1 
2 /*
3  * Copyright 2008 The Android Open Source Project
4  *
5  * Use of this source code is governed by a BSD-style license that can be
6  * found in the LICENSE file.
7  */
8 
9 
10 #include "SkMathPriv.h"
11 #include "SkPoint.h"
12 
rotateCW(SkIPoint * dst) const13 void SkIPoint::rotateCW(SkIPoint* dst) const {
14     SkASSERT(dst);
15 
16     // use a tmp in case this == dst
17     int32_t tmp = fX;
18     dst->fX = -fY;
19     dst->fY = tmp;
20 }
21 
rotateCCW(SkIPoint * dst) const22 void SkIPoint::rotateCCW(SkIPoint* dst) const {
23     SkASSERT(dst);
24 
25     // use a tmp in case this == dst
26     int32_t tmp = fX;
27     dst->fX = fY;
28     dst->fY = -tmp;
29 }
30 
31 ///////////////////////////////////////////////////////////////////////////////
32 
setIRectFan(int l,int t,int r,int b,size_t stride)33 void SkPoint::setIRectFan(int l, int t, int r, int b, size_t stride) {
34     SkASSERT(stride >= sizeof(SkPoint));
35 
36     ((SkPoint*)((intptr_t)this + 0 * stride))->set(SkIntToScalar(l),
37                                                    SkIntToScalar(t));
38     ((SkPoint*)((intptr_t)this + 1 * stride))->set(SkIntToScalar(l),
39                                                    SkIntToScalar(b));
40     ((SkPoint*)((intptr_t)this + 2 * stride))->set(SkIntToScalar(r),
41                                                    SkIntToScalar(b));
42     ((SkPoint*)((intptr_t)this + 3 * stride))->set(SkIntToScalar(r),
43                                                    SkIntToScalar(t));
44 }
45 
rotateCW(SkPoint * dst) const46 void SkPoint::rotateCW(SkPoint* dst) const {
47     SkASSERT(dst);
48 
49     // use a tmp in case this == dst
50     SkScalar tmp = fX;
51     dst->fX = -fY;
52     dst->fY = tmp;
53 }
54 
rotateCCW(SkPoint * dst) const55 void SkPoint::rotateCCW(SkPoint* dst) const {
56     SkASSERT(dst);
57 
58     // use a tmp in case this == dst
59     SkScalar tmp = fX;
60     dst->fX = fY;
61     dst->fY = -tmp;
62 }
63 
scale(SkScalar scale,SkPoint * dst) const64 void SkPoint::scale(SkScalar scale, SkPoint* dst) const {
65     SkASSERT(dst);
66     dst->set(SkScalarMul(fX, scale), SkScalarMul(fY, scale));
67 }
68 
normalize()69 bool SkPoint::normalize() {
70     return this->setLength(fX, fY, SK_Scalar1);
71 }
72 
setNormalize(SkScalar x,SkScalar y)73 bool SkPoint::setNormalize(SkScalar x, SkScalar y) {
74     return this->setLength(x, y, SK_Scalar1);
75 }
76 
setLength(SkScalar length)77 bool SkPoint::setLength(SkScalar length) {
78     return this->setLength(fX, fY, length);
79 }
80 
81 // Returns the square of the Euclidian distance to (dx,dy).
getLengthSquared(float dx,float dy)82 static inline float getLengthSquared(float dx, float dy) {
83     return dx * dx + dy * dy;
84 }
85 
86 // Calculates the square of the Euclidian distance to (dx,dy) and stores it in
87 // *lengthSquared.  Returns true if the distance is judged to be "nearly zero".
88 //
89 // This logic is encapsulated in a helper method to make it explicit that we
90 // always perform this check in the same manner, to avoid inconsistencies
91 // (see http://code.google.com/p/skia/issues/detail?id=560 ).
isLengthNearlyZero(float dx,float dy,float * lengthSquared)92 static inline bool isLengthNearlyZero(float dx, float dy,
93                                       float *lengthSquared) {
94     *lengthSquared = getLengthSquared(dx, dy);
95     return *lengthSquared <= (SK_ScalarNearlyZero * SK_ScalarNearlyZero);
96 }
97 
Normalize(SkPoint * pt)98 SkScalar SkPoint::Normalize(SkPoint* pt) {
99     float x = pt->fX;
100     float y = pt->fY;
101     float mag2;
102     if (isLengthNearlyZero(x, y, &mag2)) {
103         pt->set(0, 0);
104         return 0;
105     }
106 
107     float mag, scale;
108     if (SkScalarIsFinite(mag2)) {
109         mag = sk_float_sqrt(mag2);
110         scale = 1 / mag;
111     } else {
112         // our mag2 step overflowed to infinity, so use doubles instead.
113         // much slower, but needed when x or y are very large, other wise we
114         // divide by inf. and return (0,0) vector.
115         double xx = x;
116         double yy = y;
117         double magmag = sqrt(xx * xx + yy * yy);
118         mag = (float)magmag;
119         // we perform the divide with the double magmag, to stay exactly the
120         // same as setLength. It would be faster to perform the divide with
121         // mag, but it is possible that mag has overflowed to inf. but still
122         // have a non-zero value for scale (thanks to denormalized numbers).
