SkPathOpsTypes.h revision a2bbc6e19d5332e81784e582c290cc060f40c4c7
107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com/* 207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com * Copyright 2012 Google Inc. 307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com * 407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com * Use of this source code is governed by a BSD-style license that can be 507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com * found in the LICENSE file. 607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com */ 707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com#ifndef SkPathOpsTypes_DEFINED 807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com#define SkPathOpsTypes_DEFINED 907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 1007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com#include <float.h> // for FLT_EPSILON 1107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com#include <math.h> // for fabs, sqrt 1207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 1307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com#include "SkFloatingPoint.h" 14277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com#include "SkPath.h" 1507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com#include "SkPathOps.h" 1607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com#include "SkPathOpsDebug.h" 1707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com#include "SkScalar.h" 1807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 1907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comenum SkPathOpsMask { 2007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com kWinding_PathOpsMask = -1, 2107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com kNo_PathOpsMask = 0, 2207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com kEvenOdd_PathOpsMask = 1 2307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com}; 2407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 25c3f63570c35a1e2bc84b33906c6401d6f3062bf2caryclark@google.com// Use Almost Equal when comparing coordinates. Use epsilon to compare T values. 264fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.combool AlmostEqualUlps(float a, float b); 274fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.cominline bool AlmostEqualUlps(double a, double b) { 284fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.com return AlmostEqualUlps(SkDoubleToScalar(a), SkDoubleToScalar(b)); 2907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 3007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 317eaa53d8f7e48fd17d02b5e3bd91f90e9c1899efcaryclark@google.com// Use Almost Dequal when comparing should not special case denormalized values. 327eaa53d8f7e48fd17d02b5e3bd91f90e9c1899efcaryclark@google.combool AlmostDequalUlps(float a, float b); 337eaa53d8f7e48fd17d02b5e3bd91f90e9c1899efcaryclark@google.cominline bool AlmostDequalUlps(double a, double b) { 347eaa53d8f7e48fd17d02b5e3bd91f90e9c1899efcaryclark@google.com return AlmostDequalUlps(SkDoubleToScalar(a), SkDoubleToScalar(b)); 357eaa53d8f7e48fd17d02b5e3bd91f90e9c1899efcaryclark@google.com} 367eaa53d8f7e48fd17d02b5e3bd91f90e9c1899efcaryclark@google.com 37570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.combool NotAlmostEqualUlps(float a, float b); 38570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.cominline bool NotAlmostEqualUlps(double a, double b) { 39570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com return NotAlmostEqualUlps(SkDoubleToScalar(a), SkDoubleToScalar(b)); 40570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com} 41570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com 427eaa53d8f7e48fd17d02b5e3bd91f90e9c1899efcaryclark@google.combool NotAlmostDequalUlps(float a, float b); 437eaa53d8f7e48fd17d02b5e3bd91f90e9c1899efcaryclark@google.cominline bool NotAlmostDequalUlps(double a, double b) { 447eaa53d8f7e48fd17d02b5e3bd91f90e9c1899efcaryclark@google.com return NotAlmostDequalUlps(SkDoubleToScalar(a), SkDoubleToScalar(b)); 457eaa53d8f7e48fd17d02b5e3bd91f90e9c1899efcaryclark@google.com} 467eaa53d8f7e48fd17d02b5e3bd91f90e9c1899efcaryclark@google.com 47570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com// Use Almost Bequal when comparing coordinates in conjunction with between. 48570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.combool AlmostBequalUlps(float a, float b); 49570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.cominline bool AlmostBequalUlps(double a, double b) { 50570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com return AlmostBequalUlps(SkDoubleToScalar(a), SkDoubleToScalar(b)); 51570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com} 52570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com 53a2bbc6e19d5332e81784e582c290cc060f40c4c7caryclark@google.combool AlmostPequalUlps(float a, float b); 54a2bbc6e19d5332e81784e582c290cc060f40c4c7caryclark@google.cominline bool AlmostPequalUlps(double a, double b) { 55a2bbc6e19d5332e81784e582c290cc060f40c4c7caryclark@google.com return AlmostPequalUlps(SkDoubleToScalar(a), SkDoubleToScalar(b)); 56a2bbc6e19d5332e81784e582c290cc060f40c4c7caryclark@google.com} 57a2bbc6e19d5332e81784e582c290cc060f40c4c7caryclark@google.com 584fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.combool RoughlyEqualUlps(float a, float b); 594fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.cominline bool RoughlyEqualUlps(double a, double b) { 604fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.com return RoughlyEqualUlps(SkDoubleToScalar(a), SkDoubleToScalar(b)); 6107e97fccd2d85076cd22ef411b0773ab92a18abecaryclark@google.com} 6207e97fccd2d85076cd22ef411b0773ab92a18abecaryclark@google.com 63570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.combool AlmostLessUlps(float a, float b); 64570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.cominline bool AlmostLessUlps(double a, double b) { 65570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com return AlmostLessUlps(SkDoubleToScalar(a), SkDoubleToScalar(b)); 66570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com} 67570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com 68570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.combool AlmostLessOrEqualUlps(float a, float b); 69570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.cominline bool AlmostLessOrEqualUlps(double a, double b) { 70570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com return AlmostLessOrEqualUlps(SkDoubleToScalar(a), SkDoubleToScalar(b)); 71570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com} 72570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com 73fa2aeee27af27f2934ee52a9732148f66481fb03caryclark@google.combool AlmostBetweenUlps(float a, float b, float c); 744fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.cominline bool AlmostBetweenUlps(double a, double b, double c) { 754fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.com return AlmostBetweenUlps(SkDoubleToScalar(a), SkDoubleToScalar(b), SkDoubleToScalar(c)); 764fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.com} 774fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.com 784fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.comint UlpsDistance(float a, float b); 794fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.cominline int UlpsDistance(double a, double b) { 804fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.com return UlpsDistance(SkDoubleToScalar(a), SkDoubleToScalar(b)); 81fa2aeee27af27f2934ee52a9732148f66481fb03caryclark@google.com} 82fa2aeee27af27f2934ee52a9732148f66481fb03caryclark@google.com 8307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com// FLT_EPSILON == 1.19209290E-07 == 1 / (2 ^ 23) 8407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com// DBL_EPSILON == 2.22045e-16 8507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comconst double FLT_EPSILON_CUBED = FLT_EPSILON * FLT_EPSILON * FLT_EPSILON; 8607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comconst double FLT_EPSILON_HALF = FLT_EPSILON / 2; 87cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.comconst double FLT_EPSILON_DOUBLE = FLT_EPSILON * 2; 8807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comconst double FLT_EPSILON_SQUARED = FLT_EPSILON * FLT_EPSILON; 8907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comconst double FLT_EPSILON_SQRT = sqrt(FLT_EPSILON); 9007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comconst double FLT_EPSILON_INVERSE = 1 / FLT_EPSILON; 9107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comconst double DBL_EPSILON_ERR = DBL_EPSILON * 4; // FIXME: tune -- allow a few bits of error 92cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.comconst double DBL_EPSILON_SUBDIVIDE_ERR = DBL_EPSILON * 16; 9307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comconst double ROUGH_EPSILON = FLT_EPSILON * 64; 9407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comconst double MORE_ROUGH_EPSILON = FLT_EPSILON * 256; 9507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 9607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_zero(double x) { 9707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return fabs(x) < FLT_EPSILON; 9807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 9907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 10007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool precisely_zero(double x) { 10107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return fabs(x) < DBL_EPSILON_ERR; 10207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 10307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 104cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.cominline bool precisely_subdivide_zero(double x) { 105cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.com return fabs(x) < DBL_EPSILON_SUBDIVIDE_ERR; 106cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.com} 107cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.com 10807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_zero(float x) { 10907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return fabs(x) < FLT_EPSILON; 11007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 11107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 11207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_zero_cubed(double x) { 11307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return fabs(x) < FLT_EPSILON_CUBED; 11407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 11507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 11607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_zero_half(double x) { 11707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return fabs(x) < FLT_EPSILON_HALF; 11807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 11907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 120cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.cominline bool approximately_zero_double(double x) { 121cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.com return fabs(x) < FLT_EPSILON_DOUBLE; 122cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.com} 123cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.com 12407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_zero_squared(double x) { 12507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return fabs(x) < FLT_EPSILON_SQUARED; 12607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 12707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 12807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_zero_sqrt(double x) { 12907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return fabs(x) < FLT_EPSILON_SQRT; 13007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 13107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 132cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.cominline bool roughly_zero(double x) { 133cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.com return fabs(x) < ROUGH_EPSILON; 134cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.com} 135cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.com 13607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_zero_inverse(double x) { 13707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return fabs(x) > FLT_EPSILON_INVERSE; 13807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 13907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 14007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com// OPTIMIZATION: if called multiple times with the same denom, we want to pass 1/y instead 14107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_zero_when_compared_to(double x, double y) { 14207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return x == 0 || fabs(x / y) < FLT_EPSILON; 14307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 14407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 14507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com// Use this for comparing Ts in the range of 0 to 1. For general numbers (larger and smaller) use 14607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com// AlmostEqualUlps instead. 