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
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
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
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