK_EXT_image_view_min_lod[] d' = level_{base} + \text{clamp}(\lambda, 0, q) endif::VK_EXT_image_view_min_lod[] \end{aligned} ++++++++++++++++++++++++ [latexmath] ++++++++++++++++++++++++ \begin{aligned} nearest(d') & = \begin{cases} \left \lceil d' + 0.5\right \rceil - 1, & \text{preferred} \\ \left \lfloor d' + 0.5\right \rfloor, & \text{alternative} \end{cases} \end{aligned} ++++++++++++++++++++++++ and: ifdef::VK_EXT_image_view_min_lod[] [latexmath] ++++++++++++++++++++++++ \begin{aligned} minLod_{imageView} & = \begin{cases} minLodFloat_{imageView}, & \text{preferred} \\ minLodInteger_{imageView}, & \text{alternative} \end{cases} \\ level_{base} & = baseMipLevel \\ q & = levelCount - 1 \end{aligned} ++++++++++++++++++++++++ endif::VK_EXT_image_view_min_lod[] ifndef::VK_EXT_image_view_min_lod[] [latexmath] ++++++++++++++++++++++++ \begin{aligned} level_{base} & = baseMipLevel \\ q & = levelCount - 1 \end{aligned} ++++++++++++++++++++++++ endif::VK_EXT_image_view_min_lod[] pname:baseMipLevel and pname:levelCount are taken from the pname:subresourceRange of the image view. ifdef::VK_EXT_image_view_min_lod[] [eq]#minLod~imageView~# must: be less or equal to [eq]#level~base~ + q#. endif::VK_EXT_image_view_min_lod[] If the sampler's pname:mipmapMode is ename:VK_SAMPLER_MIPMAP_MODE_NEAREST, then the level selected is [eq]#d = d~l~#. If the sampler's pname:mipmapMode is ename:VK_SAMPLER_MIPMAP_MODE_LINEAR, two neighboring levels are selected: [latexmath] ++++++++++++++++++++++++ \begin{aligned} d_{hi} & = \left\lfloor d_{l} \right\rfloor \\ d_{lo} & = min( d_{hi} + 1, level_{base} + q ) \\ \delta & = d_{l} - d_{hi} \end{aligned} ++++++++++++++++++++++++ [eq]#{delta}# is the fractional value, quantized to the number of <>, used for <> between levels. [[textures-normalized-to-unnormalized]] === (s,t,r,q,a) to (u,v,w,a) Transformation The normalized texel coordinates are scaled by the image level dimensions and the array layer is selected. This transformation is performed once for each level used in <> (either [eq]#d#, or [eq]#d~hi~# and [eq]#d~lo~#). [latexmath] ++++++++++++++++++++++++ \begin{aligned} u(x,y) & = s(x,y) \times width_{scale} + \Delta_i\\ v(x,y) & = \begin{cases} 0 & \text{for 1D images} \\ t(x,y) \times height_{scale} + \Delta_j & \text{otherwise} \end{cases} \\ w(x,y) & = \begin{cases} 0 & \text{for 2D or Cube images} \\ r(x,y) \times depth_{scale} + \Delta_k & \text{otherwise} \end{cases} \\ \\ a(x,y) & = \begin{cases} a(x,y) & \text{for array images} \\ 0 & \text{otherwise} \end{cases} \end{aligned} ++++++++++++++++++++++++ where: {empty}:: [eq]#width~scale~ = width~level~# {empty}:: [eq]#height~scale~ = height~level~# {empty}:: [eq]#depth~scale~ = depth~level~# ifdef::VK_NV_corner_sampled_image[] for conventional images, and: {empty}:: [eq]#width~scale~ = width~level~ - 1# {empty}:: [eq]#height~scale~ = height~level~ - 1# {empty}:: [eq]#depth~scale~ = depth~level~ - 1# for corner-sampled images. endif::VK_NV_corner_sampled_image[] and where [eq]#({DeltaUpper}~i~, {DeltaUpper}~j~, {DeltaUpper}~k~)# are taken from the image instruction if it includes a code:ConstOffset or code:Offset operand, otherwise they are taken to be zero. Operations then proceed to Unnormalized Texel Coordinate Operations. == Unnormalized Texel Coordinate Operations [[textures-unnormalized-to-integer]] === (u,v,w,a) to (i,j,k,l,n) Transformation and Array Layer Selection The unnormalized texel coordinates are transformed to integer texel coordinates relative to the selected mipmap level. The layer index [eq]#l# is computed as: {empty}:: [eq]#l = clamp(RNE(a), 0, pname:layerCount - 1) {plus} pname:baseArrayLayer# where pname:layerCount is the number of layers in the image subresource range of the image view, pname:baseArrayLayer is the first layer from the subresource range, and where: [latexmath] ++++++++++++++++++++++++ \begin{aligned} \mathbin{RNE}(a) & = \begin{cases} \mathbin{roundTiesToEven}(a) & \text{preferred, from IEEE Std 754-2008 Floating-Point Arithmetic} \\ \left \lfloor a + 0.5 \right \rfloor & \text{alternative} \end{cases} \end{aligned} ++++++++++++++++++++++++ The sample index [eq]#n# is assigned the value 0. Nearest filtering (ename:VK_FILTER_NEAREST) computes the integer texel coordinates that the unnormalized coordinates lie within: [latexmath] ++++++++++++++++++++++++ \begin{aligned} i &= \left\lfloor u + shift \right\rfloor \\ j &= \left\lfloor v + shift \right\rfloor \\ k &= \left\lfloor w + shift \right\rfloor \end{aligned} ++++++++++++++++++++++++ where: {empty}:: [eq]#shift = 0.0# ifdef::VK_NV_corner_sampled_image[] for conventional images, and: {empty}:: [eq]#shift = 0.5# for corner-sampled images. endif::VK_NV_corner_sampled_image[] Linear filtering (ename:VK_FILTER_LINEAR) computes a set of neighboring coordinates which bound the unnormalized coordinates. The integer texel coordinates are combinations of [eq]#i~0~# or [eq]#i~1~#, [eq]#j~0~# or [eq]#j~1~#, [eq]#k~0~# or [eq]#k~1~#, as well as weights [eq]#{alpha}, {beta}#, and [eq]#{gamma}#. [latexmath] ++++++++++++++++++++++++ \begin{aligned} i_0 &= \left\lfloor u - shift \right\rfloor \\ i_1 &= i_0 + 1 \\ j_0 &= \left\lfloor v - shift \right\rfloor \\ j_1 &= j_0 + 1 \\ k_0 &= \left\lfloor w - shift \right\rfloor \\ k_1 &= k_0 + 1 \end{aligned} ++++++++++++++++++++++++ [latexmath] ++++++++++++++++++++++++ \begin{aligned} \alpha &= \mathbin{frac}\left(u - shift\right) \\[1em] \beta &= \mathbin{frac}\left(v - shift\right) \\[1em] \gamma &= \mathbin{frac}\left(w - shift\right) \end{aligned} ++++++++++++++++++++++++ where: {empty}:: [eq]#shift = 0.5# ifdef::VK_NV_corner_sampled_image[] for conventional images, and: {empty}:: [eq]#shift = 0.0# for corner-sampled images, endif::VK_NV_corner_sampled_image[] and where: [latexmath] ++++++++++++++++++++++++ \mathbin{frac}(x) = x - \left\lfloor x \right\rfloor ++++++++++++++++++++++++ where the number of fraction bits retained is specified by sname:VkPhysicalDeviceLimits::pname:subTexelPrecisionBits. ifdef::VK_IMG_filter_cubic,VK_EXT_filter_cubic[] Cubic filtering (ename:VK_FILTER_CUBIC_EXT) computes a set of neighboring coordinates which bound the unnormalized coordinates. The integer texel coordinates are combinations of [eq]#i~0~#, [eq]#i~1~#, [eq]#i~2~# or [eq]#i~3~#, [eq]#j~0~#, [eq]#j~1~#, [eq]#j~2~# or [eq]#j~3~#, ifndef::VK_EXT_filter_cubic[] as well as weights [eq]#{alpha}# and [eq]#{beta}#. endif::VK_EXT_filter_cubic[] ifdef::VK_EXT_filter_cubic[] [eq]#k~0~#, [eq]#k~1~#, [eq]#k~2~# or [eq]#k~3~#, as well as weights [eq]#{alpha}#, [eq]#{beta}#, and [eq]#{gamma}#. endif::VK_EXT_filter_cubic[] ifndef::VK_EXT_filter_cubic[] [latexmath] ++++++++++++++++++++++++ \begin{aligned} i_{0} & = {\left \lfloor {u - \frac{3}{2}} \right \rfloor} & i_{1} & = i_{0} + 1 & i_{2} & = i_{1} + 1 & i_{3} & = i_{2} + 1 \\[1em] j_{0} & = {\left \lfloor {v - \frac{3}{2}} \right \rfloor} & j_{1} & = j_{0} + 1 & j_{2} & = j_{1} + 1 & j_{3} & = j_{2} + 1 \end{aligned} ++++++++++++++++++++++++ [latexmath] ++++++++++++++++++++++++ \begin{aligned} alpha &= \mathbin{frac}\left(u - \frac{1}{2}\right) \\[1em] \beta &= \mathbin{frac}\left(v - \frac{1}{2}\right) \end{aligned} ++++++++++++++++++++++++ endif::VK_EXT_filter_cubic[] ifdef::VK_EXT_filter_cubic[] [latexmath] ++++++++++++++++++++++++ \begin{aligned} i_{0} & = {\left \lfloor {u - \frac{3}{2}} \right \rfloor} & i_{1} & = i_{0} + 1 & i_{2} & = i_{1} + 1 & i_{3} & = i_{2} + 1 \\[1em] j_{0} & = {\left \lfloor {v - \frac{3}{2}} \right \rfloor} & j_{1} & = j_{0} + 1 & j_{2} & = j_{1} + 1 & j_{3} & = j_{2} + 1 \\[1em] k_{0} & = {\left \lfloor {w - \frac{3}{2}} \right \rfloor} & k_{1} & = k_{0} + 1 & k_{2} & = k_{1} + 1 & k_{3} & = k_{2} + 1 \end{aligned} ++++++++++++++++++++++++ [latexmath] ++++++++++++++++++++++++ \begin{aligned} \alpha &= \mathbin{frac}\left(u - \frac{1}{2}\right) \\[1em] \beta &= \mathbin{frac}\left(v - \frac{1}{2}\right) \\[1em] \gamma &= \mathbin{frac}\left(w - \frac{1}{2}\right) \end{aligned} ++++++++++++++++++++++++ endif::VK_EXT_filter_cubic[] where: [latexmath] ++++++++++++++++++++++++ \mathbin{frac}(x) = x - \left\lfloor x \right\rfloor ++++++++++++++++++++++++ where the number of fraction bits retained is specified by sname:VkPhysicalDeviceLimits::pname:subTexelPrecisionBits. endif::VK_IMG_filter_cubic,VK_EXT_filter_cubic[] [[textures-integer-coordinate-operations]] == Integer Texel Coordinate Operations ifdef::VK_AMD_shader_image_load_store_lod[] Integer texel coordinate operations may: supply a LOD which texels are to be read from or written to using the optional SPIR-V operand code:Lod. endif::VK_AMD_shader_image_load_store_lod[] ifndef::VK_AMD_shader_image_load_store_lod[] The code:OpImageFetch and code:OpImageFetchSparse SPIR-V instructions