高级计算机图形学

Size: px

Start display at page:

Download "高级计算机图形学"

窕钏汪
9 years ago
Views:

1 高级计算机图形学讲授 : 董兰芳研究方向 : 科学计算可视化图形图像处理模式识别 Telephone: [email protected] Homepage: 中国科学技术大学视觉计算与可视化实验室 1

2 第四章几何对象和变换 (3)( 4.5 OpenGL 中的标架 4.6 建模一个彩色立方体 4.7 OpenGL 中几何变换 4.8 虚拟跟踪球 2

3 4.5 OpenGL 中的标架对象坐标系或建模坐标系世界坐标系照相机坐标系裁剪坐标系规范化的设备坐标系窗口坐标系或者屏幕坐标系 3

4 4.5 OpenGL 中的标架 4

5 4.5 OpenGL 中的标架世界坐标系下的表示到照相机坐标系下的表示的变换矩阵 : 5

6 第四章几何对象和变换 (3)( 4.5 OpenGL 中的标架 4.6 建模一个彩色立方体 4.7 OpenGL 中几何变换 4.8 虚拟跟踪球 6

7 4.6.1 建模立方体的面 void polygon(int a, int b, int c, int d) GLfloat vertices[][3] = { glbegin(gl_polygon); {{-1.0,-1.0,-1.0}, glcolor3fv(colors[a]); {1.0,-1.0,-1.0},{1.0,1.0,-1.0}, glnormal3fv(normals[a]); {-1.0,1.0,-1.0}, {-1.0,-1.0,1.0}, glvertex3fv(vertices[a]); {1.0,-1.0,1.0}, {1.0,1.0,1.0}, glcolor3fv(colors[b]); {-1.0,1.0,1.0}}; glnormal3fv(normals[b]); glvertex3fv(vertices[b]); GLfloat colors[][3] = glcolor3fv(colors[c]); {{0.0,0.0,0.0},{1.0,0.0,0.0}, glnormal3fv(normals[c]); {1.0,1.0,0.0}, {0.0,1.0,0.0}, glvertex3fv(vertices[c]); {0.0,0.0,1.0},{1.0,0.0,1.0}, glcolor3fv(colors[d]); 1.0,1.0,1.0}, {0.0,1.0,1.0}}; glnormal3fv(normals[d]); glvertex3fv(vertices[d]); glend();} 7

8 4.6.2 向内和向外的面 8

9 4.6.3 对象表示的数据结构 9

10 4.6.4 彩色立方体 void polygon(int a, int b, int c, int d) GLfloat vertices[][3] = {{-1.0,-1.0,-1.0}, { glbegin(gl_polygon); glcolor3fv(colors[a]); {1.0,-1.0,-1.0},{1.0,1.0,-1.0}, glnormal3fv(normals[a]); void colorcube(void) {-1.0,1.0,-1.0}, {-1.0,-1.0,1.0}, glvertex3fv(vertices[a]); { polygon(0,3,2,1); {1.0,-1.0,1.0}, {1.0,1.0,1.0}, glcolor3fv(colors[b]); polygon(2,3,7,6); {-1.0,1.0,1.0}}; glnormal3fv(normals[b]); polygon(0,4,7,3); glvertex3fv(vertices[b]); polygon(1,2,6,5); glcolor3fv(colors[c]); GLfloat colors[][3] = polygon(4,5,6,7); glnormal3fv(normals[c]); {{0.0,0.0,0.0},{1.0,0.0,0.0}, polygon(0,1,5,4); glvertex3fv(vertices[c]); {1.0,1.0,0.0}, {0.0,1.0,0.0}, } glcolor3fv(colors[d]); {0.0,0.0,1.0},{1.0,0.0,1.0}, glnormal3fv(normals[d]); 1.0,1.0,1.0}, {0.0,1.0,1.0}}; glvertex3fv(vertices[d]); glend();} 10

11 4.6.5 双线性插值 11

12 4.6.6 顶点数组 GLfloat vertices[][3] = {{-1.0,-1.0,-1.0}, {1.0,-1.0,-1.0},{1.0,1.0,-1.0}, {-1.0,1.0,-1.0}, {-1.0,-1.0,1.0}, {1.0,-1.0,1.0}, {1.0,1.0,1.0}, {-1.0,1.0,1.0}}; GLfloat colors[][3] = {{0.0,0.0,0.0},{1.0,0.0,0.0}, {1.0,1.0,0.0}, {0.0,1.0,0.0}, {0.0,0.0,1.0},{1.0,0.0,1.0}, 1.0,1.0,1.0}, {0.0,1.0,1.0}}; GLubyte cubeindices[]={ 0,3,2,1, 2,3,7,6, 0,4,7,3, 1,2,6,5, 4,5,6,7, 0,1,5,4}; glvertexpointer(3,gl_float, 0, vertices); glcolorpointer(3,gl_float, 0, colors); gldrawelements(gl_quads,24, GL_UNSIGNED_BYTE, cubeindices); 12

