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 13 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 22 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 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 46 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 55 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 64 void SkPoint::scale(SkScalar scale, SkPoint* dst) const { 65 SkASSERT(dst); 66 dst->set(SkScalarMul(fX, scale), SkScalarMul(fY, scale)); 67 } 68 69 bool SkPoint::normalize() { 70 return this->setLength(fX, fY, SK_Scalar1); 71 } 72 73 bool SkPoint::setNormalize(SkScalar x, SkScalar y) { 74 return this->setLength(x, y, SK_Scalar1); 75 } 76 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). 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 ). 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 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 } 128 129 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 */ 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_CPU_FLUSH_TO_ZERO 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 } 180 181 bool SkPoint::setLengthFast(float length) { 182 return this->setLengthFast(fX, fY, length); 183 } 184 185 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 /////////////////////////////////////////////////////////////////////////////// 210 211 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 } 230 231 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
