SkPathOpsTypes.h revision 2db7fe7d3b7ee875e1099a22f0af17520696f5d7
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); 332db7fe7d3b7ee875e1099a22f0af17520696f5d7commit-bot@chromium.orgbool AlmostDequalUlps(double a, double b); 347eaa53d8f7e48fd17d02b5e3bd91f90e9c1899efcaryclark@google.com 35570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.combool NotAlmostEqualUlps(float a, float b); 36570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.cominline bool NotAlmostEqualUlps(double a, double b) { 37570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com return NotAlmostEqualUlps(SkDoubleToScalar(a), SkDoubleToScalar(b)); 38570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com} 39570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com 407eaa53d8f7e48fd17d02b5e3bd91f90e9c1899efcaryclark@google.combool NotAlmostDequalUlps(float a, float b); 417eaa53d8f7e48fd17d02b5e3bd91f90e9c1899efcaryclark@google.cominline bool NotAlmostDequalUlps(double a, double b) { 427eaa53d8f7e48fd17d02b5e3bd91f90e9c1899efcaryclark@google.com return NotAlmostDequalUlps(SkDoubleToScalar(a), SkDoubleToScalar(b)); 437eaa53d8f7e48fd17d02b5e3bd91f90e9c1899efcaryclark@google.com} 447eaa53d8f7e48fd17d02b5e3bd91f90e9c1899efcaryclark@google.com 45570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com// Use Almost Bequal when comparing coordinates in conjunction with between. 46570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.combool AlmostBequalUlps(float a, float b); 47570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.cominline bool AlmostBequalUlps(double a, double b) { 48570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com return AlmostBequalUlps(SkDoubleToScalar(a), SkDoubleToScalar(b)); 49570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com} 50570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com 51a2bbc6e19d5332e81784e582c290cc060f40c4c7caryclark@google.combool AlmostPequalUlps(float a, float b); 52a2bbc6e19d5332e81784e582c290cc060f40c4c7caryclark@google.cominline bool AlmostPequalUlps(double a, double b) { 53a2bbc6e19d5332e81784e582c290cc060f40c4c7caryclark@google.com return AlmostPequalUlps(SkDoubleToScalar(a), SkDoubleToScalar(b)); 54a2bbc6e19d5332e81784e582c290cc060f40c4c7caryclark@google.com} 55a2bbc6e19d5332e81784e582c290cc060f40c4c7caryclark@google.com 564fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.combool RoughlyEqualUlps(float a, float b); 574fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.cominline bool RoughlyEqualUlps(double a, double b) { 584fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.com return RoughlyEqualUlps(SkDoubleToScalar(a), SkDoubleToScalar(b)); 5907e97fccd2d85076cd22ef411b0773ab92a18abecaryclark@google.com} 6007e97fccd2d85076cd22ef411b0773ab92a18abecaryclark@google.com 61570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.combool AlmostLessUlps(float a, float b); 62570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.cominline bool AlmostLessUlps(double a, double b) { 63570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com return AlmostLessUlps(SkDoubleToScalar(a), SkDoubleToScalar(b)); 64570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com} 65570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com 66570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.combool AlmostLessOrEqualUlps(float a, float b); 67570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.cominline bool AlmostLessOrEqualUlps(double a, double b) { 68570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com return AlmostLessOrEqualUlps(SkDoubleToScalar(a), SkDoubleToScalar(b)); 69570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com} 70570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com 71fa2aeee27af27f2934ee52a9732148f66481fb03caryclark@google.combool AlmostBetweenUlps(float a, float b, float c); 724fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.cominline bool AlmostBetweenUlps(double a, double b, double c) { 734fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.com return AlmostBetweenUlps(SkDoubleToScalar(a), SkDoubleToScalar(b), SkDoubleToScalar(c)); 744fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.com} 754fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.com 764fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.comint UlpsDistance(float a, float b); 774fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.cominline int UlpsDistance(double a, double b) { 784fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.com return UlpsDistance(SkDoubleToScalar(a), SkDoubleToScalar(b)); 79fa2aeee27af27f2934ee52a9732148f66481fb03caryclark@google.com} 80fa2aeee27af27f2934ee52a9732148f66481fb03caryclark@google.com 8107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com// FLT_EPSILON == 1.19209290E-07 == 1 / (2 ^ 23) 8207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com// DBL_EPSILON == 2.22045e-16 8307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comconst double FLT_EPSILON_CUBED = FLT_EPSILON * FLT_EPSILON * FLT_EPSILON; 8407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comconst double FLT_EPSILON_HALF = FLT_EPSILON / 2; 85cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.comconst double FLT_EPSILON_DOUBLE = FLT_EPSILON * 2; 864431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.orgconst double FLT_EPSILON_ORDERABLE_ERR = FLT_EPSILON * 16; 8707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comconst double FLT_EPSILON_SQUARED = FLT_EPSILON * FLT_EPSILON; 8807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comconst double FLT_EPSILON_SQRT = sqrt(FLT_EPSILON); 8907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comconst double FLT_EPSILON_INVERSE = 1 / FLT_EPSILON; 9007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comconst double DBL_EPSILON_ERR = DBL_EPSILON * 4; // FIXME: tune -- allow a few bits of error 91cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.comconst double DBL_EPSILON_SUBDIVIDE_ERR = DBL_EPSILON * 16; 9207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comconst double ROUGH_EPSILON = FLT_EPSILON * 64; 9307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comconst double MORE_ROUGH_EPSILON = FLT_EPSILON * 256; 9407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 9507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_zero(double x) { 9607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return fabs(x) < FLT_EPSILON; 9707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 9807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 9907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool precisely_zero(double x) { 10007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return fabs(x) < DBL_EPSILON_ERR; 10107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 10207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 103cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.cominline bool precisely_subdivide_zero(double x) { 104cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.com return fabs(x) < DBL_EPSILON_SUBDIVIDE_ERR; 105cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.com} 106cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.com 10707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_zero(float x) { 10807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return