13 第四章几何对象和变换 (3)( 4.5 OpenGL 中的标架 4.6 建模一个彩色立方体 4.7 OpenGL 中几何变换 4.8 虚拟跟踪球 13

14 4.7 OpenGL 中的几何变换当前变换矩阵 CTM: 14

15 4.7 OpenGL 中的几何变换 OpenGL 的矩阵操作指定一个 4*4 的建模观察矩阵为当前矩阵 OpenGL 中的 4 种矩阵模式 : 建模观察模式, 允许保存 32 个矩阵投影模式纹理模式颜色模式 OpenGl 按照列优先次序存储矩阵元素 15

16 4.7 OpenGL 中的几何变换旋转平移和缩放 : glrotatef(angle,vx,vy,vz); gltranslatef(dx,dy,dz); glscalef(sx,sy,sz); glloadmatrixf(pointer_to_matrix); glloadidentity(); 16

17 4.7 OpenGL 中的几何变换在 OpenGL 中实现具有任意不动点的旋转 : glmatrixmode(gl_modelview); glloadidentity(); gltranslatef(4.0,5.0,6.0); glrotatef(45.0,1.0,2.0,3.0); gltranslatef(-4.0,-5.0,-6.0); 17

18 4.7 OpenGL 中的几何变换变换的顺序 : C<-I C<-CT(4.0,5.0,6.0) C<-CR(45.0,1.0,2.0,3.0) C<-CT(-4.0,-5.0,-6.0) C=T(4.0,5.0,6.0)R(45.0,1.0,2.0,3.0) T(-4.0,-5.0,-6.0) 18

19 4.7 OpenGL 中的几何变换 glulookat(eyex, eyey, eyez, /* 视点 */ atx, aty, atz, /* 参考点 */ upx, upy, upz); /* 观察正向 */ 19

20 4.7 OpenGL 中的几何变换例 : glcolor3f (0.0, 0.0, 1.0); glrecti (50, 100, 200, 150); // Display blue rectangle. glcolor3f (1.0, 0.0, 0.0); gltranslatef (-200.0, -50.0, 0.0); // Set translation parameters. glrecti (50, 100, 200, 150); // Display red, translated rectangle. glloadidentity ( ); // Reset current matrix to identity. glrotatef (90.0, 0.0, 0.0, 1.0); // Set 90-deg. rotation about z axis. glrecti (50, 100, 200, 150); // Display red, rotated rectangle. glloadidentity ( ); // Reset current matrix to identity. glscalef (-0.5, 1.0, 1.0); // Set scale-reflection parameters. glrecti (50, 100, 200, 150); // Display red, transformed rectangle. 20

21 4.7 OpenGL 中的几何变换例 : glmatrixmode (GL_MODELVIEW); glcolor3f (0.0, 0.0, 1.0); // Set current color to blue. glrecti (50, 100, 200, 150); // Display blue rectangle. glpushmatrix ( ); // Make copy of identity (top) matrix. glcolor3f (1.0, 0.0, 0.0); // Set current color to red. gltranslatef (-200.0, -50.0, 0.0); // Set translation parameters. glrecti (50, 100, 200, 150); // Display red, translated rectangle. glpopmatrix ( ); // Throw away the translation matrix. glpushmatrix ( ); // Make copy of identity (top) matrix. glrotatef (90.0, 0.0, 0.0, 1.0); // Set 90-deg. rotation about z axis. glrecti (50, 100, 200, 150); // Display red, rotated rectangle. glpopmatrix ( ); // Throw away the rotation matrix. glscalef (-0.5, 1.0, 1.0); // Set scale-reflection parameters. glrecti (50, 100, 200, 150); // Display red, transformed rectangle. 21

22 4.7 OpenGL 中的几何变换立方体的旋转 : glutdisplayfunc(display); glutidlefunc(spincube); glutmousefunc(mouse); void spincube() { theta[axis] += 2.0; if( theta[axis] > ) theta[axis] -= 360.0; glutpostredisplay(); } void display(void) { glclear(gl_color_buffer_bit GL_DEPTH_BUFFER_BIT); glloadidentity(); glulookat(1.0,1.0,1.0,0.0,0.0,0.0,0.0,1.0,0.0); gltranslatef(0.0, 3.0, 0.0); glrotatef(theta[0], 1.0, 0.0, 0.0); glrotatef(theta[1], 0.0, 1.0, 0.0); glrotatef(theta[2], 0.0, 0.0, 1.0); glcolorpointer(3,gl_float, 0, colors); gldrawelements(gl_quads, 24, GL_UNSIGNED_BYTE, cubeindices); glutswapbuffers(); } 22

