SkPathOpsTypes.h revision 570863f2e22b8ea7d7c504bd15e4f766af097df2
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 31570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.combool NotAlmostEqualUlps(float a, float b); 32570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.cominline bool NotAlmostEqualUlps(double a, double b) { 33570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com return NotAlmostEqualUlps(SkDoubleToScalar(a), SkDoubleToScalar(b)); 34570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com} 35570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com 36570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com// Use Almost Bequal when comparing coordinates in conjunction with between. 37570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.combool AlmostBequalUlps(float a, float b); 38570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.cominline bool AlmostBequalUlps(double a, double b) { 39570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com return AlmostBequalUlps(SkDoubleToScalar(a), SkDoubleToScalar(b)); 40570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com} 41570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com 424fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.combool RoughlyEqualUlps(float a, float b); 434fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.cominline bool RoughlyEqualUlps(double a, double b) { 444fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.com return RoughlyEqualUlps(SkDoubleToScalar(a), SkDoubleToScalar(b)); 4507e97fccd2d85076cd22ef411b0773ab92a18abecaryclark@google.com} 4607e97fccd2d85076cd22ef411b0773ab92a18abecaryclark@google.com 47570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.combool AlmostLessUlps(float a, float b); 48570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.cominline bool AlmostLessUlps(double a, double b) { 49570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com return AlmostLessUlps(SkDoubleToScalar(a), SkDoubleToScalar(b)); 50570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com} 51570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com 52570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.combool AlmostLessOrEqualUlps(float a, float b); 53570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.cominline bool AlmostLessOrEqualUlps(double a, double b) { 54570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com return AlmostLessOrEqualUlps(SkDoubleToScalar(a), SkDoubleToScalar(b)); 55570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com} 56570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com 57fa2aeee27af27f2934ee52a9732148f66481fb03caryclark@google.combool AlmostBetweenUlps(float a, float b, float c); 584fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.cominline bool AlmostBetweenUlps(double a, double b, double c) { 594fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.com return AlmostBetweenUlps(SkDoubleToScalar(a), SkDoubleToScalar(b), SkDoubleToScalar(c)); 604fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.com} 614fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.com 624fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.comint UlpsDistance(float a, float b); 634fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.cominline int UlpsDistance(double a, double b) { 644fdbb229649caf74e5c1b55a1823926df903af34caryclark@google.com return UlpsDistance(SkDoubleToScalar(a), SkDoubleToScalar(b)); 65fa2aeee27af27f2934ee52a9732148f66481fb03caryclark@google.com} 66fa2aeee27af27f2934ee52a9732148f66481fb03caryclark@google.com 6707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com// FLT_EPSILON == 1.19209290E-07 == 1 / (2 ^ 23) 6807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com// DBL_EPSILON == 2.22045e-16 6907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comconst double FLT_EPSILON_CUBED = FLT_EPSILON * FLT_EPSILON * FLT_EPSILON; 7007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comconst double FLT_EPSILON_HALF = FLT_EPSILON / 2; 71cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.comconst double FLT_EPSILON_DOUBLE = FLT_EPSILON * 2; 7207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comconst double FLT_EPSILON_SQUARED = FLT_EPSILON * FLT_EPSILON; 7307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comconst double FLT_EPSILON_SQRT = sqrt(FLT_EPSILON); 7407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comconst double FLT_EPSILON_INVERSE = 1 / FLT_EPSILON; 7507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comconst double DBL_EPSILON_ERR = DBL_EPSILON * 4; // FIXME: tune -- allow a few bits of error 76cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.comconst double DBL_EPSILON_SUBDIVIDE_ERR = DBL_EPSILON * 16; 7707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comconst double ROUGH_EPSILON = FLT_EPSILON * 64; 7807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comconst double MORE_ROUGH_EPSILON = FLT_EPSILON * 256; 7907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 8007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_zero(double x) { 8107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return fabs(x) < FLT_EPSILON; 8207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 8307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 8407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool precisely_zero(double x) { 8507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return fabs(x) < DBL_EPSILON_ERR; 8607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 8707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 88cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.cominline bool precisely_subdivide_zero(double x) { 89cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.com return fabs(x) < DBL_EPSILON_SUBDIVIDE_ERR; 90cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.com} 91cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.com 9207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_zero(float x) { 9307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return fabs(x) < FLT_EPSILON; 9407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 9507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 9607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_zero_cubed(double x) { 9707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return fabs(x) < FLT_EPSILON_CUBED; 9807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 9907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 10007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_zero_half(double x) { 10107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return fabs(x) < FLT_EPSILON_HALF; 10207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 10307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 104cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.cominline bool approximately_zero_double(double x) { 105cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.com return fabs(x) < FLT_EPSILON_DOUBLE; 106cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.com} 107cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.com 10807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_zero_squared(double x) { 10907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return fabs(x) < FLT_EPSILON_SQUARED; 11007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 11107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 11207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_zero_sqrt(double x) { 11307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return fabs(x) < FLT_EPSILON_SQRT; 11407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 11507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 116cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.cominline bool roughly_zero(double x) { 117cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.com return fabs(x) < ROUGH_EPSILON; 118cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.com} 119cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.com 12007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_zero_inverse(double x) { 12107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return fabs(x) > FLT_EPSILON_INVERSE; 12207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 12307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 12407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com// OPTIMIZATION: if called multiple times with the same denom, we want to pass 1/y instead 12507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_zero_when_compared_to(double x, double y) { 12607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return x == 0 || fabs(x / y) < FLT_EPSILON; 12707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 12807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 12907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com// Use this for comparing Ts in the range of 0 to 1. For general numbers (larger and smaller) use 13007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com// AlmostEqualUlps instead. 