fabs(x) < FLT_EPSILON; 10907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 11007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 11107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_zero_cubed(double x) { 11207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return fabs(x) < FLT_EPSILON_CUBED; 11307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 11407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 11507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_zero_half(double x) { 11607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return fabs(x) < FLT_EPSILON_HALF; 11707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 11807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 119cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.cominline bool approximately_zero_double(double x) { 120cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.com return fabs(x) < FLT_EPSILON_DOUBLE; 121cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.com} 122cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.com 1234431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.orginline bool approximately_zero_orderable(double x) { 1244431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org return fabs(x) < FLT_EPSILON_ORDERABLE_ERR; 1254431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org} 1264431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org 12707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_zero_squared(double x) { 12807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return fabs(x) < FLT_EPSILON_SQUARED; 12907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 13007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 13107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_zero_sqrt(double x) { 13207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return fabs(x) < FLT_EPSILON_SQRT; 13307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 13407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 135cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.cominline bool roughly_zero(double x) { 136cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.com return fabs(x) < ROUGH_EPSILON; 137cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.com} 138cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.com 13907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_zero_inverse(double x) { 14007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return fabs(x) > FLT_EPSILON_INVERSE; 14107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 14207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 14307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com// OPTIMIZATION: if called multiple times with the same denom, we want to pass 1/y instead 14407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_zero_when_compared_to(double x, double y) { 1454431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org return x == 0 || fabs(x) < fabs(y * FLT_EPSILON); 14607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 14707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 14807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com// Use this for comparing Ts in the range of 0 to 1. For general numbers (larger and smaller) use 14907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com// AlmostEqualUlps instead. 15007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_equal(double x, double y) { 15107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return approximately_zero(x - y); 15207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 15307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 15407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool precisely_equal(double x, double y) { 15507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return precisely_zero(x - y); 15607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 15707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 158cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.cominline bool precisely_subdivide_equal(double x, double y) { 159cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.com return precisely_subdivide_zero(x - y); 160cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.com} 161cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.com 16207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_equal_half(double x, double y) { 16307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return approximately_zero_half(x - y); 16407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 16507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 166cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.cominline bool approximately_equal_double(double x, double y) { 167cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.com return approximately_zero_double(x - y); 168cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.com} 169cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.com 1704431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.orginline bool approximately_equal_orderable(double x, double y) { 1714431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org return approximately_zero_orderable(x - y); 1724431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org} 1734431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org 17407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_equal_squared(double x, double y) { 17507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return approximately_equal(x, y); 17607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 17707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 17807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_greater(double x, double y) { 17907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return x - FLT_EPSILON >= y; 18007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 18107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 1824431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.orginline bool approximately_greater_double(double x, double y) { 1834431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org return x - FLT_EPSILON_DOUBLE >= y; 1844431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org} 1854431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org 1864431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.orginline bool approximately_greater_orderable(double x, double y) { 1874431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org return x - FLT_EPSILON_ORDERABLE_ERR >= y; 1884431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org} 1894431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org 19007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_greater_or_equal(double x, double y) { 19107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return x + FLT_EPSILON > y; 19207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 19307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 1944431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.orginline bool approximately_greater_or_equal_double(double x, double y) { 1954431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org return x + FLT_EPSILON_DOUBLE > y; 1964431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org} 1974431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org 