1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
|
/*
* Bezier.java
*
* The Salamander Project - 2D and 3D graphics libraries in Java
* Copyright (C) 2004 Mark McKay
*
* This library is free software; you can redistribute it and/or
* modify it under the terms of the GNU Lesser General Public
* License as published by the Free Software Foundation; either
* version 2.1 of the License, or (at your option) any later version.
*
* This library is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
* Lesser General Public License for more details.
*
* You should have received a copy of the GNU Lesser General Public
* License along with this library; if not, write to the Free Software
* Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
*
* Mark McKay can be contacted at mark@kitfox.com. Salamander and other
* projects can be found at http://www.kitfox.com
*
* Created on January 14, 2005, 4:08 AM
*/
package com.kitfox.svg.animation;
import java.awt.geom.*;
/**
* http://mathworld.wolfram.com/BezierCurve.html
* @author kitfox
*/
public class Bezier
{
double length;
double[] coord;
public Bezier(double sx, double sy, double[] coords, int numCoords)
{
setCoords(sx, sy, coords, numCoords);
}
public void setCoords(double sx, double sy, double[] coords, int numCoords)
{
coord = new double[numCoords * 2 + 2];
coord[0] = sx;
coord[1] = sy;
for (int i = 0; i < numCoords; i++)
{
coord[i * 2 + 2] = coords[i * 2];
coord[i * 2 + 3] = coords[i * 2 + 1];
}
calcLength();
}
/**
* Retuns aproximation of the length of the bezier
*/
public double getLength()
{
return length;
}
private void calcLength()
{
length = 0;
for (int i = 2; i < coord.length; i += 2)
{
length += lineLength(coord[i - 2], coord[i - 1], coord[i], coord[i + 1]);
}
}
private double lineLength(double x1, double y1, double x2, double y2)
{
double dx = x2 - x1, dy = y2 - y1;
return Math.sqrt(dx * dx + dy * dy);
}
public Point2D.Double getFinalPoint(Point2D.Double point)
{
point.x = coord[coord.length - 2];
point.y = coord[coord.length - 1];
return point;
}
public Point2D.Double eval(double param, Point2D.Double point)
{
point.x = 0;
point.y = 0;
int numKnots = coord.length / 2;
for (int i = 0; i < numKnots; i++)
{
double scale = bernstein(numKnots - 1, i, param);
point.x += coord[i * 2] * scale;
point.y += coord[i * 2 + 1] * scale;
}
return point;
}
/**
* Calculates the bernstein polynomial for evaluating parametric bezier
* @param numKnots - one less than number of knots in this curve hull
* @param knotNo - knot we are evaluating Bernstein for
* @param param - Parametric value we are evaluating at
*/
private double bernstein(int numKnots, int knotNo, double param)
{
double iParam = 1 - param;
//Faster evaluation for easy cases:
switch (numKnots)
{
case 0:
return 1;
case 1:
{
switch (knotNo)
{
case 0:
return iParam;
case 1:
return param;
}
break;
}
case 2:
{
switch (knotNo)
{
case 0:
return iParam * iParam;
case 1:
return 2 * iParam * param;
case 2:
return param * param;
}
break;
}
case 3:
{
switch (knotNo)
{
case 0:
return iParam * iParam * iParam;
case 1:
return 3 * iParam * iParam * param;
case 2:
return 3 * iParam * param * param;
case 3:
return param * param * param;
}
break;
}
}
//If this bezier has more than four points, calculate bernstein the hard way
double retVal = 1;
for (int i = 0; i < knotNo; i++)
{
retVal *= param;
}
for (int i = 0; i < numKnots - knotNo; i++)
{
retVal *= iParam;
}
retVal *= choose(numKnots, knotNo);
return retVal;
}
private int choose(int num, int denom)
{
int denom2 = num - denom;
if (denom < denom2)
{
int tmp = denom;
denom = denom2;
denom2 = tmp;
}
int prod = 1;
for (int i = num; i > denom; i--)
{
prod *= num;
}
for (int i = 2; i <= denom2; i++)
{
prod /= i;
}
return prod;
}
}
|
