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
202
203
204
205
206
207
208
209
210
|
/*
* SVG Salamander
* Copyright (c) 2004, Mark McKay
* All rights reserved.
*
* Redistribution and use in source and binary forms, with or
* without modification, are permitted provided that the following
* conditions are met:
*
* - Redistributions of source code must retain the above
* copyright notice, this list of conditions and the following
* disclaimer.
* - Redistributions in binary form must reproduce the above
* copyright notice, this list of conditions and the following
* disclaimer in the documentation and/or other materials
* provided with the distribution.
*
* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
* COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT,
* INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
* (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
* SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
* STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
* ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
* OF THE POSSIBILITY OF SUCH DAMAGE.
*
* 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;
}
}
|
