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 13void 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 22void 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 33void 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 46void SkPoint::setRectFan(SkScalar l, SkScalar t, SkScalar r, SkScalar b, 47 size_t stride) { 48 SkASSERT(stride >= sizeof(SkPoint)); 49 50 ((SkPoint*)((intptr_t)this + 0 * stride))->set(l, t); 51 ((SkPoint*)((intptr_t)this + 1 * stride))->set(l, b); 52 ((SkPoint*)((intptr_t)this + 2 * stride))->set(r, b); 53 ((SkPoint*)((intptr_t)this + 3 * stride))->set(r, t); 54} 55 56void SkPoint::rotateCW(SkPoint* dst) const { 57 SkASSERT(dst); 58 59 // use a tmp in case this == dst 60 SkScalar tmp = fX; 61 dst->fX = -fY; 62 dst->fY = tmp; 63} 64 65void SkPoint::rotateCCW(SkPoint* dst) const { 66 SkASSERT(dst); 67 68 // use a tmp in case this == dst 69 SkScalar tmp = fX; 70 dst->fX = fY; 71 dst->fY = -tmp; 72} 73 74void SkPoint::scale(SkScalar scale, SkPoint* dst) const { 75 SkASSERT(dst); 76 dst->set(SkScalarMul(fX, scale), SkScalarMul(fY, scale)); 77} 78 79bool SkPoint::normalize() { 80 return this->setLength(fX, fY, SK_Scalar1); 81} 82 83bool SkPoint::setNormalize(SkScalar x, SkScalar y) { 84 return this->setLength(x, y, SK_Scalar1); 85} 86 87bool SkPoint::setLength(SkScalar length) { 88 return this->setLength(fX, fY, length); 89} 90 91// Returns the square of the Euclidian distance to (dx,dy). 92static inline float getLengthSquared(float dx, float dy) { 93 return dx * dx + dy * dy; 94} 95 96// Calculates the square of the Euclidian distance to (dx,dy) and stores it in 97// *lengthSquared. Returns true if the distance is judged to be "nearly zero". 98// 99// This logic is encapsulated in a helper method to make it explicit that we 100// always perform this check in the same manner, to avoid inconsistencies 101// (see http://code.google.com/p/skia/issues/detail?id=560 ). 102static inline bool isLengthNearlyZero(float dx, float dy, 103 float *lengthSquared) { 104 *lengthSquared = getLengthSquared(dx, dy); 105 return *lengthSquared <= (SK_ScalarNearlyZero * SK_ScalarNearlyZero); 106} 107 108SkScalar SkPoint::Normalize(SkPoint* pt) { 109 float x = pt->fX; 110 float y = pt->fY; 111 float mag2; 112 if (isLengthNearlyZero(x, y, &mag2)) { 113 return 0; 114 } 115 116 float mag, scale; 117 if (SkScalarIsFinite(mag2)) { 118 mag = sk_float_sqrt(mag2); 119 scale = 1 / mag; 120 } else { 121 // our mag2 step overflowed to infinity, so use doubles instead. 122 // much slower, but needed when x or y are very large, other wise we 123 // divide by inf. and return (0,0) vector. 124 double xx = x; 125 double yy = y; 126 double magmag = sqrt(xx * xx + yy * yy); 127 mag = (float)magmag; 128 // we perform the divide with the double magmag, to stay exactly the 129 // same as setLength. It would be faster to perform the divide with 130 // mag, but it is possible that mag has overflowed to inf. but still 131 // have a non-zero value for scale (thanks to denormalized numbers). 132 scale = (float)(1 / magmag); 133 } 134 pt->set(x * scale, y * scale); 135 return mag; 136} 137 138SkScalar SkPoint::Length(SkScalar dx, SkScalar dy) { 139 float mag2 = dx * dx + dy * dy; 140 if (SkScalarIsFinite(mag2)) { 141 return sk_float_sqrt(mag2); 142 } else { 143 double xx = dx; 144 double yy = dy; 145 return (float)sqrt(xx * xx + yy * yy); 146 } 147} 148 149/* 150 * We have to worry about 2 tricky conditions: 151 * 1. underflow of mag2 (compared against nearlyzero^2) 152 * 2. overflow of mag2 (compared w/ isfinite) 153 * 154 * If we underflow, we return false. If we overflow, we compute again using 155 * doubles, which is much slower (3x in a desktop test) but will not overflow. 