123         scale = (float)(1 / magmag);
124     }
125     pt->set(x * scale, y * scale);
126     return mag;
127 }
128 
Length(SkScalar dx,SkScalar dy)129 SkScalar SkPoint::Length(SkScalar dx, SkScalar dy) {
130     float mag2 = dx * dx + dy * dy;
131     if (SkScalarIsFinite(mag2)) {
132         return sk_float_sqrt(mag2);
133     } else {
134         double xx = dx;
135         double yy = dy;
136         return (float)sqrt(xx * xx + yy * yy);
137     }
138 }
139 
140 /*
141  *  We have to worry about 2 tricky conditions:
142  *  1. underflow of mag2 (compared against nearlyzero^2)
143  *  2. overflow of mag2 (compared w/ isfinite)
144  *
145  *  If we underflow, we return false. If we overflow, we compute again using
146  *  doubles, which is much slower (3x in a desktop test) but will not overflow.
147  */
setLength(float x,float y,float length)148 bool SkPoint::setLength(float x, float y, float length) {
149     float mag2;
150     if (isLengthNearlyZero(x, y, &mag2)) {
151         this->set(0, 0);
152         return false;
153     }
154 
155     float scale;
156     if (SkScalarIsFinite(mag2)) {
157         scale = length / sk_float_sqrt(mag2);
158     } else {
159         // our mag2 step overflowed to infinity, so use doubles instead.
160         // much slower, but needed when x or y are very large, other wise we
161         // divide by inf. and return (0,0) vector.
162         double xx = x;
163         double yy = y;
164     #ifdef SK_DISCARD_DENORMALIZED_FOR_SPEED
165         // The iOS ARM processor discards small denormalized numbers to go faster.
166         // Casting this to a float would cause the scale to go to zero. Keeping it
167         // as a double for the multiply keeps the scale non-zero.
168         double dscale = length / sqrt(xx * xx + yy * yy);
169         fX = x * dscale;
170         fY = y * dscale;
171         return true;
172     #else
173         scale = (float)(length / sqrt(xx * xx + yy * yy));
174     #endif
175     }
176     fX = x * scale;
177     fY = y * scale;
178     return true;
179 }
180 
setLengthFast(float length)181 bool SkPoint::setLengthFast(float length) {
182     return this->setLengthFast(fX, fY, length);
183 }
184 
setLengthFast(float x,float y,float length)185 bool SkPoint::setLengthFast(float x, float y, float length) {
186     float mag2;
187     if (isLengthNearlyZero(x, y, &mag2)) {
188         this->set(0, 0);
189         return false;
190     }
191 
192     float scale;
193     if (SkScalarIsFinite(mag2)) {
194         scale = length * sk_float_rsqrt(mag2);  // <--- this is the difference
195     } else {
196         // our mag2 step overflowed to infinity, so use doubles instead.
197         // much slower, but needed when x or y are very large, other wise we
198         // divide by inf. and return (0,0) vector.
199         double xx = x;
200         double yy = y;
201         scale = (float)(length / sqrt(xx * xx + yy * yy));
202     }
203     fX = x * scale;
204     fY = y * scale;
205     return true;
206 }
207 
208 
209 ///////////////////////////////////////////////////////////////////////////////
210 
distanceToLineBetweenSqd(const SkPoint & a,const SkPoint & b,Side * side) const211 SkScalar SkPoint::distanceToLineBetweenSqd(const SkPoint& a,
212                                            const SkPoint& b,
213                                            Side* side) const {
214 
215     SkVector u = b - a;
216     SkVector v = *this - a;
217 
218     SkScalar uLengthSqd = u.lengthSqd();
219     SkScalar det = u.cross(v);
220     if (side) {
221         SkASSERT(-1 == SkPoint::kLeft_Side &&
222                   0 == SkPoint::kOn_Side &&
223                   1 == kRight_Side);
224         *side = (Side) SkScalarSignAsInt(det);
225     }
226     SkScalar temp = det / uLengthSqd;
227     temp *= det;
228     return temp;
229 }
230 
distanceToLineSegmentBetweenSqd(const SkPoint & a,const SkPoint & b) const231 SkScalar SkPoint::distanceToLineSegmentBetweenSqd(const SkPoint& a,
232                                                   const SkPoint& b) const {
233     // See comments to distanceToLineBetweenSqd. If the projection of c onto
234     // u is between a and b then this returns the same result as that
235     // function. Otherwise, it returns the distance to the closer of a and
236     // b. Let the projection of v onto u be v'.  There are three cases:
237     //    1. v' points opposite to u. c is not between a and b and is closer
238     //       to a than b.
239     //    2. v' points along u and has magnitude less than y. c is between
240     //       a and b and the distance to the segment is the same as distance
241     //       to the line ab.
242     //    3. v' points along u and has greater magnitude than u. c is not
243     //       not between a and b and is closer to b than a.
244     // v' = (u dot v) * u / |u|. So if (u dot v)/|u| is less than zero we're
245     // in case 1. If (u dot v)/|u| is > |u| we are in case 3. Otherwise
246     // we're in case 2. We actually compare (u dot v) to 0 and |u|^2 to
247     // avoid a sqrt to compute |u|.
248 
249     SkVector u = b - a;
250     SkVector v = *this - a;
251 
252     SkScalar uLengthSqd = u.lengthSqd();
253     SkScalar uDotV = SkPoint::DotProduct(u, v);
254 
255     if (uDotV <= 0) {
256         return v.lengthSqd();
257     } else if (uDotV > uLengthSqd) {
258         return b.distanceToSqd(*this);
259     } else {
260         SkScalar det = u.cross(v);
261         SkScalar temp = det / uLengthSqd;
262         temp *= det;
263         return temp;
264     }
265 }
266