C#实现立体图形变换（vs2008）

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  1 using System;
  2 
  3 using System.Collections.Generic;
  4 
  5 using System.ComponentModel;
  6 
  7 using System.Data;
  8 
  9 using System.Drawing;
 10 
 11 using System.Linq;
 12 
 13 using System.Text;
 14 
 15 using System.Windows.Forms;
 16 
 17 using System.Drawing.Drawing2D;
 18 
 19  
 20 
 21  
 22 
 23 namespace ConbinedTransformation
 24 
 25 {
 26 
 27     public partial class Form1 : Form
 28 
 29     {
 30 
 31         int flag = 0;
 32 
 33         ///立方体初始顶点坐标
 34 
 35         float[,] Cube1 = { { -1, -0.5f, -1 }, { 1, -0.5f, -1 }, { 1, -0.5f, 1 }, { -1, -0.5f, 1 },
 36 
 37                    { -1,  0.5f, -1 }, { 1,  0.5f, -1 }, { 1,  0.5f, 1 }, { -1,  0.5f, 1 } };
 38 
 39         float[,] Cube2 = { { -1, -0.5f, -1 }, { 1, -0.5f, -1 }, { 1, -0.5f, 1 }, { -1, -0.5f, 1 },
 40 
 41                    { -1,  0.5f, -1 }, { 1,  0.5f, -1 }, { 1,  0.5f, 1 }, { -1,  0.5f, 1 } };
 42 
 43         Vector4[] tCube1 = new Vector4[8];   //变换后的Cube1顶点坐标
 44 
 45         Vector4[] tCube2 = new Vector4[8];
 46 
 47         float translationx, rotationy;//瞬时运动参数，平移、转角
 48 
 49         float xstep, rstep;        //单位时间移动、转动步长
 50 
 51         float cx, cy, cz;          //照相机位置
 52 
 53         float dx, dy, dz;         //照相机方向
 54 
 55         float upx, upy, upz;      //照相机上方
 56 
 57         float ux, uy, uz, vx, vy, vz, nx, ny, nz;    //照相机坐标系
 58 
 59         float zp;               //视平面位置
 60 
 61         float wxl, wxr, wyb, wyt;  //窗口参数
 62 
 63         float vxl, vxr, vyb, vyt;    //视区参数
 64 
 65         Graphics g;
 66 
 67  
 68 
 69         public Form1()
 70 
 71         {
 72 
 73             InitializeComponent();
 74 
 75             g = CreateGraphics();
 76 
 77             g.SmoothingMode = SmoothingMode.AntiAlias;
 78 
 79  
 80 
 81             //图形运动参数，平移、转动、平移步长，转动步长为10度
 82 
 83             translationx = 0;
 84 
 85             rotationy = 0;
 86 
 87             xstep = 0.2f;
 88 
 89             rstep = 10;
 90 
 91  
 92 
 93             cx = 2; cy = 5; cz = 12;      //照相机位置
 94 
 95             dx = -cx; dy = -cy; dz = -cz; //照相机方向
 96 
 97             upx = 0; upy = 1; upz = 0;    //照相机上方参考向量
 98 
 99             zp = cz;                      //投影面位置
100 
101  
102 
103             wxl = -5; wxr = 5; wyb = -3; wyt = 3;   //窗口参数
104 
105             vxl = 0; vxr = 640; vyb = 0; vyt = 480; //视区参数
106 
107  
108 
109             float d;  //单位化视线向量
110 
111             d = (float)Math.Sqrt(dx * dx   dy * dy   dz * dz);
112 
113  
114 
115             ///照相机坐标系第3轴，N = (dx,dy,dz)
116 
117             nx = dx / d;
118 
119             ny = dy / d;
120 
121             nz = dz / d;
122 
123  
124 
125             ///照相机坐标系第1轴，U = N * UP
126 
127             ux = (ny * upz - nz * upy);
128 
129             uy = (nz * upx - nx * upz);
130 
131             uz = (nx * upy - ny * upx);
132 
133  
134 
135             ///照相机坐标系第2轴，V = U * N
136 
137             vx = (uy * nz - uz * ny);
138 
139             vy = (uz * nx - ux * nz);
140 
141             vz = (ux * ny - uy * nx);
142 
143  
144 
145         }
146 
147  
148 
149         private void DrawString()
150 
151         {
152 
153             String str;
154 
155             str = "点击鼠标: （暂停/继续）";
156 
157             g.DrawString(str, new Font("宋体", 16, FontStyle.Regular), Brushes.Black, 300, 30);
158 
159         }
160 
161  
162 
163         private void Form1_Load(object sender, EventArgs e)
164 
165         {
166 
167  
168 
169         }
170 
171  
172 
173         private void timer1_Tick(object sender, EventArgs e)
174 
175         {
176 
177             doConbinedTransformation();
178 
179             DrawString();
180 
181         }
182 
183  
184 
185         private void doConbinedTransformation()
186 
187         {
188 
189             int i;
190 
191             Matrix4x4 M = new Matrix4x4();