14707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_equal(double x, double y) { 14807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return approximately_zero(x - y); 14907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 15007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 15107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool precisely_equal(double x, double y) { 15207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return precisely_zero(x - y); 15307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 15407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 155cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.cominline bool precisely_subdivide_equal(double x, double y) { 156cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.com return precisely_subdivide_zero(x - y); 157cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.com} 158cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.com 15907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_equal_half(double x, double y) { 16007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return approximately_zero_half(x - y); 16107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 16207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 163cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.cominline bool approximately_equal_double(double x, double y) { 164cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.com return approximately_zero_double(x - y); 165cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.com} 166cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.com 16707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_equal_squared(double x, double y) { 16807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return approximately_equal(x, y); 16907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 17007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 17107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_greater(double x, double y) { 17207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return x - FLT_EPSILON >= y; 17307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 17407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 17507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_greater_or_equal(double x, double y) { 17607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return x + FLT_EPSILON > y; 17707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 17807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 17907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_lesser(double x, double y) { 18007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return x + FLT_EPSILON <= y; 18107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 18207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 18307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_lesser_or_equal(double x, double y) { 18407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return x - FLT_EPSILON < y; 18507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 18607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 18707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_greater_than_one(double x) { 18807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return x > 1 - FLT_EPSILON; 18907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 19007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 19107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool precisely_greater_than_one(double x) { 19207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return x > 1 - DBL_EPSILON_ERR; 19307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 19407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 19507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_less_than_zero(double x) { 19607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return x < FLT_EPSILON; 19707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 19807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 19907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool precisely_less_than_zero(double x) { 20007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return x < DBL_EPSILON_ERR; 20107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 20207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 20307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_negative(double x) { 20407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return x < FLT_EPSILON; 20507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 20607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 20707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool precisely_negative(double x) { 20807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return x < DBL_EPSILON_ERR; 20907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 21007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 21107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_one_or_less(double x) { 21207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return x < 1 + FLT_EPSILON; 21307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 21407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 21507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_positive(double x) { 21607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return x > -FLT_EPSILON; 21707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 21807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 21907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_positive_squared(double x) { 22007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return x > -(FLT_EPSILON_SQUARED); 22107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 22207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 22307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_zero_or_more(double x) { 22407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return x > -FLT_EPSILON; 22507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 22607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 22707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_between(double a, double b, double c) { 22807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return a <= c ? approximately_negative(a - b) && approximately_negative(b - c) 22907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com : approximately_negative(b - a) && approximately_negative(c - b); 23007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 2310361032c0b53401030a720bc8b4930c3ec59f19ecaryclark@google.com 2320361032c0b53401030a720bc8b4930c3ec59f19ecaryclark@google.cominline bool precisely_between(double a, double b, double c) { 2330361032c0b53401030a720bc8b4930c3ec59f19ecaryclark@google.com return a <= c ? precisely_negative(a - b) && precisely_negative(b - c) 2340361032c0b53401030a720bc8b4930c3ec59f19ecaryclark@google.com : precisely_negative(b - a) && precisely_negative(c - b); 2350361032c0b53401030a720bc8b4930c3ec59f19ecaryclark@google.com} 23607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 23707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com// returns true if (a <= b <= c) || (a >= b >= c) 23807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool between(double a, double b, double c) { 23907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com SkASSERT(((a <= b && b <= c) || (a >= b && b >= c)) == ((a - b) * (c - b) <= 0)); 24007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return (a - b) * (c - b) <= 0; 24107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 24207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 24307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool more_roughly_equal(double x, double y) { 24407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return fabs(x - y) < MORE_ROUGH_EPSILON; 24507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 24607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 24707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool