Lines Matching refs:eq
18 A grid square, including its [eq]#(x,y)# framebuffer coordinates, [eq]#z#
199 Each bit [eq]#b# for mask word [eq]#w# in the sample mask corresponds to
200 sample index [eq]#i#, where [eq]#i = 32 {times} w {plus} b#.
201 pname:pSampleMask has a length equal to [eq]#{lceil}
216 pname:minSampleShading must: be in the range [eq]#[0,1]#
562 [eq]#(1,1)# and its sample points must: be located within these bounds.
601 Each sample in a set is assigned a unique _sample index_ [eq]#i# in the
602 range [eq]#[0, pname:rasterizationSamples)#.
644 Each sample in a fragment is also assigned a unique _coverage index_ [eq]#j#
645 in the range [eq]#[0, n {times} pname:rasterizationSamples)#, where [eq]#n#
659 the coverage index [eq]#j# is determined as a function of the _pixel index_
660 [eq]#p#, the _sample index_ [eq]#i#, and the number of rasterization samples
661 [eq]#r# as:
663 {empty}:: [eq]#j = i + r {times} ((f~w~ {times} f~h~) - 1 - p)#
665 where the pixel index [eq]#p# is determined as a function of the pixel's
666 framebuffer location [eq]#(x,y)# and the fragment size [eq]#(f~w~,f~h~)#:
668 {empty}:: [eq]#p~x~ = x % f~w~#
669 {empty}:: [eq]#p~y~ = y % f~h~#
670 {empty}:: [eq]#p = p~x~ + (p~y~ {times} f~w~)#
705 The coverage mask includes [eq]#B# bits packed into [eq]#W# words, defined
708 {empty}:: [eq]#B = n {times} pname:rasterizationSamples#
709 {empty}:: [eq]#W = {lceil}B/32{rceil}#
711 Bit [eq]#b# in coverage mask word [eq]#w# is `1` if the sample with coverage
712 index [eq]#j = 32{times}w + b# is covered, and `0` otherwise.
718 locations as listed in the following table, with the [eq]##i##th entry in
719 the table corresponding to sample index [eq]#i#.
732 | [eq]#(0.5,0.5)#
735 | [eq]#(0.75,0.75)# +
736 [eq]#(0.25,0.25)#
739 | [eq]#(0.375, 0.125)# +
740 [eq]#(0.875, 0.375)# +
741 [eq]#(0.125, 0.625)# +
742 [eq]#(0.625, 0.875)#
745 | [eq]#(0.5625, 0.3125)# +
746 [eq]#(0.4375, 0.6875)# +
747 [eq]#(0.8125, 0.5625)# +
748 [eq]#(0.3125, 0.1875)# +
749 [eq]#(0.1875, 0.8125)# +
750 [eq]#(0.0625, 0.4375)# +
751 [eq]#(0.6875, 0.9375)# +
752 [eq]#(0.9375, 0.0625)#
755 | [eq]#(0.5625, 0.5625)# +
756 [eq]#(0.4375, 0.3125)# +
757 [eq]#(0.3125, 0.625)# +
758 [eq]#(0.75, 0.4375)# +
759 [eq]#(0.1875, 0.375)# +
760 [eq]#(0.625, 0.8125)# +
761 [eq]#(0.8125, 0.6875)# +
762 [eq]#(0.6875, 0.1875)# +
763 [eq]#(0.375, 0.875)# +
764 [eq]#(0.5, 0.0625)# +
765 [eq]#(0.25, 0.125)# +
766 [eq]#(0.125, 0.75)# +
767 [eq]#(0.0, 0.5)# +
768 [eq]#(0.9375, 0.25)# +
769 [eq]#(0.875, 0.9375)# +
770 [eq]#(0.0625, 0.0)#
859 The sample location for sample [eq]#i# at the pixel grid location
860 [eq]#(x,y)# is taken from [eq]#pname:pSampleLocations[(x {plus} y {times}
877 [eq]#pname:sampleLocationsPerPixel {times}
899 [eq]#[pname:sampleLocationCoordinateRange[0],pname:sampleLocationCoordinateRange[1]]#
1163 equal to [eq]#(1,1)#, and both elements of pname:combinerOps are considered
1280 {empty}:: [eq]#x' = floor(x / region~x~)#
1281 {empty}:: [eq]#y' = floor(y / region~y~)#
1283 where [eq]#x'# and [eq]#y'# are the coordinates of a texel in the fragment
1284 shading rate attachment, [eq]#x# and [eq]#y# are the coordinates of the
1285 pixel in the framebuffer, and [eq]#region~x~# and [eq]#region~y~# are the
1304 {empty}:: [eq]#size~w~ = 2^((texel / 4) & 3)^#
1305 {empty}:: [eq]#size~h~ = 2^(texel & 3)^#
1307 where [eq]#texel# is the value in the first component of the identified
1308 texel, and [eq]#size~w~# and [eq]#size~h~# are the width and height of the
1312 as [eq]#size~w~ = size~h~ = 1#.