192 
193  
194 
195             for (i = 0; i < 8; i )
196 
197             {
198 
199                 tCube1[i] = new Vector4(Cube1[i, 0], Cube1[i, 1], Cube1[i, 2], 1);
200 
201                 tCube2[i] = new Vector4(Cube2[i, 0], Cube2[i, 1], Cube2[i, 2], 1);
202 
203             }
204 
205  
206 
207             translationx  = xstep;
208 
209             if ((translationx >= 5) || (translationx <= -5)) xstep = -xstep;
210 
211             rotationy  = rstep;
212 
213             if (rotationy > 360) rotationy -= 360;
214 
215  
216 
217             //Cube1的变换
218 
219             //平移x
220 
221             M.identity();
222 
223             M.e14 = translationx;
224 
225             M.e24 = 0.5f;
226 
227             for (i = 0; i < 8; i )
228 
229                 tCube1[i] = M * tCube1[i];
230 
231  
232 
233             //照相机变换
234 
235             M.identity();
236 
237             M.e14 = cx;
238 
239             M.e24 = cy;
240 
241             M.e34 = cz;
242 
243             for (i = 0; i < 8; i )
244 
245                 tCube1[i] = M * tCube1[i];
246 
247  
248 
249             M.identity();
250 
251             M.e11 = ux; M.e12 = uy; M.e13 = uz;
252 
253             M.e21 = vx; M.e22 = vy; M.e23 = vz;
254 
255             M.e31 = nx; M.e32 = ny; M.e33 = nz;
256 
257             for (i = 0; i < 8; i )
258 
259                 tCube1[i] = M * tCube1[i];
260 
261  
262 
263             //投影变换
264 
265             for (i = 0; i < 8; i )
266 
267             {
268 
269                 M.identity();
270 
271                 M.e11 = -zp / tCube1[i].z;
272 
273                 M.e22 = -zp / tCube1[i].z;
274 
275                 M.e33 = zp;
276 
277  
278 
279                 tCube1[i] = M * tCube1[i];
280 
281             }
282 
283             //视窗变换
284 
285             M.identity();
286 
287             M.e11 = (vxr - vxl) / (wxr - wxl);
288 
289             M.e22 = (vyt - vyb) / (wyt - wyb);
290 
291             M.e14 = vxl - (vxr - vxl) / (wxr - wxl) * wxl;
292 
293             M.e24 = vyb - (vyt - vyb) / (wyt - wyb) * wyb;
294 
295             for (i = 0; i < 8; i )
296 
297                 tCube1[i] = M * tCube1[i];
298 
299  
300 
301             //Cube2的变换/////////////////
302 
303             //////////////////////////////
304 
305             //y轴转动
306 
307  
308 
309             M.identity();
310 
311             M.e11 = (float)Math.Cos(rotationy * 3.14159 / 180.0);
312 
313             M.e33 = (float)Math.Cos(rotationy * 3.14159 / 180.0);
314 
315             M.e13 = (float)Math.Sin(rotationy * 3.14159 / 180.0);
316 
317             M.e31 = -(float)Math.Sin(rotationy * 3.14159 / 180.0);
318 
319             for (i = 0; i < 8; i )
320 
321                 tCube2[i] = M * tCube2[i];
322 
323  
324 
325             //平移x
326 
327             M.identity();
328 
329             M.e14 = translationx;
330 
331             M.e24 = -0.5f;
332 
333  
334 
335             for (i = 0; i < 8; i )
336 
337                 tCube2[i] = M * tCube2[i];
338 
339  
340 
341             //照相机变换
342 
343             M.identity();
344 
345             M.e14 = cx;
346 
347             M.e24 = cy;
348 
349             M.e34 = cz;
350 
351             for (i = 0; i < 8; i )
352 
353                 tCube2[i] = M * tCube2[i];
354 
355  
356 
357             M.identity();
358 
359             M.e11 = ux; M.e12 = uy; M.e13 = uz;
360 
361             M.e21 = vx; M.e22 = vy; M.e23 = vz;
362 
363             M.e31 = nx; M.e32 = ny; M.e33 = nz;
364 
365             for (i = 0; i < 8; i )
366 
367                 tCube2[i] = M * tCube2[i];
368 
369  
370 
371             //投影变换
372 
373             for (i = 0; i < 8; i )
374 
375             {
376 
377                 M.identity();
378 
379                 M.e11 = -zp / tCube2[i].z;
380 
381                 M.e22 = -zp / tCube2[i].z;
382 
383                 M.e33 = zp;
384 
385  
386 
