1 /* 2 * Copyright 2008 The Android Open Source Project 3 * 4 * Use of this source code is governed by a BSD-style license that can be 5 * found in the LICENSE file. 6 */ 7 8 9 #include "SkMathPriv.h" 10 #include "SkPoint.h" 11 12 void SkIPoint::rotateCW(SkIPoint* dst) const { 13 SkASSERT(dst); 14 15 // use a tmp in case this == dst 16 int32_t tmp = fX; 17 dst->fX = -fY; 18 dst->fY = tmp; 19 } 20 21 void SkIPoint::rotateCCW(SkIPoint* dst) const { 22 SkASSERT(dst); 23 24 // use a tmp in case this == dst 25 int32_t tmp = fX; 26 dst->fX = fY; 27 dst->fY = -tmp; 28 } 29 30 /////////////////////////////////////////////////////////////////////////////// 31 32 void SkPoint::setIRectFan(int l, int t, int r, int b, size_t stride) { 33 SkASSERT(stride >= sizeof(SkPoint)); 34 35 ((SkPoint*)((intptr_t)this + 0 * stride))->set(SkIntToScalar(l), 36 SkIntToScalar(t)); 37 ((SkPoint*)((intptr_t)this + 1 * stride))->set(SkIntToScalar(l), 38 SkIntToScalar(b)); 39 ((SkPoint*)((intptr_t)this + 2 * stride))->set(SkIntToScalar(r), 40 SkIntToScalar(b)); 41 ((SkPoint*)((intptr_t)this + 3 * stride))->set(SkIntToScalar(r), 42 SkIntToScalar(t)); 43 } 44 45 void SkPoint::rotateCW(SkPoint* dst) const { 46 SkASSERT(dst); 47 48 // use a tmp in case this == dst 49 SkScalar tmp = fX; 50 dst->fX = -fY; 51 dst->fY = tmp; 52 } 53 54 void SkPoint::rotateCCW(SkPoint* dst) const { 55 SkASSERT(dst); 56 57 // use a tmp in case this == dst 58 SkScalar tmp = fX; 59 dst->fX = fY; 60 dst->fY = -tmp; 61 } 62 63 void SkPoint::scale(SkScalar scale, SkPoint* dst) const { 64 SkASSERT(dst); 65 dst->set(fX * scale, fY * scale); 66 } 67 68 bool SkPoint::normalize() { 69 return this->setLength(fX, fY, SK_Scalar1); 70 } 71 72 bool SkPoint::setNormalize(SkScalar x, SkScalar y) { 73 return this->setLength(x, y, SK_Scalar1); 74 } 75 76 bool SkPoint::setLength(SkScalar length) { 77 return this->setLength(fX, fY, length); 78 } 79 80 // Returns the square of the Euclidian distance to (dx,dy). 81 static inline float getLengthSquared(float dx, float dy) { 82 return dx * dx + dy * dy; 83 } 84 85 // Calculates the square of the Euclidian distance to (dx,dy) and stores it in 86 // *lengthSquared. Returns true if the distance is judged to be "nearly zero". 87 // 88 // This logic is encapsulated in a helper method to make it explicit that we 89 // always perform this check in the same manner, to avoid inconsistencies 90 // (see http://code.google.com/p/skia/issues/detail?id=560 ). 91 static inline bool is_length_nearly_zero(float dx, float dy, 92 float *lengthSquared) { 93 *lengthSquared = getLengthSquared(dx, dy); 94 return *lengthSquared <= (SK_ScalarNearlyZero * SK_ScalarNearlyZero); 95 } 96 97 SkScalar SkPoint::Normalize(SkPoint* pt) { 98 float x = pt->fX; 99 float y = pt->fY; 100 float mag2; 101 if (is_length_nearly_zero(x, y, &mag2)) { 102 pt->set(0, 0); 103 return 0; 104 } 105 106 float mag, scale; 107 if (SkScalarIsFinite(mag2)) { 108 mag = sk_float_sqrt(mag2); 109 scale = 1 / mag; 110 } else { 111 // our mag2 step overflowed to infinity, so use doubles instead. 112 // much slower, but needed when x or y are very large, other wise we 113 // divide by inf. and return (0,0) vector. 114 double xx = x; 115 double yy = y; 116 double magmag = sqrt(xx * xx + yy * yy); 117 mag = (float)magmag; 118 // we perform the divide with the double magmag, to stay exactly the 119 // same as setLength. It would be faster to perform the divide with 120 // mag, but it is possible that mag has overflowed to inf. but still 121 // have a non-zero value for scale (thanks to denormalized numbers). 122 scale = (float)(1 / magmag); 123 } 124 pt->set(x * scale, y * scale); 125 return mag; 126 } 127 128 SkScalar SkPoint::Length(SkScalar dx, SkScalar dy) { 129 float mag2 = dx * dx + dy * dy; 130 if (SkScalarIsFinite(mag2)) { 131 return sk_float_sqrt(mag2); 132 } else { 133 double xx = dx; 134 double yy = dy; 135 return (float)sqrt(xx * xx + yy * yy); 136 } 137 } 138 139 /* 140 * We have to worry about 2 tricky conditions: 141 * 1. underflow of mag2 (compared against nearlyzero^2) 142 * 2. overflow of mag2 (compared w/ isfinite) 143 * 144 * If we underflow, we return false. If we overflow, we compute again using 145 * doubles, which is much slower (3x in a desktop test) but will not overflow. 