156 */ 157bool SkPoint::setLength(float x, float y, float length) { 158 float mag2; 159 if (isLengthNearlyZero(x, y, &mag2)) { 160 return false; 161 } 162 163 float scale; 164 if (SkScalarIsFinite(mag2)) { 165 scale = length / sk_float_sqrt(mag2); 166 } else { 167 // our mag2 step overflowed to infinity, so use doubles instead. 168 // much slower, but needed when x or y are very large, other wise we 169 // divide by inf. and return (0,0) vector. 170 double xx = x; 171 double yy = y; 172 #ifdef SK_DISCARD_DENORMALIZED_FOR_SPEED 173 // The iOS ARM processor discards small denormalized numbers to go faster. 174 // Casting this to a float would cause the scale to go to zero. Keeping it 175 // as a double for the multiply keeps the scale non-zero. 176 double dscale = length / sqrt(xx * xx + yy * yy); 177 fX = x * dscale; 178 fY = y * dscale; 179 return true; 180 #else 181 scale = (float)(length / sqrt(xx * xx + yy * yy)); 182 #endif 183 } 184 fX = x * scale; 185 fY = y * scale; 186 return true; 187} 188 189bool SkPoint::setLengthFast(float length) { 190 return this->setLengthFast(fX, fY, length); 191} 192 193bool SkPoint::setLengthFast(float x, float y, float length) { 194 float mag2; 195 if (isLengthNearlyZero(x, y, &mag2)) { 196 return false; 197 } 198 199 float scale; 200 if (SkScalarIsFinite(mag2)) { 201 scale = length * sk_float_rsqrt(mag2); // <--- this is the difference 202 } else { 203 // our mag2 step overflowed to infinity, so use doubles instead. 204 // much slower, but needed when x or y are very large, other wise we 205 // divide by inf. and return (0,0) vector. 206 double xx = x; 207 double yy = y; 208 scale = (float)(length / sqrt(xx * xx + yy * yy)); 209 } 210 fX = x * scale; 211 fY = y * scale; 212 return true; 213} 214 215 216/////////////////////////////////////////////////////////////////////////////// 217 218SkScalar SkPoint::distanceToLineBetweenSqd(const SkPoint& a, 219 const SkPoint& b, 220 Side* side) const { 221 222 SkVector u = b - a; 223 SkVector v = *this - a; 224 225 SkScalar uLengthSqd = u.lengthSqd(); 226 SkScalar det = u.cross(v); 227 if (side) { 228 SkASSERT(-1 == SkPoint::kLeft_Side && 229 0 == SkPoint::kOn_Side && 230 1 == kRight_Side); 231 *side = (Side) SkScalarSignAsInt(det); 232 } 233 return SkScalarMulDiv(det, det, uLengthSqd); 234} 235 236SkScalar SkPoint::distanceToLineSegmentBetweenSqd(const SkPoint& a, 237 const SkPoint& b) const { 238 // See comments to distanceToLineBetweenSqd. If the projection of c onto 239 // u is between a and b then this returns the same result as that 240 // function. Otherwise, it returns the distance to the closer of a and 241 // b. Let the projection of v onto u be v'. There are three cases: 242 // 1. v' points opposite to u. c is not between a and b and is closer 243 // to a than b. 244 // 2. v' points along u and has magnitude less than y. c is between 245 // a and b and the distance to the segment is the same as distance 246 // to the line ab. 247 // 3. v' points along u and has greater magnitude than u. c is not 248 // not between a and b and is closer to b than a. 249 // v' = (u dot v) * u / |u|. So if (u dot v)/|u| is less than zero we're 250 // in case 1. If (u dot v)/|u| is > |u| we are in case 3. Otherwise 251 // we're in case 2. We actually compare (u dot v) to 0 and |u|^2 to 252 // avoid a sqrt to compute |u|. 253 254 SkVector u = b - a; 255 SkVector v = *this - a; 256 257 SkScalar uLengthSqd = u.lengthSqd(); 258 SkScalar uDotV = SkPoint::DotProduct(u, v); 259 260 if (uDotV <= 0) { 261 return v.lengthSqd(); 262 } else if (uDotV > uLengthSqd) { 263 return b.distanceToSqd(*this); 264 } else { 265 SkScalar det = u.cross(v); 266 return SkScalarMulDiv(det, det, uLengthSqd); 267 } 268} 269