a7e483d130
working on quad/quad intersection git-svn-id: http://skia.googlecode.com/svn/trunk@5326 2bbb7eff-a529-9590-31e7-b0007b416f81
40 lines
1.3 KiB
C++
40 lines
1.3 KiB
C++
/*
|
|
* 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;
|
|
}
|