146 */ 147 bool SkPoint::setLength(float x, float y, float length) { 148 float mag2; 149 if (is_length_nearly_zero(x, y, &mag2)) { 150 this->set(0, 0); 151 return false; 152 } 153 154 float scale; 155 if (SkScalarIsFinite(mag2)) { 156 scale = length / sk_float_sqrt(mag2); 157 } else { 158 // our mag2 step overflowed to infinity, so use doubles instead. 159 // much slower, but needed when x or y are very large, other wise we 160 // divide by inf. and return (0,0) vector. 161 double xx = x; 162 double yy = y; 163 #ifdef SK_CPU_FLUSH_TO_ZERO 164 // The iOS ARM processor discards small denormalized numbers to go faster. 165 // Casting this to a float would cause the scale to go to zero. Keeping it 166 // as a double for the multiply keeps the scale non-zero. 167 double dscale = length / sqrt(xx * xx + yy * yy); 168 fX = x * dscale; 169 fY = y * dscale; 170 return true; 171 #else 172 scale = (float)(length / sqrt(xx * xx + yy * yy)); 173 #endif 174 } 175 fX = x * scale; 176 fY = y * scale; 177 return true; 178 } 179 180 bool SkPoint::setLengthFast(float length) { 181 return this->setLengthFast(fX, fY, length); 182 } 183 184 bool SkPoint::setLengthFast(float x, float y, float length) { 185 float mag2; 186 if (is_length_nearly_zero(x, y, &mag2)) { 187 this->set(0, 0); 188 return false; 189 } 190 191 float scale; 192 if (SkScalarIsFinite(mag2)) { 193 scale = length * sk_float_rsqrt(mag2); // <--- this is the difference 194 } else { 195 // our mag2 step overflowed to infinity, so use doubles instead. 196 // much slower, but needed when x or y are very large, other wise we 197 // divide by inf. and return (0,0) vector. 198 double xx = x; 199 double yy = y; 200 scale = (float)(length / sqrt(xx * xx + yy * yy)); 201 } 202 fX = x * scale; 203 fY = y * scale; 204 return true; 205 } 206 207 208 /////////////////////////////////////////////////////////////////////////////// 209 210 SkScalar SkPoint::distanceToLineBetweenSqd(const SkPoint& a, 211 const SkPoint& b, 212 Side* side) const { 213 214 SkVector u = b - a; 215 SkVector v = *this - a; 216 217 SkScalar uLengthSqd = u.lengthSqd(); 218 SkScalar det = u.cross(v); 219 if (side) { 220 SkASSERT(-1 == SkPoint::kLeft_Side && 221 0 == SkPoint::kOn_Side && 222 1 == kRight_Side); 223 *side = (Side) SkScalarSignAsInt(det); 224 } 225 SkScalar temp = det / uLengthSqd; 226 temp *= det; 227 return temp; 228 } 229 230 SkScalar SkPoint::distanceToLineSegmentBetweenSqd(const SkPoint& a, 231 const SkPoint& b) const { 232 // See comments to distanceToLineBetweenSqd. If the projection of c onto 233 // u is between a and b then this returns the same result as that 234 // function. Otherwise, it returns the distance to the closer of a and 235 // b. Let the projection of v onto u be v'. There are three cases: 236 // 1. v' points opposite to u. c is not between a and b and is closer 237 // to a than b. 238 // 2. v' points along u and has magnitude less than y. c is between 239 // a and b and the distance to the segment is the same as distance 240 // to the line ab. 241 // 3. v' points along u and has greater magnitude than u. c is not 242 // not between a and b and is closer to b than a. 243 // v' = (u dot v) * u / |u|. So if (u dot v)/|u| is less than zero we're 244 // in case 1. If (u dot v)/|u| is > |u| we are in case 3. Otherwise 245 // we're in case 2. We actually compare (u dot v) to 0 and |u|^2 to 246 // avoid a sqrt to compute |u|. 247 248 SkVector u = b - a; 249 SkVector v = *this - a; 250 251 SkScalar uLengthSqd = u.lengthSqd(); 252 SkScalar uDotV = SkPoint::DotProduct(u, v); 253 254 if (uDotV <= 0) { 255 return v.lengthSqd(); 256 } else if (uDotV > uLengthSqd) { 257 return b.distanceToSqd(*this); 258 } else { 259 SkScalar det = u.cross(v); 260 SkScalar temp = det / uLengthSqd; 261 temp *= det; 262 return temp; 263 } 264 } 265