1984431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.orginline bool approximately_greater_or_equal_orderable(double x, double y) { 1994431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org return x + FLT_EPSILON_ORDERABLE_ERR > y; 2004431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org} 2014431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org 20207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_lesser(double x, double y) { 20307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return x + FLT_EPSILON <= y; 20407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 20507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 2064431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.orginline bool approximately_lesser_double(double x, double y) { 2074431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org return x + FLT_EPSILON_DOUBLE <= y; 2084431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org} 2094431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org 2104431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.orginline bool approximately_lesser_orderable(double x, double y) { 2114431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org return x + FLT_EPSILON_ORDERABLE_ERR <= y; 2124431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org} 2134431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org 21407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_lesser_or_equal(double x, double y) { 21507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return x - FLT_EPSILON < y; 21607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 21707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 2184431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.orginline bool approximately_lesser_or_equal_double(double x, double y) { 2194431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org return x - FLT_EPSILON_DOUBLE < y; 2204431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org} 2214431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org 2224431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.orginline bool approximately_lesser_or_equal_orderable(double x, double y) { 2234431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org return x - FLT_EPSILON_ORDERABLE_ERR < y; 2244431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org} 2254431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org 22607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_greater_than_one(double x) { 22707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return x > 1 - FLT_EPSILON; 22807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 22907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 23007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool precisely_greater_than_one(double x) { 23107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return x > 1 - DBL_EPSILON_ERR; 23207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 23307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 23407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_less_than_zero(double x) { 23507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return x < FLT_EPSILON; 23607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 23707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 23807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool precisely_less_than_zero(double x) { 23907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return x < DBL_EPSILON_ERR; 24007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 24107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 24207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_negative(double x) { 24307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return x < FLT_EPSILON; 24407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 24507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 2464431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.orginline bool approximately_negative_orderable(double x) { 2474431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org return x < FLT_EPSILON_ORDERABLE_ERR; 2484431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org} 2494431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org 25007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool precisely_negative(double x) { 25107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return x < DBL_EPSILON_ERR; 25207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 25307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 25407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_one_or_less(double x) { 25507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return x < 1 + FLT_EPSILON; 25607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 25707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 2584431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.orginline bool approximately_one_or_less_double(double x) { 2594431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org return x < 1 + FLT_EPSILON_DOUBLE; 2604431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org} 2614431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org 26207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_positive(double x) { 26307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return x > -FLT_EPSILON; 26407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 26507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 26607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_positive_squared(double x) { 26707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return x > -(FLT_EPSILON_SQUARED); 26807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 26907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 27007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_zero_or_more(double x) { 27107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return x > -FLT_EPSILON; 27207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 27307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 2744431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.orginline bool approximately_zero_or_more_double(double x) { 2754431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org return x > -FLT_EPSILON_DOUBLE; 2764431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org} 2774431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org 2784431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.orginline bool approximately_between_orderable(double a, double b, double c) { 2794431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org return a <= c 2804431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org ? approximately_negative_orderable(a - b) && approximately_negative_orderable(b - c) 2814431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org : approximately_negative_orderable(b - a) && approximately_negative_orderable(c - b); 2824431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org} 2834431e7757cfcb8cfa99535eed0e9f156dabf95c2commit-bot@chromium.org 28407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_between(double a, double b, double c) { 28507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return a <= c ? approximately_negative(a - b) && approximately_negative(b - c) 