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). 11static 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 ). 21static 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 26SkScalar 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 */ 46bool 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 53 float scale; 54 if (SkScalarIsFinite(magSq)) { 55 scale = 1.0f / sk_float_sqrt(magSq); 56 } else { 57 // our magSq step overflowed to infinity, so use doubles instead. 58 // much slower, but needed when x, y or z is very large, otherwise we 59 // divide by inf. and return (0,0,0) vector. 60 double xx = fX; 61 double yy = fY; 62 double zz = fZ; 63#ifdef SK_CPU_FLUSH_TO_ZERO 64 // The iOS ARM processor discards small denormalized numbers to go faster. 65 // Casting this to a float would cause the scale to go to zero. Keeping it 66 // as a double for the multiply keeps the scale non-zero. 67 double dscale = 1.0f / sqrt(xx * xx + yy * yy + zz * zz); 68 fX = x * dscale; 69 fY = y * dscale; 70 fZ = z * dscale; 71 return true; 72#else 73 scale = (float)(1.0f / sqrt(xx * xx + yy * yy + zz * zz)); 74#endif 75 } 76 fX *= scale; 77 fY *= scale; 78 fZ *= scale; 79 return true; 80} 81