SkPoint.cpp revision 74f623d1617e0ccf3eddf37aeecabd0ac72369fd
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 12void 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 21void 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 32void SkPoint::rotateCW(SkPoint* dst) const { 33 SkASSERT(dst); 34 35 // use a tmp in case this == dst 36 SkScalar tmp = fX; 37 dst->fX = -fY; 38 dst->fY = tmp; 39} 40 41void SkPoint::rotateCCW(SkPoint* dst) const { 42 SkASSERT(dst); 43 44 // use a tmp in case this == dst 45 SkScalar tmp = fX; 46 dst->fX = fY; 47 dst->fY = -tmp; 48} 49 50void SkPoint::scale(SkScalar scale, SkPoint* dst) const { 51 SkASSERT(dst); 52 dst->set(fX * scale, fY * scale); 53} 54 55bool SkPoint::normalize() { 56 return this->setLength(fX, fY, SK_Scalar1); 57} 58 59bool SkPoint::setNormalize(SkScalar x, SkScalar y) { 60 return this->setLength(x, y, SK_Scalar1); 61} 62 63bool SkPoint::setLength(SkScalar length) { 64 return this->setLength(fX, fY, length); 65} 66 67// Returns the square of the Euclidian distance to (dx,dy). 68static inline float getLengthSquared(float dx, float dy) { 69 return dx * dx + dy * dy; 70} 71 72// Calculates the square of the Euclidian distance to (dx,dy) and stores it in 73// *lengthSquared. Returns true if the distance is judged to be "nearly zero". 74// 75// This logic is encapsulated in a helper method to make it explicit that we 76// always perform this check in the same manner, to avoid inconsistencies 77// (see http://code.google.com/p/skia/issues/detail?id=560 ). 78static inline bool is_length_nearly_zero(float dx, float dy, 79 float *lengthSquared) { 80 *lengthSquared = getLengthSquared(dx, dy); 81 return *lengthSquared <= (SK_ScalarNearlyZero * SK_ScalarNearlyZero); 82} 83 84SkScalar SkPoint::Normalize(SkPoint* pt) { 85 float x = pt->fX; 86 float y = pt->fY; 87 float mag2; 88 if (is_length_nearly_zero(x, y, &mag2)) { 89 pt->set(0, 0); 90 return 0; 91 } 92 93 float mag, scale; 94 if (SkScalarIsFinite(mag2)) { 95 mag = sk_float_sqrt(mag2); 96 scale = 1 / mag; 97 } else { 98 // our mag2 step overflowed to infinity, so use doubles instead. 99 // much slower, but needed when x or y are very large, other wise we 100 // divide by inf. and return (0,0) vector. 101 double xx = x; 102 double yy = y; 103 double magmag = sqrt(xx * xx + yy * yy); 104 mag = (float)magmag; 105 // we perform the divide with the double magmag, to stay exactly the 106 // same as setLength. It would be faster to perform the divide with 107 // mag, but it is possible that mag has overflowed to inf. but still 108 // have a non-zero value for scale (thanks to denormalized numbers). 109 scale = (float)(1 / magmag); 110 } 111 pt->set(x * scale, y * scale); 112 return mag; 113} 114 115SkScalar SkPoint::Length(SkScalar dx, SkScalar dy) { 116 float mag2 = dx * dx + dy * dy; 117 if (SkScalarIsFinite(mag2)) { 118 return sk_float_sqrt(mag2); 119 } else { 120 double xx = dx; 121 double yy = dy; 122 return sk_double_to_float(sqrt(xx * xx + yy * yy)); 123 } 124} 125 126/* 127 * We have to worry about 2 tricky conditions: 128 * 1. underflow of mag2 (compared against nearlyzero^2) 129 * 2. overflow of mag2 (compared w/ isfinite) 130 * 131 * If we underflow, we return false. If we overflow, we compute again using 132 * doubles, which is much slower (3x in a desktop test) but will not overflow. 133 */ 134bool SkPoint::setLength(float x, float y, float length) { 135 float mag2; 136 if (is_length_nearly_zero(x, y, &mag2)) { 137 this->set(0, 0); 138 return false; 139 } 140 141 float scale; 142 if (SkScalarIsFinite(mag2)) { 143 scale = length / sk_float_sqrt(mag2); 144 } else { 145 // our mag2 step overflowed to infinity, so use doubles instead. 