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/*
* Copyright 2012 Google Inc.
*
* Use of this source code is governed by a BSD-style license that can be
* found in the LICENSE file.
*/
#include "CubicLineSegments.h"
#include "QuadraticLineSegments.h"
#include <algorithm> // used for std::max
// http://cagd.cs.byu.edu/~557/text/cagd.pdf 2.7
// A hodograph is the first derivative curve
void hodograph(const Cubic& cubic, Quadratic& hodo) {
hodo[0].x = 3 * (cubic[1].x - cubic[0].x);
hodo[0].y = 3 * (cubic[1].y - cubic[0].y);
hodo[1].x = 3 * (cubic[2].x - cubic[1].x);
hodo[1].y = 3 * (cubic[2].y - cubic[1].y);
hodo[2].x = 3 * (cubic[3].x - cubic[2].x);
hodo[2].y = 3 * (cubic[3].y - cubic[2].y);
}
// A 2nd hodograph is the second derivative curve
void secondHodograph(const Cubic& cubic, _Line& hodo2) {
Quadratic hodo;
hodograph(cubic, hodo);
hodograph(hodo, hodo2);
}
// The number of line segments required to approximate the cubic
// see http://cagd.cs.byu.edu/~557/text/cagd.pdf 10.6
double subDivisions(const Cubic& cubic) {
_Line hodo2;
secondHodograph(cubic, hodo2);
double maxX = std::max(hodo2[1].x, hodo2[1].x);
double maxY = std::max(hodo2[1].y, hodo2[1].y);
double dist = sqrt(maxX * maxX + maxY * maxY);
double segments = sqrt(dist / (8 * FLT_EPSILON));
return segments;
}
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