1323 The final rate ([eq]#C~xy~'#) used for fragment shading must: be one of the
1331 If any of the following conditions are met, [eq]#C~xy~'# must: be set to
1332 [eq]#{1,1}#:
1377 derive the value of [eq]#C~xy~'#.
1393 operation of [eq]#combine(A~xy~,B~xy~) = A~xy~#.
1395 combiner operation of [eq]#combine(A~xy~,B~xy~) = B~xy~#.
1397 operation of [eq]#combine(A~xy~,B~xy~) = min(A~xy~,B~xy~)#.
1399 operation of [eq]#combine(A~xy~,B~xy~) = max(A~xy~,B~xy~)#.
1401 operation of [eq]#combine(A~xy~,B~xy~) = A~xy~*B~xy~#.
1403 where [eq]#combine(A~xy~,B~xy~)# is the combine operation, and [eq]#A~xy~#
1404 and [eq]#B~xy~# are the inputs to the operation.
1419 {empty}:: [eq]#C~xy~ = combine(A~xy~,B~xy~)#
1421 where [eq]#C~xy~# is the combined fragment area result, and [eq]#A~xy~# and
1422 [eq]#B~xy~# are the fragment areas of the fragment shading rates being
1425 Two combine operations are performed, first with [eq]#A~xy~# equal to the
1427 and [eq]#B~xy~# equal to the <<primsrast-fragment-shading-rate-primitive,
1428 primitive fragment shading rate>>, with the [eq]#combine()# operation
1430 A second combination is then performed, with [eq]#A~xy~# equal to the result
1431 of the first combination and [eq]#B~xy~# equal to the
1433 rate>>, with the [eq]#combine()# operation selected by combinerOps[1].
1439 [eq]#A~xy~# and [eq]#B~xy~#, and must: clamp the result of the second
1442 A fragment shading rate [eq]#R~xy~# representing any of [eq]#A~xy~#,
1443 [eq]#B~xy~# or [eq]#C~xy~# is clamped as follows.
1444 If [eq]#R~xy~# is one of the rates returned by
1449 used by rasterization, the clamped shading rate [eq]#R~xy~'# is [eq]#R~xy~#.
1459 . Keep only rates where [eq]#R~x~' {leq} R~x~# and [eq]#R~y~' {leq} R~y~#.
1460 ** Implementations may: also keep rates where [eq]#R~x~' {leq} R~y~# and
1461 [eq]#R~y~' {leq} R~x~#.
1462 . Keep only rates with the highest area ([eq]#R~x~' {times} R~y~'#).
1463 . Keep only rates with the lowest aspect ratio ([eq]#R~x~' {plus} R~y~'#).
1704 [eq]#A~xy~# or [eq]#B~xy~# is
1706 [eq]#combine(A~xy~,B~xy~)# produces a shading rate of
1710 [eq]#combine(A~xy~,B~xy~)# produces a shading rate whose fragment size
1711 is the smaller of the fragment sizes of [eq]#A~xy~# and [eq]#B~xy~# and
1713 [eq]#A~xy~# and [eq]#B~xy~#.
1715 [eq]#combine(A~xy~,B~xy~)# produces a shading rate whose fragment size
1716 is the larger of the fragment sizes of [eq]#A~xy~# and [eq]#B~xy~# and
1718 [eq]#A~xy~# and [eq]#B~xy~#.
1720 [eq]#combine(A~xy~,B~xy~)# produces a shading rate whose fragment size
1722 counts, respectively, of [eq]#A~xy~# and [eq]#B~xy~#.
2372 shader at least [eq]#max({lceil}
2521 [eq]#(1,0,0)#.
2524 are [eq]#(1,0,0)# and [eq]#(0,1,0)#, respectively.
2527 numbered 0, 1, and 2 are [eq]#(1,0,0)#, [eq]#(0,1,0)#, and [eq]#(0,0,1)#,
2557 [eq]#[pname:pointSizeRange[0],pname:pointSizeRange[1]]#.
