SkPathOpsTypes.h revision fa2aeee27af27f2934ee52a9732148f66481fb03
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. 26cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.combool AlmostEqualUlps(float A, float B); 2707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool AlmostEqualUlps(double A, double B) { 2807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return AlmostEqualUlps(SkDoubleToScalar(A), SkDoubleToScalar(B)); 2907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 3007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 3107e97fccd2d85076cd22ef411b0773ab92a18abecaryclark@google.combool RoughlyEqualUlps(float A, float B); 3207e97fccd2d85076cd22ef411b0773ab92a18abecaryclark@google.cominline bool RoughlyEqualUlps(double A, double B) { 3307e97fccd2d85076cd22ef411b0773ab92a18abecaryclark@google.com return RoughlyEqualUlps(SkDoubleToScalar(A), SkDoubleToScalar(B)); 3407e97fccd2d85076cd22ef411b0773ab92a18abecaryclark@google.com} 3507e97fccd2d85076cd22ef411b0773ab92a18abecaryclark@google.com 36fa2aeee27af27f2934ee52a9732148f66481fb03caryclark@google.combool AlmostBetweenUlps(float a, float b, float c); 37fa2aeee27af27f2934ee52a9732148f66481fb03caryclark@google.cominline bool AlmostBetweenUlps(double A, double B, double C) { 38fa2aeee27af27f2934ee52a9732148f66481fb03caryclark@google.com return AlmostBetweenUlps(SkDoubleToScalar(A), SkDoubleToScalar(B), SkDoubleToScalar(C)); 39fa2aeee27af27f2934ee52a9732148f66481fb03caryclark@google.com} 40fa2aeee27af27f2934ee52a9732148f66481fb03caryclark@google.com 4107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com// FLT_EPSILON == 1.19209290E-07 == 1 / (2 ^ 23) 4207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com// DBL_EPSILON == 2.22045e-16 4307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comconst double FLT_EPSILON_CUBED = FLT_EPSILON * FLT_EPSILON * FLT_EPSILON; 4407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comconst double FLT_EPSILON_HALF = FLT_EPSILON / 2; 45cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.comconst double FLT_EPSILON_DOUBLE = FLT_EPSILON * 2; 4607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comconst double FLT_EPSILON_SQUARED = FLT_EPSILON * FLT_EPSILON; 4707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comconst double FLT_EPSILON_SQRT = sqrt(FLT_EPSILON); 4807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comconst double FLT_EPSILON_INVERSE = 1 / FLT_EPSILON; 4907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comconst double DBL_EPSILON_ERR = DBL_EPSILON * 4; // FIXME: tune -- allow a few bits of error 50cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.comconst double DBL_EPSILON_SUBDIVIDE_ERR = DBL_EPSILON * 16; 5107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comconst double ROUGH_EPSILON = FLT_EPSILON * 64; 5207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comconst double MORE_ROUGH_EPSILON = FLT_EPSILON * 256; 5307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 5407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_zero(double x) { 5507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return fabs(x) < FLT_EPSILON; 5607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 5707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 5807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool precisely_zero(double x) { 5907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return fabs(x) < DBL_EPSILON_ERR; 6007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 6107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 62cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.cominline bool precisely_subdivide_zero(double x) { 63cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.com return fabs(x) < DBL_EPSILON_SUBDIVIDE_ERR; 64cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.com} 65cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.com 6607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_zero(float x) { 6707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return fabs(x) < FLT_EPSILON; 6807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 6907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 7007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_zero_cubed(double x) { 7107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return fabs(x) < FLT_EPSILON_CUBED; 7207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 7307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 7407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_zero_half(double x) { 7507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return fabs(x) < FLT_EPSILON_HALF; 7607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 7707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 78cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.cominline bool approximately_zero_double(double x) { 79cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.com return fabs(x) < FLT_EPSILON_DOUBLE; 80cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.com} 81cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.com 8207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_zero_squared(double x) { 8307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return fabs(x) < FLT_EPSILON_SQUARED; 8407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 8507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 8607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_zero_sqrt(double x) { 8707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return fabs(x) < FLT_EPSILON_SQRT; 8807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 8907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 90cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.cominline bool roughly_zero(double x) { 91cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.com return fabs(x) < ROUGH_EPSILON; 92cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.com} 93cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.com 9407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_zero_inverse(double x) { 9507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return fabs(x) > FLT_EPSILON_INVERSE; 9607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 9707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 9807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com// OPTIMIZATION: if called multiple times with the same denom, we want to pass 1/y instead 9907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_zero_when_compared_to(double x, double y) { 10007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return x == 0 || fabs(x / y) < FLT_EPSILON; 10107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 10207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 10307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com// Use this for comparing Ts in the range of 0 to 1. For general numbers (larger and smaller) use 10407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com// AlmostEqualUlps instead. 