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。
图1 三类透视示意
图2 一点透视示意
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 <GL/glut.h>
#include <stdio.h>
#include <math.h>
struct Matrix
{
double p[4][4];
Matrix operator*(Matrix &);
Matrix();//单位矩阵
};
Matrix::Matrix()
{
for(long i=0;i<4;i++){
for(long j=0;j<4;j++){
if(i==j) p[i][j] = 1;
else p[i][j] = 0;
}
}
}
Matrix Multiply(Matrix& m1, Matrix& m2)
{
Matrix m;
for(int i=0;i<4;i++)
for(int j=0;j<4;j++)
for(int k=0;k<4;k++)
m.p[i][j]+=(m1.p[i][k]*m2.p[k][j]);
return m;
}
struct Pt2D {
int x, y;
Pt2D(){x = 0; y = 0;};
Pt2D(int px, int py){x = px; y = py;};
};
struct 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 = 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 boxPt[8];
Pt2D boxPt2d[8];
FaceInfo fInfo[6];
void InitParameter()//初始化参数
{
mT.p[3][0] = lx; mT.p[3][1] = ly;mT.p[3][2] = lz;
mR.p[0][0] = cos(phi); mR.p[0][2] = -sin(phi);mR.p[2][0] = sin(phi); mR.p[2][2] = cos(phi);
mP.p[2][2] = 0;
mP.p[2][3] = -1/d;
mTemp = Multiply(mT, mR);
mA = Multiply(mTemp, mP);
}
void Project(Pt3D pt, Pt2D &pt2D)//透视变换
{
double ptH[4];
ptH[0]=pt.x;//
ptH[1]=pt.y;
ptH[2]=pt.z;
ptH[3]=1;
double res[4];
for(int i=0;i<4;i++)
res[i] = 0;
for(i=0;i<4;i++)
for(int j=0;j<4;j++)
res[i]+=(ptH[j]*mA.p[j][i]);
pt2D = Pt2D(res[0]/res[3], res[1]/res[3]);
}
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 = 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;face<6;face++)
{
int num=fInfo[face].num;//面的总边数
for(int i=0;i<num;i++)//边循环
{
ptIdx = GetPtIdx(fInfo[face], i);//面的顶点号
Project(boxPt[ptIdx], pt2D);
boxPt2d[ptIdx] = pt2D;
}
}
}
void DrawBox()
{
int ptIdx[4];
for(int face=0;face<4;face++)
{
int num =fInfo[face].num;//面的总顶点数
for(int i=0;i<num;i++)//循环
{
ptIdx[i] = GetPtIdx(fInfo[face], i+1);//面的顶点号
}
for(int j=0; j<4; j++)
{
int idx0 = ptIdx[j];
int idx1 = ((j== 3) ? ptIdx[0]:ptIdx[j+1]);
LineGL(boxPt2d[idx0], boxPt2d[idx1]);
}
}
}
void myDisplay()
{
glClear(GL_COLOR_BUFFER_BIT);
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(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 length
boxPt[0] = Pt3D(-bl/2, -bl/2, -bl/2);
boxPt[1] = Pt3D(-bl/2, bl/2, -bl/2);
boxPt[2] = Pt3D(-bl/2, bl/2, bl/2);
boxPt[3] = Pt3D(-bl/2, -bl/2, bl/2);
boxPt[4] = Pt3D(bl/2, -bl/2, -bl/2);
boxPt[5] = Pt3D(bl/2, bl/2, -bl/2);
boxPt[6] = Pt3D(bl/2, bl/2, bl/2);
boxPt[7] = Pt3D(bl/2, -bl/2, bl/2);
}
void ReadFace()//读入6个面坐标
{
fInfo[0] = FaceInfo(4, 0, 1, 2, 3);
fInfo[1] = FaceInfo(4, 0, 3, 7, 4);
fInfo[2] = FaceInfo(4, 4, 5, 6, 7);
fInfo[3] = FaceInfo(4, 5, 1, 2, 6);
fInfo[4] = FaceInfo(4, 7, 6, 2, 3);
fInfo[5] = 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。