2588 centered at the point's [eq]#(x~f~,y~f~)#.
2596 The [eq]#s# and [eq]#t# point sprite texture coordinates vary from zero to
2599 The following formulas are used to evaluate [eq]#s# and [eq]#t#:
2611 where size is the point's size; [eq]#(x~p~,y~p~)# is the location at which
2614 [eq]#(x~f~,y~f~)# is the exact, unrounded framebuffer coordinate of the
2882 Let [eq]#**p**~r~ = (x~d~, y~d~)# be the framebuffer coordinates at which
2888 Let [eq]#**p**~a~ = (x~a~, y~a~)# and [eq]#**p**~b~ = (x~b~,y~b~)# be
2892 // Equation {linet:eq}
2899 (Note that [eq]#t = 0# at [eq]#**p**~a~# and [eq]#t = 1# at [eq]#**p**~b~#.
2900 Also note that this calculation projects the vector from [eq]#**p**~a~# to
2901 [eq]#**p**~r~# onto the line, and thus computes the normalized distance of
2911 An interpolated value [eq]#f# can be determined by
2919 where [eq]#f~a~# and [eq]#f~b~# are the data associated with the starting
2920 and ending endpoints of the segment, respectively; [eq]#w~a~# and [eq]#w~b~#
2921 are the clip [eq]#w# coordinates of the starting and ending endpoints of the
2926 and an interpolated value [eq]#f# can be determined by
2928 {empty}:: [eq]#f = (1 - t) f~a~ {plus} t f~b~#
2930 where [eq]#f~a~# and [eq]#f~b~# are the data associated with the starting
2933 The clip coordinate [eq]#w# for a sample is determined using perspective
2935 The depth value [eq]#z# for a sample is determined using linear
3036 x-major line segments have slope in the closed interval [eq]#[-1,1]#; all
3044 For each fragment [eq]#f# with center at framebuffer coordinates [eq]#x~f~#
3045 and [eq]#y~f~#, define a diamond-shaped region that is the intersection of
3053 Essentially, a line segment starting at [eq]#p~a~# and ending at [eq]#p~b~#
3054 produces those fragments [eq]#f# for which the segment intersects
3055 [eq]#R~f~#, except if [eq]#p~b~# is contained in [eq]#R~f~#.
3059 To avoid difficulties when an endpoint lies on a boundary of [eq]#R~f~# we
3061 Let [eq]#p~a~# and [eq]#p~b~# have framebuffer coordinates [eq]#(x~a~,
3062 y~a~)# and [eq]#(x~b~, y~b~)#, respectively.
3063 Obtain the perturbed endpoints [eq]#p~a~'# given by [eq]#(x~a~, y~a~) -
3064 ({epsilon}, {epsilon}^2^)# and [eq]#p~b~'# given by [eq]#(x~b~, y~b~) -
3066 Rasterizing the line segment starting at [eq]#p~a~# and ending at [eq]#p~b~#
3067 produces those fragments [eq]#f# for which the segment starting at
3068 [eq]#p~a~'# and ending on [eq]#p~b~'# intersects [eq]#R~f~#, except if
3069 [eq]#p~b~'# is contained in [eq]#R~f~#.
3070 [eq]#{epsilon}# is chosen to be so small that rasterizing the line segment
3071 produces the same fragments when [eq]#{delta}# is substituted for
3072 [eq]#{epsilon}# for any [eq]#0 < {delta} {leq} {epsilon}#.
3074 When [eq]#p~a~# and [eq]#p~b~# lie on fragment centers, this
3077 that the final fragment (corresponding to [eq]#p~b~#) is not drawn.
3101 The actual width [eq]#w# of Bresenham lines is determined by rounding the
3110 If the line segment has endpoints given by [eq]#(x~0~, y~0~)# and
3111 [eq]#(x~1~, y~1~)# in framebuffer coordinates, the segment with endpoints
3228 pname:lineStippleFactor must: be in the range [eq]#[1,256]#
3291 where latexmath:[x_f^i] and latexmath:[y_f^i] are the [eq]#x# and [eq]#y#
3292 framebuffer coordinates of the [eq]##i##th vertex of the [eq]#n#-vertex
3294 computation) and [eq]#i {oplus} 1# is [eq]#(i {plus} 1) mod n#.