10507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_equal(double x, double y) { 10607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return approximately_zero(x - y); 10707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 10807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 10907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool precisely_equal(double x, double y) { 11007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return precisely_zero(x - y); 11107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 11207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 113cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.cominline bool precisely_subdivide_equal(double x, double y) { 114cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.com return precisely_subdivide_zero(x - y); 115cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.com} 116cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.com 11707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_equal_half(double x, double y) { 11807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return approximately_zero_half(x - y); 11907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 12007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 121cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.cominline bool approximately_equal_double(double x, double y) { 122cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.com return approximately_zero_double(x - y); 123cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.com} 124cffbcc3b9665f2c928544b6fc6b8a0e22a4210fbcaryclark@google.com 12507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_equal_squared(double x, double y) { 12607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return approximately_equal(x, y); 12707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 12807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 12907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_greater(double x, double y) { 13007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return x - FLT_EPSILON >= y; 13107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 13207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 13307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_greater_or_equal(double x, double y) { 13407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return x + FLT_EPSILON > y; 13507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 13607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 13707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_lesser(double x, double y) { 13807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return x + FLT_EPSILON <= y; 13907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 14007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 14107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_lesser_or_equal(double x, double y) { 14207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return x - FLT_EPSILON < y; 14307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 14407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 14507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_greater_than_one(double x) { 14607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return x > 1 - FLT_EPSILON; 14707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 14807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 14907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool precisely_greater_than_one(double x) { 15007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return x > 1 - DBL_EPSILON_ERR; 15107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 15207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 15307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_less_than_zero(double x) { 15407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return x < FLT_EPSILON; 15507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 15607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 15707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool precisely_less_than_zero(double x) { 15807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return x < DBL_EPSILON_ERR; 15907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 16007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 16107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_negative(double x) { 16207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return x < FLT_EPSILON; 16307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 16407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 16507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool precisely_negative(double x) { 16607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return x < DBL_EPSILON_ERR; 16707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 16807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 16907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_one_or_less(double x) { 17007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return x < 1 + FLT_EPSILON; 17107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 17207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 17307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_positive(double x) { 17407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return x > -FLT_EPSILON; 17507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 17607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 17707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_positive_squared(double x) { 17807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return x > -(FLT_EPSILON_SQUARED); 17907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 18007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 18107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_zero_or_more(double x) { 18207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return x > -FLT_EPSILON; 18307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 18407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 18507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool approximately_between(double a, double b, double c) { 18607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return a <= c ? approximately_negative(a - b) && approximately_negative(b - c) 18707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com : approximately_negative(b - a) && approximately_negative(c - b); 18807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 1890361032c0b53401030a720bc8b4930c3ec59f19ecaryclark@google.com 1900361032c0b53401030a720bc8b4930c3ec59f19ecaryclark@google.cominline bool precisely_between(double a, double b, double c) { 1910361032c0b53401030a720bc8b4930c3ec59f19ecaryclark@google.com return a <= c ? precisely_negative(a - b) && precisely_negative(b - c) 1920361032c0b53401030a720bc8b4930c3ec59f19ecaryclark@google.com : precisely_negative(b - a) && precisely_negative(c - b); 1930361032c0b53401030a720bc8b4930c3ec59f19ecaryclark@google.com} 19407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 19507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com// returns true if (a <= b <= c) || (a >= b >= c) 19607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool between(double a, double b, double c) { 19707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com SkASSERT(((a <= b && b <= c) || (a >= b && b >= c)) == ((a - b) * (c - b) <= 0)); 19807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return (a - b) * (c - b) <= 0; 19907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 20007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 20107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool more_roughly_equal(double x, double y) { 20207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return fabs(x - y) < MORE_ROUGH_EPSILON; 20307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 20407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 20507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline bool roughly_equal(double x, double y) { 20607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return fabs(x - y) < ROUGH_EPSILON; 20707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 20807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 20907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comstruct SkDPoint; 21007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comstruct SkDVector; 21107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comstruct SkDLine; 21207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comstruct SkDQuad; 21307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comstruct SkDTriangle; 21407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comstruct SkDCubic; 21507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comstruct SkDRect; 21607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 217277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.cominline SkPath::Verb SkPathOpsPointsToVerb(int points) { 218277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com int verb = (1 << points) >> 1; 219277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com#ifdef SK_DEBUG 220277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com switch (points) { 221277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com case 0: SkASSERT(SkPath::kMove_Verb == verb); break; 222277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com case 1: SkASSERT(SkPath::kLine_Verb == verb); break; 223277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com case 2: SkASSERT(SkPath::kQuad_Verb == verb); break; 224277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com case 3: SkASSERT(SkPath::kCubic_Verb == verb); break; 225277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com default: SkASSERT(!"should not be here"); 226277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com } 227277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com#endif 228277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com return (SkPath::Verb)verb; 229277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com} 230277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com 231277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.cominline int SkPathOpsVerbToPoints(SkPath::Verb verb) { 232277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com int points = (int) verb - ((int) verb >> 2); 233277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com#ifdef SK_DEBUG 234277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com switch (verb) { 235277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com case SkPath::kLine_Verb: SkASSERT(1 == points); break; 236277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com case SkPath::kQuad_Verb: SkASSERT(2 == points); break; 237277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com case SkPath::kCubic_Verb: SkASSERT(3 == points); break; 238277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com default: SkASSERT(!"should not get here"); 239277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com } 240277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com#endif 241277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com return points; 242277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com} 243277c3f87656c44e0a651ed0dd56efa16c0ab07b4reed@google.com 24407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline double SkDInterp(double A, double B, double t) { 24507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return A + (B - A) * t; 24607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 24707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 24807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.comdouble SkDCubeRoot(double x); 24907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 25007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com/* Returns -1 if negative, 0 if zero, 1 if positive 25107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com*/ 25207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline int SkDSign(double x) { 25307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return (x > 0) - (x < 0); 25407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 25507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 25607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com/* Returns 0 if negative, 1 if zero, 2 if positive 25707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com*/ 25807393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline int SKDSide(double x) { 25907393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return (x > 0) + (x >= 0); 26007393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 26107393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 26207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com/* Returns 1 if negative, 2 if zero, 4 if positive 26307393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com*/ 26407393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.cominline int SkDSideBit(double x) { 26507393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com return 1 << SKDSide(x); 26607393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com} 26707393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com 268fa2aeee27af27f2934ee52a9732148f66481fb03caryclark@google.cominline double SkPinT(double t) { 269fa2aeee27af27f2934ee52a9732148f66481fb03caryclark@google.com return precisely_less_than_zero(t) ? 0 : precisely_greater_than_one(t) ? 1 : t; 270fa2aeee27af27f2934ee52a9732148f66481fb03caryclark@google.com} 271fa2aeee27af27f2934ee52a9732148f66481fb03caryclark@google.com 27207393cab57ce74a4aae89a31fae9aaa9780fc19dcaryclark@google.com#endif 273