387                 tCube2[i] = M * tCube2[i];
388 
389             }
390 
391             //视窗变换
392 
393             M.identity();
394 
395             M.e11 = (vxr - vxl) / (wxr - wxl);
396 
397             M.e22 = (vyt - vyb) / (wyt - wyb);
398 
399             M.e14 = vxl - (vxr - vxl) / (wxr - wxl) * wxl;
400 
401             M.e24 = vyb - (vyt - vyb) / (wyt - wyb) * wyb;
402 
403             for (i = 0; i < 8; i )
404 
405                 tCube2[i] = M * tCube2[i];
406 
407  
408 
409             //绘图
410 
411             g.Clear(Color.White);
412 
413  
414 
415             g.DrawLine(Pens.Red, tCube1[0].x, tCube1[0].y, tCube1[1].x, tCube1[1].y);
416 
417             g.DrawLine(Pens.Red, tCube1[1].x, tCube1[1].y, tCube1[2].x, tCube1[2].y);
418 
419             g.DrawLine(Pens.Red, tCube1[2].x, tCube1[2].y, tCube1[3].x, tCube1[3].y);
420 
421             g.DrawLine(Pens.Red, tCube1[3].x, tCube1[3].y, tCube1[0].x, tCube1[0].y);
422 
423  
424 
425             g.DrawLine(Pens.Red, tCube1[4].x, tCube1[4].y, tCube1[5].x, tCube1[5].y);
426 
427             g.DrawLine(Pens.Red, tCube1[5].x, tCube1[5].y, tCube1[6].x, tCube1[6].y);
428 
429             g.DrawLine(Pens.Red, tCube1[6].x, tCube1[6].y, tCube1[7].x, tCube1[7].y);
430 
431             g.DrawLine(Pens.Red, tCube1[7].x, tCube1[7].y, tCube1[4].x, tCube1[4].y);
432 
433  
434 
435             g.DrawLine(Pens.Red, tCube1[0].x, tCube1[0].y, tCube1[4].x, tCube1[4].y);
436 
437             g.DrawLine(Pens.Red, tCube1[1].x, tCube1[1].y, tCube1[5].x, tCube1[5].y);
438 
439             g.DrawLine(Pens.Red, tCube1[2].x, tCube1[2].y, tCube1[6].x, tCube1[6].y);
440 
441             g.DrawLine(Pens.Red, tCube1[3].x, tCube1[3].y, tCube1[7].x, tCube1[7].y);
442 
443  
444 
445             g.DrawLine(Pens.Blue, tCube2[0].x, tCube2[0].y, tCube2[1].x, tCube2[1].y);
446 
447             g.DrawLine(Pens.Blue, tCube2[1].x, tCube2[1].y, tCube2[2].x, tCube2[2].y);
448 
449             g.DrawLine(Pens.Blue, tCube2[2].x, tCube2[2].y, tCube2[3].x, tCube2[3].y);
450 
451             g.DrawLine(Pens.Blue, tCube2[3].x, tCube2[3].y, tCube2[0].x, tCube2[0].y);
452 
453  
454 
455             g.DrawLine(Pens.Blue, tCube2[4].x, tCube2[4].y, tCube2[5].x, tCube2[5].y);
456 
457             g.DrawLine(Pens.Blue, tCube2[5].x, tCube2[5].y, tCube2[6].x, tCube2[6].y);
458 
459             g.DrawLine(Pens.Blue, tCube2[6].x, tCube2[6].y, tCube2[7].x, tCube2[7].y);
460 
461             g.DrawLine(Pens.Blue, tCube2[7].x, tCube2[7].y, tCube2[4].x, tCube2[4].y);
462 
463  
464 
465             g.DrawLine(Pens.Blue, tCube2[0].x, tCube2[0].y, tCube2[4].x, tCube2[4].y);
466 
467             g.DrawLine(Pens.Blue, tCube2[1].x, tCube2[1].y, tCube2[5].x, tCube2[5].y);
468 
469             g.DrawLine(Pens.Blue, tCube2[2].x, tCube2[2].y, tCube2[6].x, tCube2[6].y);
470 
471             g.DrawLine(Pens.Blue, tCube2[3].x, tCube2[3].y, tCube2[7].x, tCube2[7].y);
472 
473  
474 
475         }
476 
477  
478 
479         private void Form1_MouseClick(object sender, MouseEventArgs e)
480 
481         {
482 
483             switch (flag)
484 
485             {
486 
487                 case 0:
488 
489                     this.timer1.Enabled = false;
490 
491                     flag = 1;
492 
493                     break;
494 
495                 case 1:
496 
497                     this.timer1.Enabled = true;
498 
499                     flag = 0;
500 
501                     break;
502 
503             }
504 
505         }
506 
507  
508 
509         private void Form1_Paint(object sender, PaintEventArgs e)
510 
511         {
512 
513  
514 
515         }
516 
517  
518 
519     }
520 
521  
522 
523     /////////////////////////  数学类 Vecto3
524 
525     public class Vector4
526 
527     {
528 
529         public static float pi = 3.14159265f;
530 
531         public static float tol = 0.000000000000001f;  // float type tolerance 
532 
533  
534 
535