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/Users/lyon/j4p/src/math/Mat3.java
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1 package math;
2
3 import java.awt.*;
4
5 public class Mat3 {
6 double a[] [] =
7 {{1d, 0, 0},
8 {0d, 1, 0},
9 {0d, 0, 1}};
10
11
12 public void setTranslation(double tx, double ty) {
13 a[0][0] = 1;
14 a[1][1] = 1;
15 a[2][2] = 1;
16 a[0][2] = tx;
17 a[1][2] = ty;
18 }
19
20 public void setScale(double sx, double sy) {
21 a[0][0] = sx;
22 a[1][1] = sy;
23 a[2][2] = 1;
24 }
25
26 public void setRotation(double theta) {
27 theta = theta * Math.PI / 180;
28 double cas = Math.cos(theta);
29 double sas = Math.sin(theta);
30 a[0][0] = cas;
31 a[1][1] = cas;
32 a[0][1] = -sas;
33 a[1][0] = sas;
34 }
35
36 public void setShear(double shx, double shy) {
37 a[0][0] = 1;
38 a[1][1] = 1;
39 a[2][2] = 1;
40 a[0][1] = shx;
41 a[1][0] = shy;
42 }
43 // a00 a01 a02
44 // a10 a11 a12
45 // a20 a21 a22
46 public void setPerspective(double px, double py) {
47 a[0][0] = 1;
48 a[1][1] = 1;
49 a[2][2] = 1;
50 a[2][0] = px;
51 a[2][1] = py;
52 }
53
54 public static void main(String args[]) {
55 Mat3 tr1 = new Mat3();
56 Mat3 tr2 = new Mat3();
57 Mat3 sc = new Mat3();
58 Mat3 at;
59
60 tr1.setTranslation(1, 1);
61 sc.setScale(2, 2);
62 tr2.setTranslation(-1, -1);
63
64 at = tr1.multiply(sc);
65 at = at.multiply(tr2);
66 System.out.println("tr1=");
67 tr1.print();
68 System.out.println("tr2=");
69 tr2.print();
70 System.out.println("sc=");
71 sc.print();
72 System.out.println("at=");
73 at.print();
74
75 // at.print();
76 //at = new Mat3();
77 //int x[] = at.multiply(1, 2, 1);
78 // for (int i = 0; i < x.length; i++)
79 // System.out.println(x[i]);
80
81 }
82
83 public Polygon transform(Polygon p) {
84 Polygon pp = new Polygon();
85 int x[];
86 for (int i = 0; i < p.npoints; i++) {
87 x = multiply(p.xpoints[i], p.ypoints[i], 1);
88 pp.addPoint(x[0], x[1]);
89 }
90 return pp;
91 }
92
93 public static int[] centroid(Polygon p) {
94 int x[] = new int[2];
95 int xsum = 0;
96 int ysum = 0;
97 for (int i = 0; i < p.npoints; i++) {
98 xsum += p.xpoints[i];
99 ysum += p.ypoints[i];
100 }
101 x[0] = xsum / p.npoints;
102 x[1] = ysum / p.npoints;
103 return x;
104 }
105
106 public Mat3() {
107 };
108 public Mat3(double a_[][]) {
109 a = a_;
110 }
111
112 public double[][] getArray() {
113 return a;
114 }
115
116 /*
117 To generate a time-optimal 3x3 matrix inversion, use maple:
118 with(linalg):readlib(C):
119 a:=array(0..2,0..2,[]):
120 b:=array(0..2,0..2,[]):
121 b:=inverse(matrix(a)):
122 C(b,optimized);
123
124 */
125 public Mat3 invert() {
126 double b[] [] = new double[3][3];
127 double t4 = a[0][0] * a[1][1];
128 double t6 = a[0][0] * a[1][2];
129 double t8 = a[0][1] * a[1][0];
130 double t10 = a[0][2] * a[1][0];
131 double t12 = a[0][1] * a[2][0];
132 double t14 = a[0][2] * a[2][0];
133 double t17 =
134 1 / (-t4 * a[2][2] + t6 * a[2][1] + t8 * a[2][2] - t10 * a[2][1] - t12 * a[1][2] + t14 * a
135 [1][1]);
136 b[0][0] = -(a[1][1] * a[2][2] - a[1][2] * a[2][1]) * t17;
137 b[0][1] = -(-a[0][1] * a[2][2] + a[0][2] * a[2][1]) * t17;
138 b[0][2] = (-a[0][1] * a[1][2] + a[0][2] * a[1][1]) * t17;
139 b[1][0] = (a[1][0] * a[2][2] - a[1][2] * a[2][0]) * t17;
140 b[1][1] = (-a[0][0] * a[2][2] + t14) * t17;
141 b[1][2] = -(-t6 + t10) * t17;
142 b[2][0] = (-a[1][0] * a[2][1] + a[1][1] * a[2][0]) * t17;
