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
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
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
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