1 /* 2 * Copyright 2023 Google LLC 3 * 4 * Use of this source code is governed by a BSD-style license that can be 5 * found in the LICENSE file. 6 */ 7 #ifndef SkCubics_DEFINED 8 #define SkCubics_DEFINED 9 10 #include <cmath> 11 12 /** 13 * Utilities for dealing with cubic formulas with one variable: 14 * f(t) = A*t^3 + B*t^2 + C*t + d 15 */ 16 class SkCubics { 17 public: 18 /** 19 * Puts up to 3 real solutions to the equation 20 * A*t^3 + B*t^2 + C*t + d = 0 21 * in the provided array and returns how many roots that was. 22 */ 23 static int RootsReal(double A, double B, double C, double D, 24 double solution[3]); 25 26 /** 27 * Puts up to 3 real solutions to the equation 28 * A*t^3 + B*t^2 + C*t + D = 0 29 * in the provided array, with the constraint that t is in the range [0.0, 1.0], 30 * and returns how many roots that was. 31 */ 32 static int RootsValidT(double A, double B, double C, double D, 33 double solution[3]); 34 35 36 /** 37 * Puts up to 3 real solutions to the equation 38 * A*t^3 + B*t^2 + C*t + D = 0 39 * in the provided array, with the constraint that t is in the range [0.0, 1.0], 40 * and returns how many roots that was. 41 * This is a slower method than RootsValidT, but more accurate in circumstances 42 * where floating point error gets too big. 43 */ 44 static int BinarySearchRootsValidT(double A, double B, double C, double D, 45 double solution[3]); 46 47 /** 48 * Evaluates the cubic function with the 4 provided coefficients and the 49 * provided variable. 50 */ EvalAt(double A,double B,double C,double D,double t)51 static double EvalAt(double A, double B, double C, double D, double t) { 52 return std::fma(t, std::fma(t, std::fma(t, A, B), C), D); 53 } 54 EvalAt(double coefficients[4],double t)55 static double EvalAt(double coefficients[4], double t) { 56 return EvalAt(coefficients[0], coefficients[1], coefficients[2], coefficients[3], t); 57 } 58 }; 59 60 #endif 61