may: supply a LOD from which texels are to be fetched using the optional SPIR-V operand code:Lod. Other integer-coordinate operations must: not. endif::VK_AMD_shader_image_load_store_lod[] If the code:Lod is provided then it must: be an integer. The image level selected is: [latexmath] ++++++++++++++++++++++++ \begin{aligned} d & = level_{base} + \begin{cases} Lod & \text{(from optional SPIR-V operand)} \\ 0 & \text{otherwise} \end{cases} \\ \end{aligned} ++++++++++++++++++++++++ If [eq]#d# does not lie in the range [eq]#[pname:baseMipLevel, pname:baseMipLevel {plus} pname:levelCount)# ifdef::VK_EXT_image_view_min_lod[] or [eq]#d# is less than minLodInteger~imageView~, endif::VK_EXT_image_view_min_lod[] then any values fetched are ifdef::VK_EXT_robustness2[] zero if the <> feature is enabled, otherwise are endif::VK_EXT_robustness2[] undefined:, and any writes (if supported) are discarded. [[textures-sample-operations]] == Image Sample Operations [[textures-wrapping-operation]] === Wrapping Operation ifdef::VK_EXT_non_seamless_cube_map[] If the used sampler was created without ename:VK_SAMPLER_CREATE_NON_SEAMLESS_CUBE_MAP_BIT_EXT, endif::VK_EXT_non_seamless_cube_map[] code:Cube images ignore the wrap modes specified in the sampler. Instead, if ename:VK_FILTER_NEAREST is used within a mip level then ename:VK_SAMPLER_ADDRESS_MODE_CLAMP_TO_EDGE is used, and if ename:VK_FILTER_LINEAR is used within a mip level then sampling at the edges is performed as described earlier in the <> section. The first integer texel coordinate i is transformed based on the pname:addressModeU parameter of the sampler. [latexmath] ++++++++++++++++++++++++ \begin{aligned} i &= \begin{cases} i \bmod size & \text{for repeat} \\ (size - 1) - \mathbin{mirror} ((i \bmod (2 \times size)) - size) & \text{for mirrored repeat} \\ \mathbin{clamp}(i,0,size-1) & \text{for clamp to edge} \\ \mathbin{clamp}(i,-1,size) & \text{for clamp to border} \\ \mathbin{clamp}(\mathbin{mirror}(i),0,size-1) & \text{for mirror clamp to edge} \end{cases} \end{aligned} ++++++++++++++++++++++++ where: [latexmath] ++++++++++++++++++++++++ \begin{aligned} & \mathbin{mirror}(n) = \begin{cases} n & \text{for}\ n \geq 0 \\ -(1+n) & \text{otherwise} \end{cases} \end{aligned} ++++++++++++++++++++++++ [eq]#j# (for 2D and Cube image) and [eq]#k# (for 3D image) are similarly transformed based on the pname:addressModeV and pname:addressModeW parameters of the sampler, respectively. [[textures-gather]] === Texel Gathering SPIR-V instructions with code:Gather in the name return a vector derived from 4 texels in the base level of the image view. The rules for the ename:VK_FILTER_LINEAR minification filter are applied to identify the four selected texels. Each texel is then converted to an RGBA value according to <> and then <>. A four-component vector is then assembled by taking the component indicated by the code:Component value in the instruction from the swizzled color value of the four texels. If the operation does not use the code:ConstOffsets image operand then the four texels form the 2 {times} 2 rectangle used for texture filtering: [latexmath] ++++++++++++++++++++++++ \begin{aligned} \tau[R] &= \tau_{i0j1}[level_{base}][comp] \\ \tau[G] &= \tau_{i1j1}[level_{base}][comp] \\ \tau[B] &= \tau_{i1j0}[level_{base}][comp] \\ \tau[A] &= \tau_{i0j0}[level_{base}][comp] \end{aligned} ++++++++++++++++++++++++ If the operation does use the code:ConstOffsets image operand then the offsets allow a custom filter to be defined: [latexmath] ++++++++++++++++++++++++ \begin{aligned} \tau[R] &= \tau_{i0j0 + \Delta_0}[level_{base}][comp] \\ \tau[G] &= \tau_{i0j0 + \Delta_1}[level_{base}][comp] \\ \tau[B] &= \tau_{i0j0 + \Delta_2}[level_{base}][comp] \\ \tau[A] &= \tau_{i0j0 + \Delta_3}[level_{base}][comp] \end{aligned} ++++++++++++++++++++++++ where: [latexmath] ++++++++++++++++++++++++ \begin{aligned} \tau[level_{base}][comp] &= \begin{cases} \tau[level_{base}][R], & \text{for}\ comp = 0 \\ \tau[level_{base}][G], & \text{for}\ comp = 1 \\ \tau[level_{base}][B], & \text{for}\ comp = 2 \\ \tau[level_{base}][A], & \text{for}\ comp = 3 \end{cases}\\ comp & \,\text{from SPIR-V operand Component} \end{aligned} ++++++++++++++++++++++++ ifdef::VK_VERSION_1_1,VK_KHR_sampler_ycbcr_conversion[] code:OpImage*Gather must: not be used on a sampled image with <> enabled. endif::VK_VERSION_1_1,VK_KHR_sampler_ycbcr_conversion[] ifdef::VK_EXT_image_view_min_lod[] If [eq]#level~base~ < minLodInteger~imageView~#, then any values fetched are ifdef::VK_EXT_robustness2[] zero if <> is enabled. Otherwise values are endif::VK_EXT_robustness2[] undefined:. endif::VK_EXT_image_view_min_lod[] [[textures-texel-filtering]] === Texel Filtering Texel filtering is first performed for each level (either [eq]#d# or [eq]#d~hi~# and [eq]#d~lo~#). If [eq]#{lambda}# is less than or equal to zero, the texture is said to be _magnified_, and the filter mode within a mip level is selected by the pname:magFilter in the sampler. If [eq]#{lambda}# is greater than zero, the texture is said to be _minified_, and the filter mode within a mip level is selected by the pname:minFilter in the sampler. [[textures-texel-nearest-filtering]] ==== Texel Nearest Filtering Within a mip level, ename:VK_FILTER_NEAREST filtering selects a single value using the [eq]#(i, j, k)# texel coordinates, with all texels taken from layer l. [latexmath] ++++++++++++++++++++++++ \begin{aligned} \tau[level] &= \begin{cases} \tau_{ijk}[level], & \text{for 3D image} \\ \tau_{ij}[level], & \text{for 2D or Cube image} \\ \tau_{i}[level], & \text{for 1D image} \end{cases} \end{aligned} ++++++++++++++++++++++++ [[textures-texel-linear-filtering]] ==== Texel Linear Filtering Within a mip level, ename:VK_FILTER_LINEAR filtering combines 8 (for 3D), 4 (for 2D or Cube), or 2 (for 1D) texel values, together with their linear weights. The linear weights are derived from the fractions computed earlier: [latexmath] ++++++++++++++++++++++++ \begin{aligned} w_{i_0} &= (1-\alpha) \\ w_{i_1} &= (\alpha) \\ w_{j_0} &= (1-\beta) \\ w_{j_1} &= (\beta) \\ w_{k_0} &= (1-\gamma) \\ w_{k_1} &= (\gamma) \end{aligned} ++++++++++++++++++++++++ ifndef::VK_VERSION_1_2,VK_EXT_sampler_filter_minmax[] The values of multiple texels, together with their weights, are combined using a weighted average to produce a filtered value: endif::VK_VERSION_1_2,VK_EXT_sampler_filter_minmax[] ifdef::VK_VERSION_1_2,VK_EXT_sampler_filter_minmax[] The values of multiple texels, together with their weights, are combined to produce a filtered value. The slink:VkSamplerReductionModeCreateInfo::pname:reductionMode can: control the process by which multiple texels, together with their weights, are combined to produce a filtered texture value. When the pname:reductionMode is set (explicitly or implicitly) to ename:VK_SAMPLER_REDUCTION_MODE_WEIGHTED_AVERAGE, a weighted average is computed: endif::VK_VERSION_1_2,VK_EXT_sampler_filter_minmax[] [latexmath] ++++++++++++++++++++++++ \begin{aligned} \tau_{3D} &= \sum_{k=k_0}^{k_1}\sum_{j=j_0}^{j_1}\sum_{i=i_0}^{i_1}(w_{i})(w_{j})(w_{k})\tau_{ijk} \\ \tau_{2D} &= \sum_{j=j_0}^{j_1}\sum_{i=i_0}^{i_1}(w_{i})(w_{j})\tau_{ij} \\ \tau_{1D} &= \sum_{i=i_0}^{i_1}(w_{i})\tau_{i} \end{aligned} ++++++++++++++++++++++++ ifdef::VK_VERSION_1_2,VK_EXT_sampler_filter_minmax[] However, if the reduction mode is ename:VK_SAMPLER_REDUCTION_MODE_MIN or ename:VK_SAMPLER_REDUCTION_MODE_MAX, the process operates on the above set of multiple texels, together with their weights, computing a component-wise minimum or maximum, respectively, of the components of the set of texels with non-zero weights. endif::VK_VERSION_1_2,VK_EXT_sampler_filter_minmax[] ifdef::VK_IMG_filter_cubic,VK_EXT_filter_cubic[] [[textures-texel-cubic-filtering]] ==== Texel Cubic Filtering Within a mip level, ename:VK_FILTER_CUBIC_EXT, filtering computes a weighted average of ifdef::VK_EXT_filter_cubic[] 64 (for 3D), endif::VK_EXT_filter_cubic[] 16 (for 2D), or 4 (for 1D) texel values, together with their ifndef::VK_QCOM_filter_cubic_weights[] Catmull-Rom weights. endif::VK_QCOM_filter_cubic_weights[] ifdef::VK_QCOM_filter_cubic_weights[] Catmull-Rom, Zero Tangent Cardinal, B-Spline, or Mitchell-Netravali weights as specified by slink:VkSamplerCubicWeightsCreateInfoQCOM. endif::VK_QCOM_filter_cubic_weights[] Catmull-Rom weights ifdef::VK_QCOM_filter_cubic_weights[] specified by ename:VK_CUBIC_FILTER_WEIGHTS_CATMULL_ROM_QCOM endif::VK_QCOM_filter_cubic_weights[] are derived from the fractions computed earlier. ifndef::VK_EXT_filter_cubic[] [latexmath] ++++++++++++++++++++++++ \begin{aligned} \begin{bmatrix} w_{i_0}\phantom{,} w_{i_1}\phantom{,} w_{i_2}\phantom{,} w_{i_3} \end{bmatrix} = \frac{1}{2} \begin{bmatrix} 1 & \alpha & \alpha^2 & \alpha^3 \end{bmatrix} \begin{bmatrix} \phantom{-}0 & \phantom{-}2 & \phantom{-}0 & \phantom{-}0 \\ -1 & \phantom{-}0 & \phantom{-}1 & \phantom{-}0 \\ \phantom{-}2 & -5 & \phantom{-}4 & -1 \\ -1 & \phantom{-}3 & -3 & \phantom{-}1 \end{bmatrix} \\ \begin{bmatrix} w_{j_0}\phantom{,} w_{j_1}\phantom{,} w_{j_2}\phantom{,} w_{j_3} \end{bmatrix} = \frac{1}{2} \begin{bmatrix} 1 & \beta & \beta^2 & \beta^3 \end{bmatrix} \begin{bmatrix} \phantom{-}0 & \phantom{-}2 & \phantom{-}0 & \phantom{-}0 \\ -1 & \phantom{-}0 & \phantom{-}1 & \phantom{-}0 \\ \phantom{-}2 & -5 & \phantom{-}4 & -1 \\ -1 & \phantom{-}3 & -3 & \phantom{-}1 \end{bmatrix} \end{aligned} ++++++++++++++++++++++++ The values of multiple texels, together with their weights, are combined using a weighted average to produce a filtered value: [latexmath] ++++++++++++++++++++++++ \begin{aligned} \tau_{2D} &= \sum_{j=j_0}^{j_3}\sum_{i=i_0}^{i_3}(w_{i})(w_{j})\tau_{ij} \\ \tau_{1D} &= \sum_{i=i_0}^{i_3}(w_{i})\tau_{i} \end{aligned} ++++++++++++++++++++++++ endif::VK_EXT_filter_cubic[] ifdef::VK_EXT_filter_cubic[] [latexmath] ++++++++++++++++++++++++ \begin{aligned} \begin{bmatrix} w_{i_0}\phantom{,} w_{i_1}\phantom{,} w_{i_2}\phantom{,} w_{i_3} \end{bmatrix} = \frac{1}{2} \begin{bmatrix} 1 & \alpha & \alpha^2 & \alpha^3 \end{bmatrix} \begin{bmatrix} \phantom{-}0 & \phantom{-}2 & \phantom{-}0 & \phantom{-}0 \\ -1 & \phantom{-}0 & \phantom{-}1 & \phantom{-}0 \\ \phantom{-}2 & -5 & \phantom{-}4 & -1 \\ -1 & \phantom{-}3 & -3 & \phantom{-}1 \end{bmatrix} \\ \begin{bmatrix} w_{j_0}\phantom{,} w_{j_1}\phantom{,} w_{j_2}\phantom{,} w_{j_3} \end{bmatrix} = \frac{1}{2} \begin{bmatrix} 1 & \beta & \beta^2 & \beta^3 \end{bmatrix} \begin{bmatrix} \phantom{-}0 & \phantom{-}2 & \phantom{-}0 & \phantom{-}0 \\ -1 & \phantom{-}0 & \phantom{-}1 & \phantom{-}0 \\ \phantom{-}2 & -5 & \phantom{-}4 & -1 \\ -1 & \phantom{-}3 & -3 & \phantom{-}1 \end{bmatrix} \\ \begin{bmatrix} w_{k_0}\phantom{,} w_{k_1}\phantom{,} w_{k_2}\phantom{,} w_{k_3} \end{bmatrix} = \frac{1}{2} \begin{bmatrix} 1 & \gamma & \gamma^2 & \gamma^3 \end{bmatrix} \begin{bmatrix} \phantom{-}0 & \phantom{-}2 & \phantom{-}0 & \phantom{-}0 \\ -1 & \phantom{-}0 & \phantom{-}1 & \phantom{-}0 \\ \phantom{-}2 & -5 & \phantom{-}4 & -1 \\ -1 & \phantom{-}3 & -3 & \phantom{-}1 \end{bmatrix} \end{aligned} ++++++++++++++++++++++++ ifdef::VK_QCOM_filter_cubic_weights[] Zero Tangent Cardinal weights specified by ename:VK_CUBIC_FILTER_WEIGHTS_ZERO_TANGENT_CARDINAL_QCOM are derived from the fractions computed earlier. [latexmath] ++++++++++++++++++++++++ \begin{aligned} \begin{bmatrix} w_{i_0}\phantom{,} w_{i_1}\phantom{,} w_{i_2}\phantom{,} w_{i_3} \end{bmatrix} = \frac{1}{2} \begin{bmatrix} 1 & \alpha & \alpha^2 & \alpha^3 \end{bmatrix} \begin{bmatrix} \phantom{-}0 & \phantom{-}2 & \phantom{-}0 & \phantom{-}0 \\ -2 & \phantom{-}0 & \phantom{-}2 & \phantom{-}0 \\ \phantom{-}4 & -4 & \phantom{-}2 & -2 \\ -2 & \phantom{-}2 & -2 & \phantom{-}1 \end{bmatrix} \\ \begin{bmatrix} w_{j_0}\phantom{,} w_{j_1}\phantom{,} w_{j_2}\phantom{,} w_{j_3} \end{bmatrix} = \frac{1}{2} \begin{bmatrix} 1 & \beta & \beta^2 & \beta^3 \end{bmatrix} \begin{bmatrix} \phantom{-}0 & \phantom{-}2 & \phantom{-}0 & \phantom{-}0 \\ -2 & \phantom{-}0 & \phantom{-}2 & \phantom{-}0 \\ \phantom{-}4 & -4 & \phantom{-}2 & -2 \\ -2 & \phantom{-}2 & -2 & \phantom{-}1 \end{bmatrix} \\ \begin{bmatrix} w_{k_0}\phantom{,} w_{k_1}\phantom{,} w_{k_2}\phantom{,} w_{k_3} \end{bmatrix} = \frac{1}{2} \begin{bmatrix} 1 & \gamma & \gamma^2 & \gamma^3 \end{bmatrix} \begin{bmatrix} \phantom{-}0 & \phantom{-}2 & \phantom{-}0 & \phantom{-}0 \\ -2 & \phantom{-}0 & \phantom{-}2 & \phantom{-}0 \\ \phantom{-}4 & -4 & \phantom{-}2 & -2 \\ -2 & \phantom{-}2 & -2 & \phantom{-}1 \end{bmatrix} \end{aligned} ++++++++++++++++++++++++ B-Spline weights specified by ename:VK_CUBIC_FILTER_WEIGHTS_B_SPLINE_QCOM are derived from the fractions computed earlier. [latexmath] ++++++++++++++++++++++++ \begin{aligned} \begin{bmatrix} w_{i_0}\phantom{,} w_{i_1}\phantom{,} w_{i_2}\phantom{,} w_{i_3} \end{bmatrix} = \frac{1}{6} \begin{bmatrix} 1 & \alpha & \alpha^2 & \alpha^3 \end{bmatrix} \begin{bmatrix} \phantom{-}1 & \phantom{-}4 & \phantom{-}1 & \phantom{-}0 \\ -3 & \phantom{-}0 & \phantom{-}3 & \phantom{-}0 \\ \phantom{-}3 & -6 & \phantom{-}3 & \phantom{-}0 \\ -1 & \phantom{-}3 & -3 & \phantom{-}1 \end{bmatrix} \\ \begin{bmatrix} w_{j_0}\phantom{,} w_{j_1}\phantom{,} w_{j_2}\phantom{,} w_{j_3} \end{bmatrix} = \frac{1}{6} \begin{bmatrix} 1 & \beta & \beta^2 & \beta^3 \end{bmatrix} \begin{bmatrix} \phantom{-}1 & \phantom{-}4 & \phantom{-}1 & \phantom{-}0 \\ -3 & \phantom{-}0 & \phantom{-}3 & \phantom{-}0 \\ \phantom{-}3 & -6 & \phantom{-}3 & \phantom{-}0 \\ -1 & \phantom{-}3 & -3 & \phantom{-}1 \end{bmatrix} \\ \begin{bmatrix} w_{k_0}\phantom{,} w_{k_1}\phantom{,} w_{k_2}\phantom{,} w_{k_3} \end{bmatrix} = \frac{1}{6} \begin{bmatrix} 1 & \gamma & \gamma^2 & \gamma^3 \end{bmatrix} \begin{bmatrix} \phantom{-}1 & \phantom{-}4 & \phantom{-}1 & \phantom{-}0 \\ -3 & \phantom{-}0 & \phantom{-}3 & \phantom{-}0 \\ \phantom{-}3 & -6 & \phantom{-}3 & \phantom{-}0 \\ -1 & \phantom{-}3 & -3 & \phantom{-}1 \end{bmatrix} \end{aligned} ++++++++++++++++++++++++ Mitchell-Netravali weights specified by ename:VK_CUBIC_FILTER_WEIGHTS_MITCHELL_NETRAVALI_QCOM are derived from the fractions computed earlier. [latexmath] ++++++++++++++++++++++++ \begin{aligned} \begin{bmatrix} w_{i_0}\phantom{,} w_{i_1}\phantom{,} w_{i_2}\phantom{,} w_{i_3} \end{bmatrix} = \frac{1}{18} \begin{bmatrix} 1 & \alpha & \alpha^2 & \alpha^3 \end{bmatrix} \begin{bmatrix} \phantom{-}1 & \phantom{-}16 & \phantom{-}1 & \phantom{-}0 \\ -9 & \phantom{-}0 & \phantom{-}9 & \phantom{-}0 \\ \phantom{-}15 & -36 & \phantom{-}27 & -6 \\ -7 & \phantom{-}21 & -21 & \phantom{-}7 \end{bmatrix} \\ \begin{bmatrix} w_{j_0}\phantom{,} w_{j_1}\phantom{,} w_{j_2}\phantom{,} w_{j_3} \end{bmatrix} = \frac{1}{18} \begin{bmatrix} 1 & \beta & \beta^2 & \beta^3 \end{bmatrix} \begin{bmatrix} \phantom{-}1 & \phantom{-}16 & \phantom{-}1 & \phantom{-}0 \\ -9 & \phantom{-}0 & \phantom{-}9 & \phantom{-}0 \\ \phantom{-}15 & -36 & \phantom{-}27 & -6 \\ -7 & \phantom{-}21 & -21 & \phantom{-}7 \end{bmatrix} \\ \begin{bmatrix} w_{k_0}\phantom{,} w_{k_1}\phantom{,} w_{k_2}\phantom{,} w_{k_3} \end{bmatrix} = \frac{1}{18} \begin{bmatrix} 1 & \gamma & \gamma^2 & \gamma^3 \end{bmatrix} \begin{bmatrix} \phantom{-}1 & \phantom{-}16 & \phantom{-}1 & \phantom{-}0 \\ -9 & \phantom{-}0 & \phantom{-}9 & \phantom{-}0 \\ \phantom{-}15 & -36 & \phantom{-}27 & -6 \\ -7 & \phantom{-}21 & -21 & \phantom{-}7 \end{bmatrix} \end{aligned} ++++++++++++++++++++++++ endif::VK_QCOM_filter_cubic_weights[] The values of multiple texels, together with their weights, are combined to produce a filtered value. The slink:VkSamplerReductionModeCreateInfo::pname:reductionMode can: control the process by which multiple texels, together with their weights, are combined to produce a filtered texture value. When the pname:reductionMode is set (explicitly or implicitly) to ename:VK_SAMPLER_REDUCTION_MODE_WEIGHTED_AVERAGE ifdef::VK_QCOM_filter_cubic_clamp[] or ename:VK_SAMPLER_REDUCTION_MODE_WEIGHTED_AVERAGE_RANGECLAMP_QCOM endif::VK_QCOM_filter_cubic_clamp[] , a weighted average is computed: [latexmath] ++++++++++++++++++++++++ \begin{aligned} \tau_{3D} &= \sum_{k=j_0}^{k_3}\sum_{j=j_0}^{j_3}\sum_{i=i_0}^{i_3}(w_{i})(w_{j})(w_{k})\tau_{ijk} \\ \tau_{2D} &= \sum_{j=j_0}^{j_3}\sum_{i=i_0}^{i_3}(w_{i})(w_{j})\tau_{ij} \\ \tau_{1D} &= \sum_{i=i_0}^{i_3}(w_{i})\tau_{i} \end{aligned} ++++++++++++++++++++++++ ifdef::VK_VERSION_1_2,VK_EXT_sampler_filter_minmax[] However, if the reduction mode is ename:VK_SAMPLER_REDUCTION_MODE_MIN or ename:VK_SAMPLER_REDUCTION_MODE_MAX, the process operates on the above set of multiple texels, together with their weights, computing a component-wise minimum or maximum, respectively, of the components of the set of texels with non-zero weights. endif::VK_VERSION_1_2,VK_EXT_sampler_filter_minmax[] ifdef::VK_QCOM_filter_cubic_clamp[] [[textures-texel-range-clamp]] ==== Texel Range Clamp When the pname:reductionMode is set to ename:VK_SAMPLER_REDUCTION_MODE_WEIGHTED_AVERAGE_RANGECLAMP_QCOM, the weighted average is clamped to be within the component-wise minimum and maximum of the set of texels with non-zero weights. endif::VK_QCOM_filter_cubic_clamp[] endif::VK_EXT_filter_cubic[] endif::VK_IMG_filter_cubic,VK_EXT_filter_cubic[] [[textures-texel-mipmap-filtering]] ==== Texel Mipmap Filtering ename:VK_SAMPLER_MIPMAP_MODE_NEAREST filtering returns the value of a single mipmap level, [eq]#{tau} = {tau}[d]#. ename:VK_SAMPLER_MIPMAP_MODE_LINEAR filtering combines the values of multiple mipmap levels ({tau}[hi] and {tau}[lo]), together with their linear weights. The linear weights are derived from the fraction computed earlier: [latexmath] ++++++++++++++++++++++++ \begin{aligned} w_{hi} &= (1-\delta) \\ w_{lo} &= (\delta) \\ \end{aligned} ++++++++++++++++++++++++ ifndef::VK_VERSION_1_2,VK_EXT_sampler_filter_minmax[] The values of multiple mipmap levels together with their linear weights, are combined using a weighted average to produce a final filtered value: endif::VK_VERSION_1_2,VK_EXT_sampler_filter_minmax[] ifdef::VK_VERSION_1_2,VK_EXT_sampler_filter_minmax[] The values of multiple mipmap levels, together with their weights, are combined to produce a final filtered value. The slink:VkSamplerReductionModeCreateInfo::pname:reductionMode can: control the process by which multiple texels, together with their weights, are combined to produce a filtered texture value. When the pname:reductionMode is set (explicitly or implicitly) to ename:VK_SAMPLER_REDUCTION_MODE_WEIGHTED_AVERAGE, a weighted average is computed: endif::VK_VERSION_1_2,VK_EXT_sampler_filter_minmax[] [latexmath] ++++++++++++++++++++++++ \begin{aligned} \tau &= (w_{hi})\tau[hi]+(w_{lo})\tau[lo] \end{aligned} ++++++++++++++++++++++++ ifdef::VK_VERSION_1_2,VK_EXT_sampler_filter_minmax[] However, if the reduction mode is ename:VK_SAMPLER_REDUCTION_MODE_MIN or ename:VK_SAMPLER_REDUCTION_MODE_MAX, the process operates on the above values, together with their weights, computing a component-wise minimum or maximum, respectively, of the components of the values with non-zero weights. endif::VK_VERSION_1_2,VK_EXT_sampler_filter_minmax[] [[textures-texel-anisotropic-filtering]] ==== Texel Anisotropic Filtering Anisotropic filtering is enabled by the pname:anisotropyEnable in the sampler. When enabled, the image filtering scheme accounts for a degree of anisotropy. The particular scheme for anisotropic texture filtering is implementation-dependent. Implementations should: consider the pname:magFilter, pname:minFilter and pname:mipmapMode of the sampler to control the specifics of the anisotropic filtering scheme used. In addition, implementations should: consider pname:minLod and pname:maxLod of the sampler. [NOTE] .Note ==== For historical reasons, vendor implementations of anisotropic filtering interpret these sampler parameters in different ways, particularly in corner cases such as pname:magFilter, pname:minFilter of ename:NEAREST or pname:maxAnisotropy equal to 1.0. Applications should not expect consistent behavior in such cases, and should use anisotropic filtering only with parameters which are expected to give a quality improvement relative to etext:LINEAR filtering. The following describes one particular approach to implementing anisotropic filtering for the 2D Image case; implementations may: choose other methods: Given a pname:magFilter, pname:minFilter of ename:VK_FILTER_LINEAR and a pname:mipmapMode of ename:VK_SAMPLER_MIPMAP_MODE_NEAREST: Instead of a single isotropic sample, N isotropic samples are sampled within the image footprint of the image level [eq]#d# to approximate an anisotropic filter. The sum [eq]#{tau}~2Daniso~# is defined using the single isotropic [eq]#{tau}~2D~(u,v)# at level [eq]#d#. [latexmath] ++++++++++++++++++++++++ \begin{aligned} \tau_{2Daniso} & = \frac{1}{N}\sum_{i=1}^{N} {\tau_{2D}\left ( u \left ( x - \frac{1}{2} + \frac{i}{N+1} , y \right ), v \left (x-\frac{1}{2}+\frac{i}{N+1}, y \right ) \right )}, & \text{when}\ \rho_{x} > \rho_{y} \\ \tau_{2Daniso} &= \frac{1}{N}\sum_{i=1}^{N} {\tau_{2D}\left ( u \left ( x, y - \frac{1}{2} + \frac{i}{N+1} \right ), v \left (x,y-\frac{1}{2}+\frac{i}{N+1} \right ) \right )}, & \text{when}\ \rho_{y} \geq \rho_{x} \end{aligned} ++++++++++++++++++++++++ ifdef::VK_VERSION_1_2,VK_EXT_sampler_filter_minmax[] When slink:VkSamplerReductionModeCreateInfo::pname:reductionMode is set to ename:VK_SAMPLER_REDUCTION_MODE_WEIGHTED_AVERAGE, the above summation is used. However, if the reduction mode is ename:VK_SAMPLER_REDUCTION_MODE_MIN or ename:VK_SAMPLER_REDUCTION_MODE_MAX, the process operates on the above values, together with their weights, computing a component-wise minimum or maximum, respectively, of the components of the values with non-zero weights. endif::VK_VERSION_1_2,VK_EXT_sampler_filter_minmax[] ==== ifdef::VK_NV_shader_image_footprint[] [[textures-footprint]] == Texel Footprint Evaluation The SPIR-V instruction code:OpImageSampleFootprintNV evaluates the set of texels from a single mip level that would be accessed during a <> operation. In addition to the inputs that would be accepted by an equivalent code:OpImageSample* instruction, code:OpImageSampleFootprintNV accepts two additional inputs. The code:Granularity input is an integer identifying the size of texel groups used to evaluate the footprint. Each bit in the returned footprint mask corresponds to an aligned block of texels whose size is given by the following table: .Texel footprint granularity values [width="50%",options="header"] |==== | code:Granularity | code:Dim = 2D | code:Dim = 3D | 0 | unsupported | unsupported | 1 | 2x2 | 2x2x2 | 2 | 4x2 | unsupported | 3 | 4x4 | 4x4x2 | 4 | 8x4 | unsupported | 5 | 8x8 | unsupported | 6 | 16x8 | unsupported | 7 | 16x16 | unsupported | 8 | unsupported | unsupported | 9 | unsupported | unsupported | 10 | unsupported | 16x16x16 | 11 | 64x64 | 32x16x16 | 12 | 128x64 | 32x32x16 | 13 | 128x128 | 32x32x32 | 14 | 256x128 | 64x32x32 | 15 | 256x256 | unsupported |==== The code:Coarse input is used to select between the two mip levels that may: be accessed during texel filtering when using a pname:mipmapMode of ename:VK_SAMPLER_MIPMAP_MODE_LINEAR. When filtering between two mip levels, a code:Coarse value of code:true requests the footprint in the lower-resolution mip level (higher level number), while code:false requests the footprint in the higher-resolution mip level. If texel filtering would access only a single mip level, the footprint in that level would be returned when code:Coarse is set to code:false; an empty footprint would be returned when code:Coarse is set to code:true. The footprint for code:OpImageSampleFootprintNV is returned in a structure with six members: * The first member is a boolean value that is true if the texel filtering operation would access only a single mip level. * The second member is a two- or three-component integer vector holding the footprint anchor location. For two-dimensional images, the returned components are in units of eight texel groups. For three-dimensional images, the returned components are in units of four texel groups. * The third member is a two- or three-component integer vector holding a footprint offset relative to the anchor. All returned components are in units of texel groups. * The fourth member is a two-component integer vector mask, which holds a bitfield identifying the set of texel groups in an 8x8 or 4x4x4 neighborhood relative to the anchor and offset. * The fifth member is an integer identifying the mip level containing the footprint identified by the anchor, offset, and mask. * The sixth member is an integer identifying the granularity of the returned footprint. For footprints in two-dimensional images (code:Dim2D), the mask returned by code:OpImageSampleFootprintNV indicates whether each texel group in a 8x8 local neighborhood of texel groups would have one or more texels accessed during texel filtering. In the mask, the texel group with local group coordinates latexmath:[(lgx,lgy)] is considered covered if and only if [latexmath] +++++++++++++++++++ \begin{aligned} 0 \neq ((mask.x + (mask.y << 32)) \text{ \& } (1 << (lgy \times 8 + lgx))) \end{aligned} +++++++++++++++++++ where: * latexmath:[0 \leq lgx < 8] and latexmath:[0 \leq lgy < 8]; and * latexmath:[mask] is the returned two-component mask. The local group with coordinates latexmath:[(lgx,lgy)] in the mask is considered covered if and only if the texel filtering operation would access one or more texels latexmath:[\tau_{ij}] in the returned mip level where: [latexmath] +++++++++++++++++++ \begin{aligned} i0 & = \begin{cases} gran.x \times (8 \times anchor.x + lgx), & \text{if } lgx + offset.x < 8 \\ gran.x \times (8 \times (anchor.x - 1) + lgx), & \text{otherwise} \end{cases} \\ i1 & = i0 + gran.x - 1 \\ j0 & = \begin{cases} gran.y \times (8 \times anchor.y + lgy), & \text{if } lgy + offset.y < 8 \\ gran.y \times (8 \times (anchor.y - 1) + lgy), & otherwise \end{cases} \\ j1 & = j0 + gran.y - 1 \end{aligned} +++++++++++++++++++ and * latexmath:[i0 \leq i \leq i1] and latexmath:[j0 \leq j \leq j1]; * latexmath:[gran] is a two-component vector holding the width and height of the texel group identified by the granularity; * latexmath:[anchor] is the