28607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com : approximately_negative(b - a) && approximately_negative(c - b); 28707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 2880361032c0b53401030a720bc8b4930c3ec59f19ecaryclark@google.com 2890361032c0b53401030a720bc8b4930c3ec59f19ecaryclark@google.cominline bool precisely_between(double a, double b, double c) { 2900361032c0b53401030a720bc8b4930c3ec59f19ecaryclark@google.com return a <= c ? precisely_negative(a - b) && precisely_negative(b - c) 2910361032c0b53401030a720bc8b4930c3ec59f19ecaryclark@google.com : precisely_negative(b - a) && precisely_negative(c - b); 2920361032c0b53401030a720bc8b4930c3ec59f19ecaryclark@google.com} 29307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 29407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com// returns true if (a <= b <= c) || (a >= b >= c) 29507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool between(double a, double b, double c) { 29607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com SkASSERT(((a <= b && b <= c) || (a >= b && b >= c)) == ((a - b) * (c - b) <= 0)); 29707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return (a - b) * (c - b) <= 0; 29807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 29907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 30007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool more_roughly_equal(double x, double y) { 30107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return fabs(x - y) < MORE_ROUGH_EPSILON; 30207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 30307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 30407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool roughly_equal(double x, double y) { 30507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return fabs(x - y) < ROUGH_EPSILON; 30607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 30707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 30807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comstruct SkDPoint; 30907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comstruct SkDVector; 31007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comstruct SkDLine; 31107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comstruct SkDQuad; 31207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comstruct SkDTriangle; 31307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comstruct SkDCubic; 31407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comstruct SkDRect; 31507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 316277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.cominline SkPath::Verb SkPathOpsPointsToVerb(int points) { 317277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com int verb = (1 << points) >> 1; 318277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com#ifdef SK_DEBUG 319277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com switch (points) { 320277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com case 0: SkASSERT(SkPath::kMove_Verb == verb); break; 321277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com case 1: SkASSERT(SkPath::kLine_Verb == verb); break; 322277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com case 2: SkASSERT(SkPath::kQuad_Verb == verb); break; 323277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com case 3: SkASSERT(SkPath::kCubic_Verb == verb); break; 324330313a8a8343876ee596da39da06a5d69badd9cmtklein@google.com default: SkDEBUGFAIL("should not be here"); 325277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com } 326277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com#endif 327277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com return (SkPath::Verb)verb; 328277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com} 329277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com 330277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.cominline int SkPathOpsVerbToPoints(SkPath::Verb verb) { 331277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com int points = (int) verb - ((int) verb >> 2); 332277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com#ifdef SK_DEBUG 333277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com switch (verb) { 334277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com case SkPath::kLine_Verb: SkASSERT(1 == points); break; 335277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com case SkPath::kQuad_Verb: SkASSERT(2 == points); break; 336277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com case SkPath::kCubic_Verb: SkASSERT(3 == points); break; 337330313a8a8343876ee596da39da06a5d69badd9cmtklein@google.com default: SkDEBUGFAIL("should not get here"); 338277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com } 339277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com#endif 340277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com return points; 341277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com} 342277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com 34307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline double SkDInterp(double A, double B, double t) { 34407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return A + (B - A) * t; 34507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 34607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 34707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comdouble SkDCubeRoot(double x); 34807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 34907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com/* Returns -1 if negative, 0 if zero, 1 if positive 35007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com*/ 35107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline int SkDSign(double x) { 35207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return (x > 0) - (x < 0); 35307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 35407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 35507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com/* Returns 0 if negative, 1 if zero, 2 if positive 35607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com*/ 35707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline int SKDSide(double x) { 35807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return (x > 0) + (x >= 0); 35907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 36007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 36107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com/* Returns 1 if negative, 2 if zero, 4 if positive 36207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com*/ 36307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline int SkDSideBit(double x) { 36407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return 1 << SKDSide(x); 36507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 36607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 367fa2aeee27af27f2934ee52a9732148f66481fb03caryclark@google.cominline double SkPinT(double t) { 368fa2aeee27af27f2934ee52a9732148f66481fb03caryclark@google.com return precisely_less_than_zero(t) ? 0 : precisely_greater_than_one(t) ? 1 : t; 369fa2aeee27af27f2934ee52a9732148f66481fb03caryclark@google.com} 370fa2aeee27af27f2934ee52a9732148f66481fb03caryclark@google.com 37107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com#endif 372