13107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_equal(double x, double y) { 13207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return approximately_zero(x - y); 13307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 13407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 13507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool precisely_equal(double x, double y) { 13607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return precisely_zero(x - y); 13707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 13807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 139cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.cominline bool precisely_subdivide_equal(double x, double y) { 140cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.com return precisely_subdivide_zero(x - y); 141cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.com} 142cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.com 14307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_equal_half(double x, double y) { 14407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return approximately_zero_half(x - y); 14507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 14607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 147cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.cominline bool approximately_equal_double(double x, double y) { 148cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.com return approximately_zero_double(x - y); 149cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.com} 150cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.com 15107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_equal_squared(double x, double y) { 15207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return approximately_equal(x, y); 15307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 15407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 15507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_greater(double x, double y) { 15607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return x - FLT_EPSILON >= y; 15707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 15807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 15907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_greater_or_equal(double x, double y) { 16007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return x + FLT_EPSILON > y; 16107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 16207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 16307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_lesser(double x, double y) { 16407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return x + FLT_EPSILON <= y; 16507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 16607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 16707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_lesser_or_equal(double x, double y) { 16807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return x - FLT_EPSILON < y; 16907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 17007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 17107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_greater_than_one(double x) { 17207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return x > 1 - FLT_EPSILON; 17307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 17407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 17507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool precisely_greater_than_one(double x) { 17607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return x > 1 - DBL_EPSILON_ERR; 17707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 17807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 17907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_less_than_zero(double x) { 18007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return x < FLT_EPSILON; 18107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 18207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 18307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool precisely_less_than_zero(double x) { 18407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return x < DBL_EPSILON_ERR; 18507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 18607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 18707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_negative(double x) { 18807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return x < FLT_EPSILON; 18907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 19007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 19107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool precisely_negative(double x) { 19207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return x < DBL_EPSILON_ERR; 19307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 19407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 19507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_one_or_less(double x) { 19607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return x < 1 + FLT_EPSILON; 19707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 19807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 19907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_positive(double x) { 20007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return x > -FLT_EPSILON; 20107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 20207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 20307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_positive_squared(double x) { 20407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return x > -(FLT_EPSILON_SQUARED); 20507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 20607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 20707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_zero_or_more(double x) { 20807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return x > -FLT_EPSILON; 20907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 21007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 21107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_between(double a, double b, double c) { 21207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return a <= c ? approximately_negative(a - b) && approximately_negative(b - c) 21307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com : approximately_negative(b - a) && approximately_negative(c - b); 21407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 2150361032c0b53401030a720bc8b4930c3ec59f19ecaryclark@google.com 2160361032c0b53401030a720bc8b4930c3ec59f19ecaryclark@google.cominline bool precisely_between(double a, double b, double c) { 2170361032c0b53401030a720bc8b4930c3ec59f19ecaryclark@google.com return a <= c ? precisely_negative(a - b) && precisely_negative(b - c) 2180361032c0b53401030a720bc8b4930c3ec59f19ecaryclark@google.com : precisely_negative(b - a) && precisely_negative(c - b); 2190361032c0b53401030a720bc8b4930c3ec59f19ecaryclark@google.com} 