146 // much slower, but needed when x or y are very large, other wise we 147 // divide by inf. and return (0,0) vector. 148 double xx = x; 149 double yy = y; 150 #ifdef SK_CPU_FLUSH_TO_ZERO 151 // The iOS ARM processor discards small denormalized numbers to go faster. 152 // Casting this to a float would cause the scale to go to zero. Keeping it 153 // as a double for the multiply keeps the scale non-zero. 154 double dscale = length / sqrt(xx * xx + yy * yy); 155 fX = x * dscale; 156 fY = y * dscale; 157 return true; 158 #else 159 scale = (float)(length / sqrt(xx * xx + yy * yy)); 160 #endif 161 } 162 fX = x * scale; 163 fY = y * scale; 164 return true; 165} 166 167bool SkPoint::setLengthFast(float length) { 168 return this->setLengthFast(fX, fY, length); 169} 170 171bool SkPoint::setLengthFast(float x, float y, float length) { 172 float mag2; 173 if (is_length_nearly_zero(x, y, &mag2)) { 174 this->set(0, 0); 175 return false; 176 } 177 178 float scale; 179 if (SkScalarIsFinite(mag2)) { 180 scale = length * sk_float_rsqrt(mag2); // <--- this is the difference 181 } else { 182 // our mag2 step overflowed to infinity, so use doubles instead. 183 // much slower, but needed when x or y are very large, other wise we 184 // divide by inf. and return (0,0) vector. 185 double xx = x; 186 double yy = y; 187 scale = (float)(length / sqrt(xx * xx + yy * yy)); 188 } 189 fX = x * scale; 190 fY = y * scale; 191 return true; 192} 193 194 195/////////////////////////////////////////////////////////////////////////////// 196 197SkScalar SkPoint::distanceToLineBetweenSqd(const SkPoint& a, 198 const SkPoint& b, 199 Side* side) const { 200 201 SkVector u = b - a; 202 SkVector v = *this - a; 203 204 SkScalar uLengthSqd = u.lengthSqd(); 205 SkScalar det = u.cross(v); 206 if (side) { 207 SkASSERT(-1 == SkPoint::kLeft_Side && 208 0 == SkPoint::kOn_Side && 209 1 == kRight_Side); 210 *side = (Side) SkScalarSignAsInt(det); 211 } 212 SkScalar temp = det / uLengthSqd; 213 temp *= det; 214 return temp; 215} 216 217SkScalar SkPoint::distanceToLineSegmentBetweenSqd(const SkPoint& a, 218 const SkPoint& b) const { 219 // See comments to distanceToLineBetweenSqd. If the projection of c onto 220 // u is between a and b then this returns the same result as that 221 // function. Otherwise, it returns the distance to the closer of a and 222 // b. Let the projection of v onto u be v'. There are three cases: 223 // 1. v' points opposite to u. c is not between a and b and is closer 224 // to a than b. 225 // 2. v' points along u and has magnitude less than y. c is between 226 // a and b and the distance to the segment is the same as distance 227 // to the line ab. 228 // 3. v' points along u and has greater magnitude than u. c is not 229 // not between a and b and is closer to b than a. 230 // v' = (u dot v) * u / |u|. So if (u dot v)/|u| is less than zero we're 231 // in case 1. If (u dot v)/|u| is > |u| we are in case 3. Otherwise 232 // we're in case 2. We actually compare (u dot v) to 0 and |u|^2 to 233 // avoid a sqrt to compute |u|. 234 235 SkVector u = b - a; 236 SkVector v = *this - a; 237 238 SkScalar uLengthSqd = u.lengthSqd(); 239 SkScalar uDotV = SkPoint::DotProduct(u, v); 240 241 if (uDotV <= 0) { 242 return v.lengthSqd(); 243 } else if (uDotV > uLengthSqd) { 244 return b.distanceToSqd(*this); 245 } else { 246 SkScalar det = u.cross(v); 247 SkScalar temp = det / uLengthSqd; 248 temp *= det; 249 return temp; 250 } 251} 252