143 b[2][1] = -(-a[0][0] * a[2][1] + t12) * t17;
144 b[2][2] = (-t4 + t8) * t17;
145
146 return new Mat3(b);
147 }
148 /* To generate a new matrix, transposed:
149 with(linalg):readlib(C):a:=matrix(3,3);
150 b:=transpose(a);C(b,optimized);
151 */
152 public Mat3 transpose() {
153 double b[][] = new double[3][3];
154 b[0][0] = a[0][0];
155 b[0][1] = a[1][0];
156 b[0][2] = a[2][0];
157 b[1][0] = a[0][1];
158 b[1][1] = a[1][1];
159 b[1][2] = a[2][1];
160 b[2][0] = a[0][2];
161 b[2][1] = a[1][2];
162 b[2][2] = a[2][2];
163 return new Mat3(b);
164 }
165
166
167 public Mat3 multiply(Mat3 bmat3) {
168 double WW [][] = new double[3][3];
169 double b [][] = bmat3.getArray();
170 WW[0][0] = a[0][0] * b[0][0] + a[0][1] * b[1][0] + a[0][2] * b[2][0];
171 WW[0][1] = a[0][0] * b[0][1] + a[0][1] * b[1][1] + a[0][2] * b[2][1];
172 WW[0][2] = a[0][0] * b[0][2] + a[0][1] * b[1][2] + a[0][2] * b[2][2];
173 WW[1][0] = a[1][0] * b[0][0] + a[1][1] * b[1][0] + a[1][2] * b[2][0];
174 WW[1][1] = a[1][0] * b[0][1] + a[1][1] * b[1][1] + a[1][2] * b[2][1];
175 WW[1][2] = a[1][0] * b[0][2] + a[1][1] * b[1][2] + a[1][2] * b[2][2];
176 WW[2][0] = a[2][0] * b[0][0] + a[2][1] * b[1][0] + a[2][2] * b[2][0];
177 WW[2][1] = a[2][0] * b[0][1] + a[2][1] * b[1][1] + a[2][2] * b[2][1];
178 WW[2][2] = a[2][0] * b[0][2] + a[2][1] * b[1][2] + a[2][2] * b[2][2];
179 return (new Mat3(WW));
180 }
181
182 /*
183 In maple:
184 vec3:=vector([v1, v2, v3]):
185 C(multiply(matrix(a),vec3),optimized):
186
187 does a post-multiplication, v*A
188 */
189
190 public int[] multiply(int v1, int v2, int v3) {
191 int x[] = new int[3];
192 x[0] = (int) (a[0][0] * v1 + a[0][1] * v2 + a[0][2] * v3);
193 x[1] = (int) (a[1][0] * v1 + a[1][1] * v2 + a[1][2] * v3);
194 x[2] = (int) (a[2][0] * v1 + a[2][1] * v2 + a[2][2] * v3);
195 return x;
196 }
197
198 public float[] multiply(float v1, float v2, float v3) {
199 float x[] = new float[3];
200 x[0] = (int) (a[0][0] * v1 + a[0][1] * v2 + a[0][2] * v3);
201 x[1] = (int) (a[1][0] * v1 + a[1][1] * v2 + a[1][2] * v3);
202 x[2] = (int) (a[2][0] * v1 + a[2][1] * v2 + a[2][2] * v3);
203 return x;
204 }
205
206 // The following is premultiplied!
207 public int[] premultiply(int v1, int v2) {
208 int x[] = new int[2];
209 x[0] = (int) (v1 * a[0][0] + v2 * a[1][0] + a[2][0]);
210 x[1] = (int) (v1 * a[0][1] + v2 * a[1][1] + a[2][1]);
211 return x;
212 }
213
214 /*
215 In maple:
216 vec3:=vector([v1, v2, v3]):
217 C(multiply(vec3,matrix(a)),optimized):
218
219 does a pre-multiplication, v*A
220 */
221 public double[] premultiply(double v1, double v2, double v3) {
222 double x[] = new double[3];
223 x[0] = v1 * a[0][0] + v2 * a[1][0] + v3 * a[2][0];
224 x[1] = v1 * a[0][1] + v2 * a[1][1] + v3 * a[2][1];
225 x[2] = v1 * a[0][2] + v2 * a[1][2] + v3 * a[2][2];
226 return x;
227 }
228
229 public float[] premultiply(float v1, float v2, float v3) {
230 float x[] = new float[3];
231 x[0] = (float) (v1 * a[0][0] + v2 * a[1][0] + v3 * a[2][0]);
232 x[1] = (float) (v1 * a[0][1] + v2 * a[1][1] + v3 * a[2][1]);
233 x[2] = (float) (v1 * a[0][2] + v2 * a[1][2] + v3 * a[2][2]);
234 return x;
235 }
236
237 public void print(String s) {
238 System.out.println(s);
239 print();
240 }
241
242 public void print() {
243 for (int i = 0; i < a.length; i++) {
244 for (int j = 0; j < a[0].length; j++)
245 System.out.print(a[i][j] + " ");
246 System.out.println();
247 }
248 }
249
250 }
251
252