3296 The interpretation of the sign of [eq]#a# is determined by the
3449 _Barycentric coordinates_ are a set of three numbers, [eq]#a#, [eq]#b#, and
3450 [eq]#c#, each in the range [eq]#[0,1]#, with [eq]#a {plus} b {plus} c = 1#.
3451 These coordinates uniquely specify any point [eq]#p# within the triangle or
3454 {empty}:: [eq]#p = a p~a~ {plus} b p~b~ {plus} c p~c~#
3456 where [eq]#p~a~#, [eq]#p~b~#, and [eq]#p~c~# are the vertices of the
3458 [eq]#a#, [eq]#b#, and [eq]#c# are determined by:
3467 where [eq]#A(lmn)# denotes the area in framebuffer coordinates of the
3468 triangle with vertices [eq]#l#, [eq]#m#, and [eq]#n#.
3470 Denote an associated datum at [eq]#p~a~#, [eq]#p~b~#, or [eq]#p~c~# as
3471 [eq]#f~a~#, [eq]#f~b~#, or [eq]#f~c~#, respectively.
3477 An interpolated value [eq]#f# can be determined by
3485 where [eq]#w~a~#, [eq]#w~b~#, and [eq]#w~c~# are the clip [eq]#w#
3486 coordinates of [eq]#p~a~#, [eq]#p~b~#, and [eq]#p~c~#, respectively.
3487 [eq]#a#, [eq]#b#, and [eq]#c# are the barycentric coordinates of the
3492 and an interpolated value [eq]#f# can be determined by
3494 {empty}:: [eq]#f = a f~a~ {plus} b f~b~ {plus} c f~c~#
3496 where [eq]#f~a~#, [eq]#f~b~#, and [eq]#f~c~# are the data associated with
3497 [eq]#p~a~#, [eq]#p~b~#, and [eq]#p~c~#, respectively.
3499 The clip coordinate [eq]#w# for a sample is determined using perspective
3501 The depth value [eq]#z# for a sample is determined using linear
3517 where [eq]#n# is the number of vertices in the polygon and [eq]#f~i~# is the
3518 value of [eq]#f# at vertex [eq]#i#.
3519 For each [eq]#i#, [eq]#0 {leq} a~i~ {leq} 1# and
3521 The values of [eq]#a~i~# may: differ from fragment to fragment, but at
3522 vertex [eq]#i#, [eq]#a~i~ = 1# and [eq]#a~j~ = 0# for [eq]#j {neq} i#.
3563 extend outside the range [eq]#[0,1]# when these primitives are shaded.
3728 * pname:depthBiasSlopeFactor scales the maximum depth slope [eq]#m# of the
3730 * pname:depthBiasConstantFactor scales the parameter [eq]#r# of the depth
3743 The maximum depth slope [eq]#m# of a triangle is
3751 where [eq]#(x~f~, y~f~, z~f~)# is a point on the triangle.
3752 [eq]#m# may: be approximated as
3763 ename:VK_DEPTH_BIAS_REPRESENTATION_FLOAT_EXT, [eq]#r#, for the given
3766 {empty}:: [eq]#r = 1#
3771 [eq]#r# is the minimum resolvable difference that depends on the depth
3778 is the smallest difference in framebuffer coordinate [eq]#z# values that is
3782 otherwise identical vertices, but [eq]#pname:z~f~# values that differ by
3783 [eq]#r#, will have distinct depth values.
3790 [eq]#r# is constant throughout the range of the entire depth attachment.
3795 {empty}:: [eq]#r = 2^-n^#
3803 {empty}:: [eq]#r = 2 {times} 2^-n^#
3805 where [eq]#n# is the number of bits used for the depth
3818 dependent on the maximum exponent, [eq]#e#, in the range of [eq]#z# values
3820 If [eq]#n# is the number of bits in the floating-point mantissa, the minimum
3821 resolvable difference, [eq]#r#, for the given primitive is defined as
3823 {empty}:: [eq]#r = 2^e-n^#
3832 If no depth attachment is present, [eq]#r# is undefined:.
3834 The bias value [eq]#o# for a polygon is
3849 [eq]#m# is computed as described above.
3850 If the depth attachment uses a fixed-point representation, [eq]#m# is a
3851 function of depth values in the range [eq]#[0,1]#, and [eq]#o# is applied to
3946 [eq]#r# as described in <<primsrast-depthbias-computation>>.
3949 [eq]#r# defined by the bit-size or mantissa of the format as described
3952 bias representation is a factor of constant [eq]#r# equal to 1.