returned two-component anchor vector; and * latexmath:[offset] is the returned two-component offset vector. For footprints in three-dimensional images (code:Dim3D), the mask returned by code:OpImageSampleFootprintNV indicates whether each texel group in a 4x4x4 local neighborhood of texel groups would have one or more texels accessed during texel filtering. In the mask, the texel group with local group coordinates latexmath:[(lgx,lgy,lgz)], is considered covered if and only if: [latexmath] +++++++++++++++++++ \begin{aligned} 0 \neq ((mask.x + (mask.y << 32)) \text{ \& } (1 << (lgz \times 16 + lgy \times 4 + lgx))) \end{aligned} +++++++++++++++++++ where: * latexmath:[0 \leq lgx < 4], latexmath:[0 \leq lgy < 4], and latexmath:[0 \leq lgz < 4]; and * latexmath:[mask] is the returned two-component mask. The local group with coordinates latexmath:[(lgx,lgy,lgz)] in the mask is considered covered if and only if the texel filtering operation would access one or more texels latexmath:[\tau_{ijk}] in the returned mip level where: [latexmath] +++++++++++++++++++ \begin{aligned} i0 & = \begin{cases} gran.x \times (4 \times anchor.x + lgx), & \text{if } lgx + offset.x < 4 \\ gran.x \times (4 \times (anchor.x - 1) + lgx), & \text{otherwise} \end{cases} \\ i1 & = i0 + gran.x - 1 \\ j0 & = \begin{cases} gran.y \times (4 \times anchor.y + lgy), & \text{if } lgy + offset.y < 4 \\ gran.y \times (4 \times (anchor.y - 1) + lgy), & otherwise \end{cases} \\ j1 & = j0 + gran.y - 1 \\ k0 & = \begin{cases} gran.z \times (4 \times anchor.z + lgz), & \text{if } lgz + offset.z < 4 \\ gran.z \times (4 \times (anchor.z - 1) + lgz), & otherwise \end{cases} \\ k1 & = k0 + gran.z - 1 \end{aligned} +++++++++++++++++++ and * latexmath:[i0 \leq i \leq i1], latexmath:[j0 \leq j \leq j1], latexmath:[k0 \leq k \leq k1]; * latexmath:[gran] is a three-component vector holding the width, height, and depth of the texel group identified by the granularity; * latexmath:[anchor] is the returned three-component anchor vector; and * latexmath:[offset] is the returned three-component offset vector. If the sampler used by code:OpImageSampleFootprintNV enables anisotropic texel filtering via pname:anisotropyEnable, it is possible that the set of texel groups accessed in a mip level may be too large to be expressed using an 8x8 or 4x4x4 mask using the granularity requested in the instruction. In this case, the implementation uses a texel group larger than the requested granularity. When a larger texel group size is used, code:OpImageSampleFootprintNV returns an integer granularity value that can: be interpreted in the same manner as the granularity value provided to the instruction to determine the texel group size used. If anisotropic texel filtering is disabled in the sampler, or if an anisotropic footprint can be represented as an 8x8 or 4x4x4 mask with the requested granularity, code:OpImageSampleFootprintNV will use the requested granularity as-is and return a granularity value of zero. code:OpImageSampleFootprintNV supports only two- and three-dimensional image accesses (code:Dim2D and code:Dim3D), and the footprint returned is undefined: if a sampler uses an addressing mode other than ename:VK_SAMPLER_ADDRESS_MODE_CLAMP_TO_EDGE. endif::VK_NV_shader_image_footprint[] ifdef::VK_QCOM_image_processing[] [[textures-weightimage]] == Weight Image Sampling The SPIR-V instruction code:OpImageWeightedSampleQCOM specifies a texture sampling operation involving two images: the _sampled image_ and the _weight image_. It is similar to bilinear filtering except more than 2x2 texels may participate in the filter and the filter weights are user-specified rather than computed by fixed-function hardware. The weight image view defines a 2D kernel weights used during sampling. The code:OpImageWeightedSampleQCOM support normalized or unnormalized texel coordinates. In addition to the inputs that would be accepted by an equivalent code:OpImageSample* instruction, code:OpImageWeightedSampleQCOM accepts a code:weight input that specifies the view of a sample weight image The input code:weight must: be a view of a 2D or 1D image with code:miplevels equal to `1`, code:samples equal to ename:VK_SAMPLE_COUNT_1_BIT, created with an identity swizzle, and created with code:usage that includes ename:VK_IMAGE_USAGE_SAMPLE_WEIGHT_BIT_QCOM. The slink:VkImageViewSampleWeightCreateInfoQCOM specifies additional parameters of the view: pname:filterCenter, pname:filterSize, and pname:numPhases. described in more detail below. The code:weight input must: be bound using a <> descriptor type. The code:weight view defines a filtering kernel that is a region of view's subresource range. The kernel spans a region from integer texel coordinate [eq]#(0,0)# to [eq]#(pname:filterSize.x-1, pname:filterSize.y-1)#. It is valid for the view's subresource to have dimensions larger than the kernel but the texels with integer coordinates greater than [eq]#(pname:filterSize.width-1, pname:filterSize.height-1)# are ignored by weight sampling. The value returned by queries code:OpImageQuerySize, code:OpImageQuerySizeLod, code:OpImageQueryLevels, and code:OpImageQuerySamples return for a weight image is undefined:. pname:filterCenter designates an integer texel coordinate within the filter kernel as being the 'center' of the kernel. The center must: be in the range [eq]#(0,0)# to [eq]#(pname:filterSize.x-1, pname:filterSize.y-1)#. pname:numPhases describes the number of filter phases used to provide sub-pixel filtering. Both are described in more detail below. [[textures-weightimage-layout]] === Weight Image Layout The weight image specifies filtering kernel weight values. A 2D image view can be used to specify a 2D matrix of filter weights. For separable filers, a 1D image view can be used to specity the horizontal and vertical weights. ==== 2D Non-Separable Weight Filters A 2D image view defined with slink:VkImageViewSampleWeightCreateInfoQCOM describes a 2D matrix [eq]#(pname:filterSize.width {times} pname:filterSize.height)# of weight elements with filter's center point at pname:filterCenter. Note that pname:filterSize can be smaller than the view's subresource, but the filter will always be located starting at integer texel coordinate [eq]#(0,0)#. The following figure illustrates a 2D convolution filter having pname:filterSize of [eq]#(4,3)# and pname:filterCenter at [eq]#(1, 1)#. image::{images}/weight_filter_2d.svg[align="center",title="2D Convolution Filter",opts="{imageopts}"] For a 2D weight filter, the phases are stored as layers of a 2D array image. The width and height of the view's subresource range must: be less than or equal to slink:VkPhysicalDeviceImageProcessingPropertiesQCOM::pname:maxWeightFilterDimension. The layers are stored in horizontal phase major order. Expressed as a formula, the layer index for a each filter phase is computed as: [source,c] ---- layerIndex(horizPhase,vertPhase,horizPhaseCount) = (vertPhase * horizPhaseCount) + horizPhase ---- ==== 1D Separable Weight Filters A separable weight filter is a 2D filter that can be specified by two 1D filters in the [eq]#x# and [eq]#y# directions such that their product yields the 2D filter. The following example shows a 2D filter and its associated separable 1D horizontal and vertical filters. image::{images}/weight_filter_1d_separable.svg[align="center",title="Separable 2D Convolution Filter",opts="{imageopts}"] A 1D array image view defined with slink:VkImageViewSampleWeightCreateInfoQCOM and with pname:layerCount equal to '2' describes a separable weight filter. The horizontal weights are specified in slice '0' and the vertical weights in slice '1'. The pname:filterSize and pname:filterCenter specify the size and origin of the of the horizontal and vertical filters. For many use cases, 1D separable filters can offer a performance advantage over 2D filters. For a 1D separable weight filter, the phases are arranged into a 1D array image with two layers. The horizontal weights are stored in layer 0 and the vertical weights in layer 1. Within each layer of the 1D array image, the weights are arranged into groups of 4, and then arranged by phase. Expressed as a formula, the 1D texel offset for each weight within each layer is computed as: [source,c] ---- // Let horizontal weights have a weightIndex of [0, filterSize.width - 1] // Let vertical weights have a weightIndex of [0, filterSize.height - 1] // Let phaseCount be the number of phases in either the vertical or horizontal direction. texelOffset(phaseIndex,weightIndex,phaseCount) = (phaseCount * 4 * (weightIndex / 4)) + (phaseIndex * 4) + (weightIndex % 4) ---- [[textures-weightimage-filterphases]] === Weight Sampling Phases When using weight image sampling, the texture coordinates