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