1 /* 2 * Copyright 2015 Google Inc. 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 #include "SkPoint3.h" 9 10 // Returns the square of the Euclidian distance to (x,y,z). 11 static inline float get_length_squared(float x, float y, float z) { 12 return x * x + y * y + z * z; 13 } 14 15 // Calculates the square of the Euclidian distance to (x,y,z) and stores it in 16 // *lengthSquared. Returns true if the distance is judged to be "nearly zero". 17 // 18 // This logic is encapsulated in a helper method to make it explicit that we 19 // always perform this check in the same manner, to avoid inconsistencies 20 // (see http://code.google.com/p/skia/issues/detail?id=560 ). 21 static inline bool is_length_nearly_zero(float x, float y, float z, float *lengthSquared) { 22 *lengthSquared = get_length_squared(x, y, z); 23 return *lengthSquared <= (SK_ScalarNearlyZero * SK_ScalarNearlyZero); 24 } 25 26 SkScalar SkPoint3::Length(SkScalar x, SkScalar y, SkScalar z) { 27 float magSq = get_length_squared(x, y, z); 28 if (SkScalarIsFinite(magSq)) { 29 return sk_float_sqrt(magSq); 30 } else { 31 double xx = x; 32 double yy = y; 33 double zz = z; 34 return (float)sqrt(xx * xx + yy * yy + zz * zz); 35 } 36 } 37 38 /* 39 * We have to worry about 2 tricky conditions: 40 * 1. underflow of magSq (compared against nearlyzero^2) 41 * 2. overflow of magSq (compared w/ isfinite) 42 * 43 * If we underflow, we return false. If we overflow, we compute again using 44 * doubles, which is much slower (3x in a desktop test) but will not overflow. 45 */ 46 bool SkPoint3::normalize() { 47 float magSq; 48 if (is_length_nearly_zero(fX, fY, fZ, &magSq)) { 49 this->set(0, 0, 0); 50 return false; 51 } 52 // sqrtf does not provide enough precision; since sqrt takes a double, 53 // there's no additional penalty to storing invScale in a double 54 double invScale; 55 if (sk_float_isfinite(magSq)) { 56 invScale = magSq; 57 } else { 58 // our magSq step overflowed to infinity, so use doubles instead. 59 // much slower, but needed when x, y or z is very large, otherwise we 60 // divide by inf. and return (0,0,0) vector. 61 double xx = fX; 62 double yy = fY; 63 double zz = fZ; 64 invScale = xx * xx + yy * yy + zz * zz; 65 } 66 // using a float instead of a double for scale loses too much precision 67 double scale = 1 / sqrt(invScale); 68 fX *= scale; 69 fY *= scale; 70 fZ *= scale; 71 if (!sk_float_isfinite(fX) || !sk_float_isfinite(fY) || !sk_float_isfinite(fZ)) { 72 this->set(0, 0, 0); 73 return false; 74 } 75 return true; 76 } 77