may not align with a texel center in the sampled image. In this case, the filter weights can be adjusted based on the subpixel location. This is termed "`subpixel filtering`" to indicate that the origin of the filter lies at a subpixel location other than the texel center. Conceptually, this means that the weight filter is positioned such that filter taps do not align with sampled texels exactly. In such a case, modified filter weights may be needed to adjust for the off-center filter taps. Unlike bilinear filtering where the subpixel weights are computed by the implementation, subpixel weight image sampling requires that the per-phase filter weights are pre-computed by the application and stored in an array where each slice of the array is a "`filter phase`". The array is indexed by the implementation based on subpixel positioning. Rather than a single 2D kernel of filter weights, the application provides an array of kernels, one set of filter weights per phase. The number of phases are restricted by following requirements, which apply to both separable and non-separable filters: * The number of phases in the vertical direction, [eq]#phaseCount~vert~#, must: be a power of two (i.e., 1, 2, 4, etc.). * The number of phases in the horizontal direction [eq]#phaseCount~horiz~#, must: equal [eq]#phaseCount~vert~#. * The total number of phases, [eq]#phaseCount~vert~ {times} phaseCount~horiz~#, must: be less than or equal to slink:VkPhysicalDeviceImageProcessingPropertiesQCOM::pname:maxWeightFilterPhases. [[textures-weightimage-sampler]] === Weight Sampler Parameters Weight sampling requires sname:VkSamplerCreateInfo pname:addressModeU and pname:addressModeV must: be set to ename:VK_SAMPLER_ADDRESS_MODE_CLAMP_TO_EDGE or ename:VK_SAMPLER_ADDRESS_MODE_CLAMP_TO_BORDER. If ename:VK_SAMPLER_ADDRESS_MODE_CLAMP_TO_BORDER is used, then the border color must: be set to transparent black. [[textures-weightimage-filteroperation]] === Weight Sampling Operation The 2D unnormalized texel coordinates latexmath:[(u,v)] are transformed by latexmath:[filterCenter] to specify coordinates latexmath:[i_{0}, j_{0}]. [latexmath] ++++++++++++++++++++++++ \begin{aligned} i_{0} &= \left\lfloor u - filterCenter_{x} \right\rfloor \\[1em] j_{0} &= \left\lfloor v - filterCenter_{y} \right\rfloor \end{aligned} ++++++++++++++++++++++++ where latexmath:[filterCenter] is specified by slink:VkImageViewSampleWeightCreateInfoQCOM::pname:filterCenter. Two sets of neighboring integer 2D texel coordinates are generated. The first set is used for selecting texels from the sampled image latexmath:[\tau] and the second set used for selecting texels from the weight image latexmath:[w]. The first set of neighboring coordinates are combinations of latexmath:[i_{0}] to latexmath:[i_{filterWidth-1}] and latexmath:[j_{0}] to latexmath:[j_{filterHeight-1}]. The second set of neighboring coordinates are combinations of latexmath:[k_{0}] to latexmath:[k_{filterWidth-1}] and latexmath:[l_{0}] to latexmath:[l_{filterHeight-1}]. The first and second sets each contain latexmath:[(filterWidth \times filterHeight)] of pairs of latexmath:[(i,j)] and latexmath:[(k,l)] coordinates respectively. [latexmath] ++++++++++++++++++++++++ \begin{aligned} \{i_q\}_{q=0}^{q=filterWidth-1} \quad &= i_{0} + q \\[1em] \{j_q\}_{q=0}^{q=filterHeight-1} \quad &= j_{0} + q \\[1em] \{k_q\}_{q=0}^{q=filterWidth-1} \quad &= q \\[1em] \{l_q\}_{q=0}^{q=filterHeight-1} \quad &= q \end{aligned} ++++++++++++++++++++++++ where latexmath:[filterWidth] and latexmath:[filterHeight] are specified by slink:VkImageViewSampleWeightCreateInfoQCOM::pname:filterSize. Each of the generated integer coordinates latexmath:[({i_q}, {j_q})] is transformed by <>, followed by <>, If any coordinate fails coordinate validation, it is a Border Texel and <> is performed. The phase index latexmath:[\psi] is computed from the fraction bits of the unnormalized 2D texel coordinates: [latexmath] ++++++++++++++++++++++++ \begin{aligned} phaseCount_{h} = phaseCount_{v} &= \sqrt{numPhases} \\[1em] hPhase &= \left\lfloor\mathbin{frac}\left( u \right) \times phaseCount_{h} \right\rfloor \\[1em] vPhase &= \left\lfloor\mathbin{frac}\left( v \right) \times phaseCount_{v} \right\rfloor \\[1em] \psi &= \left(vPhase \times phaseCount_{h}\right) + hPhase \end{aligned} ++++++++++++++++++++++++ where the number of fraction bits retained is latexmath:[\mathbin{log2}\left( numPhases \right)] specified by slink:VkImageViewSampleWeightCreateInfoQCOM::pname:numPhases Each pair of texel coordinates latexmath:[(i,j)] in the first set selects a single texel value latexmath:[\tau_{ij}] from the sampled image. Each pair of texel coordinates latexmath:[(k,l)] in the second set, combined with phaseIndex latexmath:[\psi], selects a single weight from the weight image latexmath:[w(k,l,\psi)] . [latexmath] ++++++++++++++++++++++++ \begin{aligned} w(k,l,\psi) &= \begin{cases} w_{kl}[\psi]\quad\text{(}\psi\text{ as layer index)} & \text{for 2D array view (non-separable filter) } \\ weight_{h} \times weight_{v} & \text{for 1D array view (separable filter) } \\ \end{cases} \end{aligned} ++++++++++++++++++++++++ If latexmath:[w] is a 2D array view, then non-separable filtering is specified, and integer coordinates latexmath:[(k,l)] are used to select texels from layer latexmath:[\psi] of latexmath:[(w)]. If latexmath:[w] is a 1D array view, then separable filtering is specified and integer coordinates latexmath:[(k,l)] are transformed to latexmath:[(k_{packed},l_{packed})], and used to select horizontal weight latexmath:[(weight_{h})] and vertical weight latexmath:[(weight_{v})] texels from layer 0 and layer 1 of latexmath:[(w)] respectively. [latexmath] ++++++++++++++++++++++++ \begin{aligned} k_{packed} &= \left(phaseCount_{h} \times 4 \times \left\lfloor k / 4 \right\rfloor\right) + \left(hPhase \times 4\right) + \left(k \mathbin{\%} 4\right) \\[1em] l_{packed}& = \left(phaseCount_{v} \times 4 \times \left\lfloor l / 4 \right\rfloor\right) + \left(vPhase \times 4\right) + \left(l \mathbin{\%} 4\right) \\[1em] weight_{h} &= w_{k_{packed}}[0] & \text{(horizontal weights packed in layer 0)} \\[1em] weight_{v} &= w_{l_{packed}}[1] & \text{(vertical weights packed in layer 1)} \end{aligned} ++++++++++++++++++++++++ Where latexmath:[\mathbin{\%}] refers to the integer modulo operator. The values of multiple texels, together with their weights, are combined to produce a filtered value. [latexmath] ++++++++++++++++++++++++ \begin{aligned} \tau_{weightSampling} &= \sum_{{j=j_0} \atop {l=l_0}}^{j_{blockHeight-1} \atop {l_{blockHeight-1}}}\quad \sum_{{i=i_0}\atop {k=k_0}}^{i_{blockWidth-1} \atop {k_{blockWidth-1}}}w(k,l,\psi)\tau_{ij} \\ \end{aligned} ++++++++++++++++++++++++ When slink:VkSamplerReductionModeCreateInfo::pname:reductionMode is set to ename:VK_SAMPLER_REDUCTION_MODE_WEIGHTED_AVERAGE, the above summation is used. However, if the reduction mode is ename:VK_SAMPLER_REDUCTION_MODE_MIN or ename:VK_SAMPLER_REDUCTION_MODE_MAX, the process operates on the above values, computing a component-wise minimum or maximum of the texels with non-zero weights. If the reduction mode is ename:VK_SAMPLER_REDUCTION_MODE_MIN or ename:VK_SAMPLER_REDUCTION_MODE_MAX, each latexmath:[w(k,l,\psi)] weight must: be equal to 0.0 or 1.0, otherwise the undefined: values are returned. Finally, the operations described in <> and <> are performed and the final result is returned to the shader. [[textures-blockmatch]] == Block Matching The SPIR-V instruction code:opImageBlockMatchSAD and code:opImageBlockMatchSSD specify texture block matching operations where a block or region of texels within a _target image_ is compared with a same-sized region a _reference image_. The instructions make use of two image views: the _target view_ and the _reference view_. The target view and reference view can be the same view, allowing block matching of two blocks within a single image. Similar to an equivalent code:OpImageFetch instruction, code:opImageBlockMatchSAD and code:opImageBlockMatchSAD specify a code:image and an integer texel code:coordinate which which describes the bottom-left texel of the target block. There are three additional inputs. The code:reference and code:refCoodinate specifies bottom-left texel of the reference block. The code:blockSize specifies the integer width and height of the target and reference blocks to be compared, and must: not be greater than slink:VkPhysicalDeviceImageProcessingPropertiesQCOM.code:maxBlockMatchRegion. ifdef::VK_QCOM_image_processing2[] code:opImageBlockMatchWindowSAD and code:opImageBlockMatchWindowSAD take the same input parameters as the corresponding non-window instructions. The block matching comparison is performed for all pixel