1 /* 2 * Copyright 2012 Google Inc. 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 #include "CubicLineSegments.h" 8 #include "QuadraticLineSegments.h" 9 10 // http://cagd.cs.byu.edu/~557/text/cagd.pdf 2.7 11 // A hodograph is the first derivative curve hodograph(const Cubic & cubic,Quadratic & hodo)12void hodograph(const Cubic& cubic, Quadratic& hodo) { 13 hodo[0].x = 3 * (cubic[1].x - cubic[0].x); 14 hodo[0].y = 3 * (cubic[1].y - cubic[0].y); 15 hodo[1].x = 3 * (cubic[2].x - cubic[1].x); 16 hodo[1].y = 3 * (cubic[2].y - cubic[1].y); 17 hodo[2].x = 3 * (cubic[3].x - cubic[2].x); 18 hodo[2].y = 3 * (cubic[3].y - cubic[2].y); 19 } 20 21 // A 2nd hodograph is the second derivative curve secondHodograph(const Cubic & cubic,_Line & hodo2)22void secondHodograph(const Cubic& cubic, _Line& hodo2) { 23 Quadratic hodo; 24 hodograph(cubic, hodo); 25 hodograph(hodo, hodo2); 26 } 27 28 // The number of line segments required to approximate the cubic 29 // see http://cagd.cs.byu.edu/~557/text/cagd.pdf 10.6 subDivisions(const Cubic & cubic)30double subDivisions(const Cubic& cubic) { 31 _Line hodo2; 32 secondHodograph(cubic, hodo2); 33 double maxX = SkTMax(hodo2[1].x, hodo2[1].x); 34 double maxY = SkTMax(hodo2[1].y, hodo2[1].y); 35 double dist = sqrt(maxX * maxX + maxY * maxY); 36 double segments = sqrt(dist / (8 * FLT_EPSILON)); 37 return segments; 38 } 39