22007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 22107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com// returns true if (a <= b <= c) || (a >= b >= c) 22207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool between(double a, double b, double c) { 22307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com SkASSERT(((a <= b && b <= c) || (a >= b && b >= c)) == ((a - b) * (c - b) <= 0)); 22407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return (a - b) * (c - b) <= 0; 22507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 22607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 22707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool more_roughly_equal(double x, double y) { 22807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return fabs(x - y) < MORE_ROUGH_EPSILON; 22907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 23007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 23107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool roughly_equal(double x, double y) { 23207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return fabs(x - y) < ROUGH_EPSILON; 23307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 23407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 23507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comstruct SkDPoint; 23607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comstruct SkDVector; 23707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comstruct SkDLine; 23807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comstruct SkDQuad; 23907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comstruct SkDTriangle; 24007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comstruct SkDCubic; 24107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comstruct SkDRect; 24207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 243277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.cominline SkPath::Verb SkPathOpsPointsToVerb(int points) { 244277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com int verb = (1 << points) >> 1; 245277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com#ifdef SK_DEBUG 246277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com switch (points) { 247277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com case 0: SkASSERT(SkPath::kMove_Verb == verb); break; 248277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com case 1: SkASSERT(SkPath::kLine_Verb == verb); break; 249277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com case 2: SkASSERT(SkPath::kQuad_Verb == verb); break; 250277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com case 3: SkASSERT(SkPath::kCubic_Verb == verb); break; 251330313a8a8343876ee596da39da06a5d69badd9cmtklein@google.com default: SkDEBUGFAIL("should not be here"); 252277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com } 253277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com#endif 254277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com return (SkPath::Verb)verb; 255277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com} 256277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com 257277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.cominline int SkPathOpsVerbToPoints(SkPath::Verb verb) { 258277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com int points = (int) verb - ((int) verb >> 2); 259277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com#ifdef SK_DEBUG 260277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com switch (verb) { 261277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com case SkPath::kLine_Verb: SkASSERT(1 == points); break; 262277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com case SkPath::kQuad_Verb: SkASSERT(2 == points); break; 263277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com case SkPath::kCubic_Verb: SkASSERT(3 == points); break; 264330313a8a8343876ee596da39da06a5d69badd9cmtklein@google.com default: SkDEBUGFAIL("should not get here"); 265277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com } 266277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com#endif 267277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com return points; 268277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com} 269277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com 27007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline double SkDInterp(double A, double B, double t) { 27107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return A + (B - A) * t; 27207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 27307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 27407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comdouble SkDCubeRoot(double x); 27507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 27607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com/* Returns -1 if negative, 0 if zero, 1 if positive 27707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com*/ 27807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline int SkDSign(double x) { 27907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return (x > 0) - (x < 0); 28007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 28107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 28207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com/* Returns 0 if negative, 1 if zero, 2 if positive 28307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com*/ 28407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline int SKDSide(double x) { 28507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return (x > 0) + (x >= 0); 28607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 28707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 28807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com/* Returns 1 if negative, 2 if zero, 4 if positive 28907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com*/ 29007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline int SkDSideBit(double x) { 29107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return 1 << SKDSide(x); 29207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 29307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 294fa2aeee27af27f2934ee52a9732148f66481fb03caryclark@google.cominline double SkPinT(double t) { 295fa2aeee27af27f2934ee52a9732148f66481fb03caryclark@google.com return precisely_less_than_zero(t) ? 0 : precisely_greater_than_one(t) ? 1 : t; 296fa2aeee27af27f2934ee52a9732148f66481fb03caryclark@google.com} 297fa2aeee27af27f2934ee52a9732148f66481fb03caryclark@google.com 298570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com#ifdef SK_DEBUG 299570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.cominline void DebugDumpDouble(double x) { 300570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com if (x == floor(x)) { 301570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com SkDebugf("%.0f", x); 302570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com } else { 303570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com SkDebugf("%1.17g", x); 304570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com } 305570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com} 306570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com 307570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.cominline void DebugDumpFloat(float x) { 308570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com if (x == floorf(x)) { 309570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com SkDebugf("%.0f", x); 310570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com } else { 311570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com SkDebugf("%1.9gf", x); 312570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com } 313570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com} 314570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com#endif 315570863f2e22b8ea7d7c504bd15e4f766af097df2caryclark@google.com 31607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com#endif 317