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