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 public float x; 536 537 public float y; 538 539 public float z; 540 541 public float w; 542 543 544 545 public Vector4() 546 547 { 548 549 x = 0; y = 0; z = 0; w = 1; 550 551 } 552 553 554 555 public Vector4(float xi, float yi, float zi, float wi) 556 557 { 558 559 x = xi; 560 561 y = yi; 562 563 z = zi; 564 565 w = wi; 566 567 } 568 569 570 571 public float Magnitude() 572 573 { 574 575 return (float)Math.Sqrt(x * x y * y z * z); 576 577 } 578 579 public void Normalize() 580 581 { 582 583 if (w != 1) 584 585 { 586 587 x /= w; 588 589 y /= w; 590 591 z /= w; 592 593 w = 1; 594 595 } 596 597 } 598 599 600 601 } 602 603 ////////////////// 矩阵类 604 605 public class Matrix4x4 606 607 { 608 609 // elements eij: i -> row, j -> column 610 611 public float e11, e12, e13, e14, e21, e22, e23, e24, e31, e32, e33, e34, e41, e42, e43, e44; 612 613 614 615 public Matrix4x4() 616 617 { 618 619 e11 = 1; e12 = 0; e13 = 0; e14 = 0; 620 621 e21 = 0; e22 = 1; e23 = 0; e24 = 0; 622 623 e31 = 0; e32 = 0; e33 = 1; e34 = 0; 624 625 e41 = 0; e42 = 0; e43 = 0; e44 = 1; 626 627 } 628 629 public Matrix4x4(float r1c1, float r1c2, float r1c3, float r1c4, 630 631 float r2c1, float r2c2, float r2c3, float r2c4, 632 633 float r3c1, float r3c2, float r3c3, float r3c4, 634 635 float r4c1, float r4c2, float r4c3, float r4c4) 636 637 { 638 639 e11 = r1c1; e12 = r1c2; e13 = r1c3; e14 = r1c4; 640 641 e21 = r2c1; e22 = r2c2; e23 = r2c3; e24 = r2c4; 642 643 e31 = r3c1; e32 = r3c2; e33 = r3c3; e34 = r3c4; 644 645 e41 = r4c1; e42 = r4c2; e43 = r4c3; e44 = r4c4; 646 647 } 648 649 public void identity() 650 651 { 652 653 e11 = 1; e12 = 0; e13 = 0; e14 = 0; 654 655 e21 = 0; e22 = 1; e23 = 0; e24 = 0; 656 657 e31 = 0; e32 = 0; e33 = 1; e34 = 0; 658 659 e41 = 0; e42 = 0; e43 = 0; e44 = 1; 660 661 } 662 663 public Matrix4x4 Transpose() 664 665 { 666 667 return new Matrix4x4(e11, e21, e31, e41, e12, e22, e32, e42, e13, e23, e33, e43, e41, e42, e43, e44); 668 669 } 670 671 672 673 public static Matrix4x4 operator *(Matrix4x4 m1, Matrix4x4 m2) 674 675 { 676 677 return new Matrix4x4(m1.e11 * m2.e11 m1.e12 * m2.e21 m1.e13 * m2.e31 m1.e14 * m2.e41, 678 679 m1.e11 * m2.e12 m1.e12 * m2.e22 m1.e13 * m2.e32 m1.e14 * m2.e42, 680 681 m1.e11 * m2.e13 m1.e12 * m2.e23 m1.e13 * m2.e33 m1.e14 * m2.e43, 682 683 m1.e11 * m2.e14 m1.e12 * m2.e24 m1.e13 * m2.e34 m1.e14 * m2.e44, 684 685 686 687 m1.e21 * m2.e11 m1.e22 * m2.e21 m1.e23 * m2.e31 m1.e24 * m2.e41, 688 689 m1.e21 * m2.e12 m1.e22 * m2.e22 m1.e23 * m2.e32 m1.e24 * m2.e42, 690 691 m1.e21 * m2.e13 m1.e22 * m2.e23 m1.e23 * m2.e33 m1.e24 * m2.e43, 692 693 m1.e21 * m2.e14 m1.e22 * m2.e24 m1.e23 * m2.e34 m1.e24 * m2.e44, 694 695 696 697 m1.e31 * m2.e11 m1.e32 * m2.e21 m1.e33 * m2.e31 m1.e34 * m2.e41, 698 699 m1.e31 * m2.e12 m1.e32 * m2.e22 m1.e33 * m2.e32 m1.e34 * m2.e42, 700 701 m1.e31 * m2.e13 m1.e32 * m2.e23 m1.e33 * m2.e33 m1.e34 * m2.e43, 702 703 m1.e31 * m2.e14 m1.e32 * m2.e24 m1.e33 * m2.e34 m1.e34 * m2.e44, 704 705 706 707 m1.e41 * m2.e11 m1.e42 * m2.e21 m1.e43 * m2.e31 m1.e44 * m2.e41, 708 709 m1.e41 * m2.e12 m1.e42 * m2.e22 m1.e43 * m2.e32 m1.e44 * m2.e42, 710 711 m1.e41 * m2.e13 m1.e42 * m2.e23 m1.e43 * m2.e33 m1.e44 * m2.e43, 712 713 m1.e41 * m2.e14 m1.e42 * m2.e24 m1.e43 * m2.e34 m1.e44 * m2.e44 714 715 ); 716 717 } 718 719 720 721 public static Vector4 operator *(Matrix4x4 m, Vector4 u) 722 723 { 724 725 return new Vector4(m.e11 * u.x m.e12 * u.y m.e13 * u.z m.e14 * u.w, 726 727 m.e21 * u.x m.e22 * u.y m.e23 * u.z m.e24 * u.w, 728 729 m.e31 * u.x m.e32 * u.y m.e33 * u.z m.e34 * u.w, 730 731 m.e41 * u.x m.e42 * u.y m.e43 * u.z m.e44 * u.w); 732 733 } 734 735 } 736 737 }