values within a 2D window whose dimensions are specified in the sampler. endif::VK_QCOM_image_processing2[] [[textures-blockmatch-sampler]] === Block Matching Sampler Parameters For code:opImageBlockMatchSAD and code:opImageBlockMatchSSD, the input code:sampler must: be created with code:addressModeU and code:addressModeV, equal to ename:VK_SAMPLER_ADDRESS_MODE_CLAMP_TO_EDGE, or ename:VK_SAMPLER_ADDRESS_MODE_CLAMP_TO_BORDER with ename:VK_BORDER_COLOR_FLOAT_TRANSPARENT_BLACK. The input code:sampler must: be created with code:unnormalizedCoordinates equal to ename:VK_TRUE. The input code:sampler must: be created with pname:components equal to ename:VK_COMPONENT_SWIZZLE_IDENTITY. ifdef::VK_QCOM_image_processing2[] For code:opImageBlockMatchWindowSAD and code:opImageBlockMatchWindowSSD instructions, the code:target sampler must: have been created with slink:VkSamplerBlockMatchWindowCreateInfoQCOM in the code:pNext chain. For code:opImageBlockMatchWindowSAD, code:opImageBlockMatchWindowSSD, code:opImageBlockMatchGatherSAD, or code:opImageBlockMatchGatherSSDinstructions, the input code:sampler must: be created with code:addressModeU and code:addressModeV, equal to ename:VK_SAMPLER_ADDRESS_MODE_CLAMP_TO_BORDER with ename:VK_BORDER_COLOR_FLOAT_TRANSPARENT_BLACK. endif::VK_QCOM_image_processing2[] Other sampler states are ignored. [[textures-blockmatch-filteroperation]] === Block Matching Operation Block matching SPIR-V instructions code:opImageBlockMatchSAD and code:opImageBlockMatchSSD specify two sets of 2D integer texel coordinates: target coordinates latexmath:[(u,v)] and reference coordinates latexmath:[(s,t)]. The coordinates define the bottom-left texel of the target block latexmath:[(i_{0}, j_{0})] and the reference block latexmath:[(k_{0}, l_{0})]. [latexmath] ++++++++++++++++++++++++ \begin{aligned} i_{0} &= u \\[1em] j_{0} &= v \\[1em] k_{0} &= s \\[1em] l_{0} &= t \end{aligned} ++++++++++++++++++++++++ For the target block, a set of neighboring integer texel coordinates are generated. The neighboring coordinates are combinations of latexmath:[i_{0}] to latexmath:[i_{blockWidth-1}] and latexmath:[j_{0}] to latexmath:[j_{blockHeight-1}]. The set is of size latexmath:[blockWidth \times blockHeight]. [latexmath] ++++++++++++++++++++++++ \begin{aligned} \{i_q\}_{q=0}^{q=blockWidth-1} \quad &= i_{0} + q \\[1em] \{j_q\}_{q=0}^{q=blockHeight-1} \quad &= j_{0} + q \end{aligned} ++++++++++++++++++++++++ where latexmath:[blockWidth] and latexmath:[blockHeight] is specified by the code:blockSize operand. If any target integer texel coordinate latexmath:[(i,j)] in the set fails <>, then the texel is an invalid texel and <> is performed. Similarly for the reference block, a set of neighboring integer texel coordinates are generated. [latexmath] ++++++++++++++++++++++++ \begin{aligned} \{k_q\}_{q=0}^{q=blockWidth-1} \quad &= k_{0} + q \\[1em] \{l_q\}_{q=0}^{q=blockHeight-1} \quad &= l_{0} + q \end{aligned} ++++++++++++++++++++++++ Each reference texel coordinate latexmath:[(k,l)] in the set must: not fail <>. To avoid undefined: behavior, application shader should guarantee that the reference block is fully within the bounds of the reference image. Each pair of texel coordinates latexmath:[(i,j)] in the set selects a single texel value from the target image latexmath:[\tau_{ij}]. Each pair of texel coordinates latexmath:[(k,l)] in the set selects a single texel value from the reference image latexmath:[\upsilon_{kl}]. The difference between target and reference texel values is summed to compute a difference metric. The code:opTextureBlockMatchSAD computes the sum of absolute differences. [latexmath] ++++++++++++++++++++++++ \begin{aligned} \tau_{SAD} &= \sum_{{j=j_0} \atop {l=l_0}}^{{j_{blockHeight-1}} \atop {l_{blockHeight-1}}} \quad\sum_{{i=i_0} \atop {k=k_0}}^{{i_{blockWidth-1}} \atop {k_{blockWidth-1}}}|\upsilon_{kl}-\tau_{ij}| \\ \end{aligned} ++++++++++++++++++++++++ The code:opImageBlockMatchSSD computes the sum of the squared differences. [latexmath] ++++++++++++++++++++++++ \begin{aligned} \tau_{SSD} &= \sum_{{j=j_0} \atop {l=l_0}}^{{j_{blockHeight-1}} \atop {l_{blockHeight-1}}} \quad\sum_{{i=i_0} \atop {k=k_0}}^{{i_{blockWidth-1}} \atop {k_{blockWidth-1}}}|\upsilon_{kl}-\tau_{ij}|^2 \\ \end{aligned} ++++++++++++++++++++++++ When slink:VkSamplerReductionModeCreateInfo::pname:reductionMode is set to ename:VK_SAMPLER_REDUCTION_MODE_WEIGHTED_AVERAGE, the above summation is used. However, if the reduction mode is ename:VK_SAMPLER_REDUCTION_MODE_MIN or ename:VK_SAMPLER_REDUCTION_MODE_MAX, the process operates on the above values, computing a component-wise minimum or maximum of latexmath:[|\upsilon_{kl}-\tau_{ij}|], respectively. For latexmath:[\tau_{SAD}], the minimum or maximum difference is computed and for latexmath:[\tau_{SSD}], the square of the minimum or maximum is computed. Finally, the operations described in <> and <> are performed and the final result is returned to the shader. The component swizzle is specified by the _target image_ descriptor; any swizzle specified by the _reference image_ descriptor is ignored. ifdef::VK_QCOM_image_processing2[] [[textures-blockmatchwindow-filteroperation]] ==== Block Matching Window Operation Window block matching SPIR-V instructions code:opImageBlockMatchWindowSAD and code:opImageBlockMatchWindowSSD specify two sets of 2D integer texel coordinates: target coordinates latexmath:[(u,v)] and reference coordinates latexmath:[(s,t)]. The <> is performed repeatedly, for multiple sets of target integer coordinates within the specified window. These instructions effectively search a region or "`window`" within the target texture and identify the window coordinates where the minimum or maximum error metric is found. These instructions only support single component image formats. The target coordinates are combinations of coordinates from latexmath:[(u,v)] to latexmath:[(u + windowWidth - 1, v + windowHeight - 1)] where latexmath:[windowHeight] and latexmath:[windowWidth] are specified by slink:VkSamplerBlockMatchWindowCreateInfoQCOM::pname:windowExtent. At each each target coordinate, a <> is performed, resulting in a difference metric. The the reference coordinate latexmath:[(s,t)] is fixed. The block matching operation is repeated latexmath:[windowWidth \times windowHeight] times. The resulting minimum or maximum error is returned in the R component of the output. The integer window coordinates latexmath:[(x,y)] are returned in the G and B components of the output. The A component is 0. The minimum or maximum behavior is selected by slink:VkSamplerBlockMatchWindowCreateInfoQCOM::pname:windowCompareMode. The following psuedocode describes the operation code:opImageBlockMatchWindowSAD. The pseudocode for code:opImageBlockMatchWindowSSD follows an identical pattern. [source,c] ---- vec4 opImageBlockMatchGatherSAD( sampler2D target, uvec2 targetCoord, samler2D reference, uvec2 refCoord, uvec2 blocksize) { // Two parameters are sourced from the VkSampler associated with // `target`: // compareMode (which can be either `MIN` or `MAX`) // uvec2 window (which defines the search window) minSAD = INF; maxSAD = -INF; uvec2 minCoord; uvec2 maxCoord; for (uint x=0, x maxSAD) { maxSAD = SAD; maxCoord = uvec2(x,y); } } } if (compareMode==MIN) { return vec4(minSAD, minCoord.x, minCoord.y, 0.0); } else { return vec4(maxSAD, maxCoord.x, maxCoord.y, 0.0); } } ---- [[textures-blockmatchgather-filteroperation]] ==== Block Matching Gather Operation Block matching Gather SPIR-V instructions code:opImageBlockMatchGatherSAD and code:opImageBlockMatchGatherSSD specify two sets of 2D integer texel coordinates: target coordinates latexmath:[(u,v)] and reference coordinates latexmath:[(s,t)]. These instructions perform the <> 4 times, using integer target coordinates latexmath:[(u,v)], latexmath:[(u+1,v)], latexmath:[(u+2,v)], and latexmath:[(u+3,v)]. The R component from each of those 4 operations is gathered and returned in the R, G, B, and A components of the output respectively. For each block match operation, the reference coordinate is latexmath:[(s,t)]. For each block match operation, only the R component of the target and reference images are compared. The following psuedocode describes the operation opImageBlockMatchGatherSAD. The pseudocode for opImageBlockMatchGatherSSD follows an identical pattern. [source,c] ---- vec4 opImageBlockMatchGatherSAD(sampler2D target, uvec2 targetCoord, samler2D reference, uvec2 refCoord, uvec2 blocksize) { vec4 out; for (uint x=0, x<4; x++) { float SAD = textureBlockMatchSAD(target, targetCoord + uvec2(x, 0), reference, refCoord, blocksize).x; if (x == 0) { out.x = SAD; } if (x == 1) { out.y = SAD; } if (x == 2) { out.z = SAD; } if (x == 3) { out.w = SAD; } } return out; } ---- endif::VK_QCOM_image_processing2[] [[textures-boxfilter]] == Box Filter Sampling The SPIR-V instruction code:OpImageBoxFilterQCOM specifies texture box filtering operation where a weighted average of a region of texels is computed, with the weights proportional to the coverage of each of the texels. In addition to the inputs that would be accepted by an equivalent code:OpImageSample* instruction, code:OpImageBoxFilterQCOM accepts one additional input, code:boxSize which specifies the width and height in texels of the region to be averaged. The figure below shows an example of using code:OpImageBoxFilterQCOM to sample from a [eq]#8 {times} 4# texel two-dimensional image, with unnormalized texture coordinates [eq]#(4.125, 2.625)# and code:boxSize of [eq]#(2.75, 2.25)#. The filter will read 12 texel values and compute a weights based portion of of each texel covered by the box. [[textures-box-filter-diagrams]] image::{images}/vulkantexture_boxFilter.svg[align="center",title="Box Filter Sampling Example",opts="{imageopts}"] If code:boxSize has height and width both equal to 1.0, then this instruction will behave as traditional bilinear filtering. The code:boxSize parameter must: be greater than or equal to 1.0 and must: not be greater than slink:VkPhysicalDeviceImageProcessingPropertiesQCOM.code:maxBoxFilterBlockSize. [[textures-boxfilter-sampler]] === Box Filter Sampler Parameters The input code:sampler must: be created with code:addressModeU and code:addressModeV, equal to ename:VK_SAMPLER_ADDRESS_MODE_CLAMP_TO_EDGE, or ename:VK_SAMPLER_ADDRESS_MODE_CLAMP_TO_BORDER with ename:VK_BORDER_COLOR_FLOAT_TRANSPARENT_BLACK. [[textures-boxfilter-filteroperation]] === Box Filter Operation The 2D unnormalized texel coordinates latexmath:[(u,v)] are transformed by latexmath:[boxSize] to specify integer texel coordinates latexmath:[(i_{0}, j_{0})] of the bottom left texel for the filter. [latexmath] ++++++++++++++++++++++++ \begin{aligned} i_{0} &= \left\lfloor u - \frac{boxWidth}{2} \right\rfloor \\[1em] j_{0} &= \left\lfloor v - \frac{boxHeight}{2} \right\rfloor \end{aligned} ++++++++++++++++++++++++ where latexmath:[boxWidth] and latexmath:[boxHeight] are specified by the code:(x,y) components of the code:boxSize operand. The filter dimensions latexmath:[(filterWidth \times filterHeight)] are computed from the fractional portion of the latexmath:[(u,v)] coordinates and the latexmath:[boxSize]. [latexmath] ++++++++++++++++++++++++ \begin{aligned} startFracU &= \mathbin{frac}\left(u - \frac{boxWidth}{2} \right) \\[1em] startFracV &= \mathbin{frac}\left(v - \frac{boxHeight}{2} \right) \\[1em] endFracU &= \mathbin{frac}\left( startFracU + boxWidth \right) \\[1em] endFracV &= \mathbin{frac}\left( startFracV + boxHeight \right) \\[1em] filterWidth &= \left\lceil startFracU + boxWidth \right\rceil \\[1em] filterHeight &= \left\lceil startFracV + boxHeight \right\rceil \end{aligned} ++++++++++++++++++++++++ where the number of fraction bits retained by latexmath:[frac()] is specified by sname:VkPhysicalDeviceLimits::pname:subTexelPrecisionBits. A set of neighboring integer texel coordinates are generated. The neighboring coordinates are combinations of latexmath:[i_{0}] to latexmath:[i_{filterWidth-1}] and latexmath:[j_{0}] to latexmath:[j_{filterHeight-1}], with latexmath:[i_{0}, j_{0}] being the top-left coordinate of this set. The set is of size latexmath:[(filterWidth \times filterHeight)]. [latexmath] ++++++++++++++++++++++++ \begin{aligned} \{i_q\}_{q=0}^{q=filterWidth-1} \quad &= i_{0} + q \\[1em] \{j_q\}_{q=0}^{q=filterHeight-1} \quad &= j_{0} + q \end{aligned} ++++++++++++++++++++++++ Each of the generated integer coordinates latexmath:[({i_q}, {j_q})] is transformed by <>, followed by <>, If any coordinate fails coordinate validation, it is a Border Texel and <> is performed. Horizontal weights latexmath:[horizWeight_{0}] to latexmath:[horizWeight_{boxWidth-1}] and vertical weights latexmath:[vertWeight_{0}] to latexmath:[vertWeight_{boxHeight-1}] are computed. Texels that are fully covered by the box will have a horizontal and vertical weight of 1. Texels partially covered by the box will have will have a reduced weights proportional to the coverage. [latexmath] ++++++++++++++++++++++++ \begin{aligned} horizWeight_{i} &= \begin{cases} \left(1-startFracU \right), & \text{for } (i == 0) \\ \left(endFracU \right), & \text{for } (i == filterWidth-1) \text{ and } (endFracU != 0) \\ \left(1\right), & \text{otherwise} \\ \end{cases} \end{aligned} ++++++++++++++++++++++++ [latexmath] ++++++++++++++++++++++++ \begin{aligned} vertWeight_{j} &= \begin{cases} \left(1-startFracV \right), & \text{for } (j == 0) \\ \left(endFracV \right), & \text{for } (j == filterHeight-1) \text{ and } (endFracV !=0) \\ \left(1\right), & \text{otherwise} \\ \end{cases} \end{aligned} ++++++++++++++++++++++++ The values of multiple texels, together with their horizontal and vertical weights, are combined to produce a box filtered value. [latexmath] ++++++++++++++++++++++++ \begin{aligned} \tau_{boxFilter} &= \frac{1}{boxHeight \times boxWidth} \sum_{j=j_0}^{j_{filterHeight-1}}\quad\sum_{i=i_0}^{i_{filterWidth-1}}(horizWeight_i)(vertWeight_j)\tau_{ij} \\ \end{aligned} ++++++++++++++++++++++++ When slink:VkSamplerReductionModeCreateInfo::pname:reductionMode is set to ename:VK_SAMPLER_REDUCTION_MODE_WEIGHTED_AVERAGE, the above summation is used. However, if the reduction mode is ename:VK_SAMPLER_REDUCTION_MODE_MIN or ename:VK_SAMPLER_REDUCTION_MODE_MAX, the process operates on the above values, computing a component-wise minimum or maximum of the texels. endif::VK_QCOM_image_processing[] [[textures-instructions]] == Image Operation Steps Each step described in this chapter is performed by a subset of the image instructions: * Texel Input Validation Operations, Format Conversion, Texel Replacement, Conversion to RGBA, and Component Swizzle: Performed by all instructions except code:OpImageWrite. * Depth Comparison: Performed by code:OpImage*Dref instructions. * All Texel output operations: Performed by code:OpImageWrite. * Projection: Performed by all code:OpImage*Proj instructions. * Derivative Image Operations, Cube Map Operations, Scale Factor Operation, LOD Operation and Image Level(s) Selection, and Texel Anisotropic Filtering: Performed by all code:OpImageSample* and code:OpImageSparseSample* instructions. * (s,t,r,q,a) to (u,v,w,a) Transformation, Wrapping, and (u,v,w,a) to (i,j,k,l,n) Transformation And Array Layer Selection: Performed by all code:OpImageSample, code:OpImageSparseSample, and code:OpImage*Gather instructions. * Texel Gathering: Performed by code:OpImage*Gather instructions. ifdef::VK_NV_shader_image_footprint[] * Texel Footprint Evaluation: Performed by code:OpImageSampleFootprint instructions. endif::VK_NV_shader_image_footprint[] * Texel Filtering: Performed by all code:OpImageSample* and code:OpImageSparseSample* instructions. * Sparse Residency: Performed by all code:OpImageSparse* instructions. ifdef::VK_QCOM_image_processing[] * (s,t,r,q,a) to (u,v,w,a) Transformation, Wrapping, and Weight Image Sampling: Performed by code:OpImageWeightedSample* instructions. * (s,t,r,q,a) to (u,v,w,a) Transformation, Wrapping, and Block Matching: Performed by code:opImageBlockMatch* instructions. * (s,t,r,q,a) to (u,v,w,a) Transformation, Wrapping, and Box Filter Sampling: Performed by code:OpImageBoxFilter* instructions. endif::VK_QCOM_image_processing[] [[textures-queries]] == Image Query Instructions === Image Property Queries code:OpImageQuerySize, code:OpImageQuerySizeLod, code:OpImageQueryLevels, and code:OpImageQuerySamples query properties of the image descriptor that would be accessed by a shader image operation. ifdef::VK_EXT_robustness2[] They return 0 if the bound descriptor is a null descriptor. endif::VK_EXT_robustness2[] code:OpImageQuerySizeLod returns the size of the image level identified by the code:Level code:of code:Detail operand. If that level does not exist in the image, ifdef::VK_EXT_robustness2[and the descriptor is not null,] then the value returned is undefined:. === Lod Query code:OpImageQueryLod returns the Lod parameters that would be used in an image operation with the given image and coordinates. ifdef::VK_EXT_robustness2[] If the descriptor that would be accessed is a null descriptor then [eq]#(0,0)# is returned. endif::VK_EXT_robustness2[] ifdef::VK_EXT_robustness2[Otherwise, the] ifndef::VK_EXT_robustness2[The] steps described in this chapter are performed as if for code:OpImageSampleImplicitLod, up to <>. The return value is the vector [eq]#({lambda}', d~l~)#. These values may: be subject to implementation-specific maxima and minima for very large, out-of-range values.