23 4.7 OpenGL 中的几何变换立方体的旋转变换矩阵的加载进栈和出栈 : glloadmatrixf(myarray) glmultmatrixf(myarray) Glfloat m[4][4]; Glfloat myarray[16]; glpushmatrix(); gltranslatef( ); gltranslatef( ); gltranslatef( ); glpopmatrix(); for(i=0;i<3;i++) for(j=0;j<3;j++) myarray[4*j+i]=m[i][j]; 23

24 第四章几何对象和变换 (3)( 4.5 OpenGL 中的标架 4.6 建模一个彩色立方体 4.7 OpenGL 中的几何变换 4.8 虚拟跟踪球 24

25 4.8 虚拟跟踪球 25

26 4.8 虚拟跟踪球 int float bool bool bool winwidth, winheight; angle = 0.0, axis[3], trans[3]; trackingmouse = false; redrawcontinue = false; trackballmove = false; main(int argc, char **argv) { glutinit(&argc, argv); glutinitdisplaymode(glut_double GLUT_RGB GLUT_DEPTH); glutinitwindowsize(500, 500); glutcreatewindow("colorcube"); glutreshapefunc(myreshape); glutdisplayfunc(display); glutidlefunc(spincube); glutmousefunc(mousebutton); glutmotionfunc(mousemotion); glenable(gl_depth_test); glmatrixmode(gl_projection); glloadidentity(); glortho(-2.0, 2.0, -2.0, 2.0, -2.0, 2.0); glmatrixmode(gl_modelview); glutmainloop(); } 26

27 4.8 虚拟跟踪球 void display(void) { glclear(gl_color_buffer_bit GL_DEPTH_BUFFER_BIT); /* view transform */ //glpushmatrix(); if (trackballmove) { glrotatef(angle, axis[0], axis[1], axis[2]); } colorcube(); //glpopmatrix(); glutswapbuffers(); } void mousebutton(int button, int state, int x, int y) { if(button==glut_right_button) exit(0); if(button==glut_left_button) switch(state) { case GLUT_DOWN: y=winheight-y; startmotion( x,y); break; case GLUT_UP: stopmotion( x,y); break; } } 27

28 4.8 虚拟跟踪球 startmotion(int x, int y) { } trackingmouse = true; redrawcontinue = false; startx = x; starty = y; curx = x; cury = y; trackball_ptov(x, y, winwidth, winheight, lastpos); trackballmove=true; stopmotion(int x, int y) { trackingmouse = false; if (startx!= x starty!= y) { redrawcontinue = true; } else { angle = 0.0F; redrawcontinue = false; trackballmove = false; } } 28

29 4.8 虚拟跟踪球 mousemotion(int x, int y) { float curpos[3], dx, dy, dz; trackball_ptov(x, y, winwidth, winheight, curpos); if(trackingmouse) {dx = curpos[0] - lastpos[0]; dy = curpos[1] - lastpos[1]; dz = curpos[2] - lastpos[2]; if (dx dy dz) { angle = 90.0F * sqrt(dx*dx + dy*dy + dz*dz); axis[0] = lastpos[1]*curpos[2] - lastpos[2]*curpos[1]; axis[1] = lastpos[2]*curpos[0] - lastpos[0]*curpos[2]; axis[2] = lastpos[0]*curpos[1] - lastpos[1]*curpos[0]; lastpos[0] = curpos[0]; lastpos[1] = curpos[1]; lastpos[2] = curpos[2]; }} glutpostredisplay();} 29

30 4.8 虚拟跟踪球 trackball_ptov(int x, int y, int width, int height, float v[3]) { float d, a; /* project x,y onto a hemi-sphere centered within width, height */ v[0] = (2.0F*x - width) / width; v[1] = (height - 2.0F*y) / height; d = (float) sqrt(v[0]*v[0] + v[1]*v[1]); v[2] = (float) cos((m_pi/2.0f) * ((d < 1.0F)? d : 1.0F)); a = 1.0F / (float) sqrt(v[0]*v[0] + v[1]*v[1] + v[2]*v[2]); v[0] *= a; v[1] *= a; v[2] *= a; } 30

31 第四章几何对象和变换 (3)( 4.5 OpenGL 中的标架 4.6 建模一个彩色立方体 4.7 OpenGL 中几何变换 4.8 虚拟跟踪球 31

高级计算机图形学

高级计算机图形学讲授 : 董兰芳研究方向 : 科学计算可视化图形图像处理模式识别 Telephone:0551-3603484 Email:[email protected] Homepage: http://staff.ustc.edu.cn/~lfdong 中国科学技术大学视觉计算与可视化实验室 1 第四章几何对象和变换 (3)( 4.9 变换的级联 4.10 OpenGL 变换矩阵 4.11