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1、课程实验指导五实验5 投影1实验目的：了解透视图投影原理，利用VC+OpenGL实现立方体的一点、两点、三点透视图算法。2实验内容：（1） 理解投影原理；（2） 读懂示范代码；（3） 增加键盘控制，控制一点透视点产生正方体的移动、旋转效果；（4） 实现两点透图效果。3实验原理：本次实验内容为绘制立方体的一点透视图。透视投影按照主灭点的个数分为一点透视、二点透视和三点透视，如下图1所示。灭点灭点灭点灭点灭点灭点 图1 立方体的三类透视其中一点透视情况如图2所示，设z轴上有一观察点（即视点）V(0,0,d)，从V点出发将物体上的点P( x, y, z)投影到XOY平面上得到P (x,y,0)，由相
2、似三角形可知一点透视变换矩阵为：图2 一点透视示意1 / 8.(1)根据以上，可得一点透视变换的步骤如下：(1)将三维形体平移到适当位置lx、ly、lz；(2)令视点在z轴(0,0,d)，利用上述公式(1)进行透视变换；4实验代码：/ Projection.cpp : Defines the entry point for the console application./#include stdafx.h#include #include #include struct Matrix double p44; Matrix operator*(Matrix &); Matrix();/单位矩阵
3、;Matrix:Matrix() for(long i=0;i4;i+) for(long j=0;j4;j+) if(i=j) pij = 1; else pij = 0; Matrix Multiply(Matrix& m1, Matrix& m2)Matrix m;for(int i=0;i4;i+)for(int j=0;j4;j+)for(int k=0;k4;k+)m.pij+=(m1.pik*m2.pkj);return m;struct Pt2D int x, y;Pt2D()x = 0; y = 0;Pt2D(int px, int py)x = px; y = py;str
4、uct Pt3D float x, y, z;Pt3D()x = 0; y = 0; z = 0;Pt3D(float px, float py, float pz)x = px; y = py; z = pz;struct FaceInfo /第一列为每个面的顶点数；其余列为面的顶点编号int num, idx1, idx2, idx3, idx4;FaceInfo()num = 0; idx1 = 0; idx2 = 0;idx3 = 0; idx4 = 0;FaceInfo(int fnum, int fidx1, int fidx2, int fidx3, int fidx4)num
5、= fnum; idx1 = fidx1; idx2 = fidx2;idx3 = fidx3;idx4 = fidx4;double lx = 480, ly = 460, lz = 240;double phi = 0;double d = -500;Matrix mT, mR, mP, mTemp, mA;Pt3D boxPt8;Pt2D boxPt2d8;FaceInfo fInfo6;void InitParameter()/初始化参数mT.p30 = lx; mT.p31 = ly;mT.p32 = lz;mR.p00 = cos(phi); mR.p02 = -sin(phi);
6、mR.p20 = sin(phi); mR.p22 = cos(phi);mP.p22 = 0;mP.p23 = -1/d;mTemp = Multiply(mT, mR);mA = Multiply(mTemp, mP);void Project(Pt3D pt, Pt2D &pt2D)/透视变换double ptH4;ptH0=pt.x;/ptH1=pt.y;ptH2=pt.z;ptH3=1;double res4;for(int i=0;i4;i+)resi = 0;for(i=0;i4;i+)for(int j=0;j4;j+)resi+=(ptHj*mA.pji);pt2D = Pt
7、2D(res0/res3, res1/res3);void LineGL(Pt2D pt0, Pt2D pt1)glBegin (GL_LINES);glColor3f (1.0f, 0.0f, 0.0f); glVertex2f (pt0.x,pt0.y);glColor3f (0.0f, 1.0f, 0.0f); glVertex2f (pt1.x,pt1.y);glEnd ();int GetPtIdx(FaceInfo fInfo, int ptIdx)int idx = 0; switch (ptIdx)case 1:idx = fInfo.idx1;break;case 2:idx
8、 = fInfo.idx2;break;case 3:idx = fInfo.idx3;break;case 4:idx = fInfo.idx4;break;default:break;return idx;void BoxProject()int ptIdx;Pt2D pt2D;for(int face=0;face6;face+)int num=fInfoface.num;/面的总边数for(int i=0;inum;i+)/边循环ptIdx = GetPtIdx(fInfoface, i);/面的顶点号Project(boxPtptIdx, pt2D);boxPt2dptIdx = p
9、t2D;void DrawBox()int ptIdx4;for(int face=0;face4;face+)int num =fInfoface.num;/面的总顶点数for(int i=0;inum;i+)/循环ptIdxi = GetPtIdx(fInfoface, i+1);/面的顶点号for(int j=0; j4; j+)int idx0 = ptIdxj;int idx1 = (j= 3) ? ptIdx0:ptIdxj+1);LineGL(boxPt2didx0, boxPt2didx1);void myDisplay()glClear(GL_COLOR_BUFFER_BIT
10、);glColor3f (1.0f, 0.0f, 0.0f); InitParameter();BoxProject();DrawBox();glutSwapBuffers();void Init()glClearColor(0.0, 0.0, 0.0, 0.0);glShadeModel(GL_FLAT);printf(Hello Cube!n);void Reshape(int w, int h)glViewport(0, 0, (GLsizei) w, (GLsizei) h);glMatrixMode(GL_PROJECTION);glLoadIdentity();gluOrtho2D
11、(0.0, (GLdouble) w, 0.0, (GLdouble) h);void keyboard(unsigned char key, int x, int y)switch (key)case x:break;default:break;void ReadPoint()/读入8个顶点坐标float bl = 200;/box lengthboxPt0 = Pt3D(-bl/2, -bl/2, -bl/2);boxPt1 = Pt3D(-bl/2, bl/2, -bl/2);boxPt2 = Pt3D(-bl/2, bl/2, bl/2);boxPt3 = Pt3D(-bl/2, -b
12、l/2, bl/2);boxPt4 = Pt3D(bl/2, -bl/2, -bl/2);boxPt5 = Pt3D(bl/2, bl/2, -bl/2);boxPt6 = Pt3D(bl/2, bl/2, bl/2);boxPt7 = Pt3D(bl/2, -bl/2, bl/2);void ReadFace()/读入6个面坐标fInfo0 = FaceInfo(4, 0, 1, 2, 3);fInfo1 = FaceInfo(4, 0, 3, 7, 4);fInfo2 = FaceInfo(4, 4, 5, 6, 7);fInfo3 = FaceInfo(4, 5, 1, 2, 6);fI
13、nfo4 = FaceInfo(4, 7, 6, 2, 3);fInfo5 = FaceInfo(4, 4, 5, 1, 0);int main(int argc, char *argv)glutInit(&argc, argv);glutInitDisplayMode(GLUT_RGB | GLUT_DOUBLE);glutInitWindowPosition(100, 100);glutInitWindowSize(640, 480);glutCreateWindow(Hello World!);ReadPoint();ReadFace();glutDisplayFunc(myDisplay);glutReshapeFunc(Reshape);glutKeyboardFunc(keyboard);glutMainLoop();return 0;5. 思考题：请修改上述代码，使之实现两点透视图。