roughly_equal(double x, double y) { 24807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return fabs(x - y) < ROUGH_EPSILON; 24907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 25007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 25107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comstruct SkDPoint; 25207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comstruct SkDVector; 25307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comstruct SkDLine; 25407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comstruct SkDQuad; 25507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comstruct SkDTriangle; 25607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comstruct SkDCubic; 25707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comstruct SkDRect; 25807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 259277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.cominline SkPath::Verb SkPathOpsPointsToVerb(int points) { 260277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com int verb = (1 << points) >> 1; 261277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com#ifdef SK_DEBUG 262277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com switch (points) { 263277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com case 0: SkASSERT(SkPath::kMove_Verb == verb); break; 264277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com case 1: SkASSERT(SkPath::kLine_Verb == verb); break; 265277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com case 2: SkASSERT(SkPath::kQuad_Verb == verb); break; 266277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com case 3: SkASSERT(SkPath::kCubic_Verb == verb); break; 267330313a8a8343876ee596da39da06a5d69badd9cmtklein@google.com default: SkDEBUGFAIL("should not be here"); 268277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com } 269277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com#endif 270277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com return (SkPath::Verb)verb; 271277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com} 272277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com 273277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.cominline int SkPathOpsVerbToPoints(SkPath::Verb verb) { 274277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com int points = (int) verb - ((int) verb >> 2); 275277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com#ifdef SK_DEBUG 276277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com switch (verb) { 277277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com case SkPath::kLine_Verb: SkASSERT(1 == points); break; 278277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com case SkPath::kQuad_Verb: SkASSERT(2 == points); break; 279277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com case SkPath::kCubic_Verb: SkASSERT(3 == points); break; 280330313a8a8343876ee596da39da06a5d69badd9cmtklein@google.com default: SkDEBUGFAIL("should not get here"); 281277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com } 282277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com#endif 283277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com return points; 284277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com} 285277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com 28607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline double SkDInterp(double A, double B, double t) { 28707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return A + (B - A) * t; 28807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 28907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 29007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comdouble SkDCubeRoot(double x); 29107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 29207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com/* Returns -1 if negative, 0 if zero, 1 if positive 29307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com*/ 29407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline int SkDSign(double x) { 29507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return (x > 0) - (x < 0); 29607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 29707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 29807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com/* Returns 0 if negative, 1 if zero, 2 if positive 29907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com*/ 30007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline int SKDSide(double x) { 30107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return (x > 0) + (x >= 0); 30207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 30307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 30407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com/* Returns 1 if negative, 2 if zero, 4 if positive 30507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com*/ 30607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline int SkDSideBit(double x) { 30707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return 1 << SKDSide(x); 30807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 30907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 310fa2aeee27af27f2934ee52a9732148f66481fb03caryclark@google.cominline double SkPinT(double t) { 311fa2aeee27af27f2934ee52a9732148f66481fb03caryclark@google.com return precisely_less_than_zero(t) ? 0 : precisely_greater_than_one(t) ? 1 : t; 312fa2aeee27af27f2934ee52a9732148f66481fb03caryclark@google.com} 313fa2aeee27af27f2934ee52a9732148f66481fb03caryclark@google.com 314570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com#ifdef SK_DEBUG 315570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.cominline void DebugDumpDouble(double x) { 316570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com if (x == floor(x)) { 317570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com SkDebugf("%.0f", x); 318570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com } else { 319570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com SkDebugf("%1.17g", x); 320570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com } 321570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com} 322570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com 323570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.cominline void DebugDumpFloat(float x) { 324570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com if (x == floorf(x)) { 325570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com SkDebugf("%.0f", x); 326570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com } else { 327570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com SkDebugf("%1.9gf", x); 328570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com } 329570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com} 330570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com#endif 331570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com 33207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com#endif 333