1、计算机图形学专业课程设计透视投影图三视图计算机图形学程序课程设计题目：分别在四个视区内显示空间四面体三视图、透视投影图。学院：信息科学和技术学院专业：计算机科学和技术姓名：oc学号：oc电话：oc邮箱：oc一、设计概述 (1)设计题目。2(2)设计要求。2(3)设计原理。2(4)算法设计。5(5)程序运行结果。9二、关键算法步骤图。10三、程序源代码。12四、程序运行结果分析。24五、设计总结分析。25六、参考文件。26一设计概述设计题目计算机图形学基础(第二版)陆枫 何云峰 编著电子工业出版社P228-7.16：利用OpenGL中多视区，分别在四个视区内显示图7-41所表示空间四面体主视图、
2、俯视图、侧视图、透视投影图。设计要求 设计内容： 1. 掌握主视图、俯视图、侧视图和透视投影变换矩阵； 2. 掌握透视投影图、三视图生成原理；功效要求：分别在四个视区内显示P228-图7-41所表示空间四面体主视图、俯视图、侧视图、透视投影图。设计原理正投影正投影依据投影面和坐标轴夹角可分为三视图和正轴测图。当投影面和某一坐标轴垂直时，得到投影为三视图，这时投影方向和这个坐标轴方向一致，不然，得到投影为正轴测图。1.主视图（V面投影）将三维物体向XOZ平面作垂直投影，得到主视图。由投影变换前后三维物体上点到主视图上点关系，其变换矩阵为：Tv=Txoz= 1 0 0 0 0 0 0 0 0 0
3、1 0 0 0 0 1Tv为主视图投影变换矩阵。简称主视图投影变换矩阵。2.侧视图（W面投影）将三维物体向YOZ平面作垂直投影，得到侧视图。为使侧视图和主视图在一个平面内，就要使W面绕Z轴正向旋转90。同时为了确保侧视图和主视图有一段距离，还要使W面再沿X方向平移一段距离x0，这么即得到侧视图。变换矩阵为：Tv=Tyoz= 0 0 0 0 -1 0 0 0 0 0 1 0 -x0 0 0 1Tv为主视图投影变换矩阵。简称主视图投影变换矩阵。3.俯视图（H面投影）将三维物体向XOY平面作垂直投影，得到俯视图。为使俯视图和主视图在一个平面内，就要使H面绕X轴负向旋转90。同时为了确保侧视图和主视图
4、有一段距离，还要使H面再沿Z方向平移一段距离-z0，这么即得到侧视图。变换矩阵为：Tv=Txoy= 1 0 0 0 0 0 -1 0 0 0 0 0 0 0z0 1Tv为主视图投影变换矩阵。简称主视图投影变换矩阵。三视图常作为关键工程施工图纸，因为在三视图上能够测量距离和角度。但一个三视图只有物体在一面投影，所以单独从某一个方面三视图极难想象出物体三维形状，只有将主视图、侧视图和俯视图放在一起，才有可能综合处物体空间形状。总来说三视图中主视图、俯视图和侧视图全部是经过变换矩阵得来。透视投影-一点透视一点透视只有一个主灭点。灭点能够看做是无限远处一个点在投影面上点。一点透视通常步骤：将三维物体平
5、移到合适位置l,m,n.令视点在z轴，进行透视变换。最终，向xoy面做正投影变换，将结果变换到xoy面上。如此一点透视变换矩阵为：Tv=Txoy= 1 0 0 0 0 1 0 0 0 0 0 1/d l m 0 1+n/d算法设计关键算法1.结构类表示三维坐标系下点struct DefPoint double x, y, z, tag;2.为顶点建立顶点表：PointMaxNum,TPointMaxNum,XOZPointMaxNum,XOYPointMaxNum,YOZPointMaxNum,YOYPointMaxNum3.定义各个视图变换矩阵和变换函数变换矩阵：double Matrix4
6、4 = 1, 0, 0, 0 , 0, 1, 0, 0 , 0, 0, 1, 0 , 500, 300, 300, 1 ;/初始化为单位矩阵double XOZ44 = 1, 0, 0, 0 , 0, 0, 0, 0 , 0, 0, 1, 0 , 0, 0, 0, 1 ;/主视图变换矩阵double XOY44 = 1, 0, 0, 0 , 0, 0, -1, 0 , 0, 0, 0, 0 , 0, 0, -50, 1 ;/俯视图变换矩阵double YOZ44 = 0, 0, 0, 0 , -1, 0, 0, 0 , 0, 0, 1, 0 , -150, 0, 0, 1 ;/侧视图变换矩阵d
7、ouble DD= -400, NN = -200, MM = -360, LL = -500;/DD视点，平移到合适距离NN.MM.LLdouble YOY44 = 1, 0, 0, 0 , 0, 1, 0, 0 , 0, 0, 0, 1 / DD , LL, MM, 0, 1 + NN / DD ;/一点透视矩阵变换函数：void TransForm(DefPoint NewPoint, DefPoint OldPoint, double Tran44)变换函数关键功效是将三维图形顶点和变换矩阵相乘得到变换后矩阵。4.四个视图显示算法。void Display() glClear(GL_C
8、OLOR_BUFFER_BIT); OnCoordinate(); glColor3f(0.0f, 0.0f, 0.0f); glBegin(GL_LINES); glVertex2d(winWidth / 2, 0); glVertex2d(winWidth / 2, winHeight); glVertex2d(0, winHeight / 2); glVertex2d(winWidth, winHeight / 2); glEnd(); glColor3f(1.0f, 0.0f, 0.0f); OnDraw(XOZPoint); glColor3f(0.0f, 1.0f, 0.0f);
9、OnDraw(XOYPoint); glColor3f(0.0f, 0.0f, 1.0f); OnDraw(YOZPoint); glColor3f(1.0f, 0.0f, 0.0f); OnDraw_O(YOYPoint); glutSwapBuffers();5.三视图划线算法/绘制指定图形void OnDraw(DefPoint TempPoint) glBegin(GL_LINES); for (int i = 0; iFaceNum; i+) int size = Facei.size(); for (int j = 0; jsize; j+) glVertex2d(TempPoin
10、tFaceij.x, TempPointFaceij.z); glVertex2d(TempPointFacei(j + 1) % size.x, TempPointFacei(j + 1) % size.z); glEnd();6一点透视划线算法/绘制指定图形void OnDraw_O(DefPoint TempPoint) glColor3f(1.0f, 0.0f, 0.0f); glBegin(GL_LINES); glVertex2d(TempPoint0.x, TempPoint0.y); glVertex2d(TempPoint1.x, TempPoint1.y); glVerte
11、x2d(TempPoint0.x, TempPoint0.y); glVertex2d(TempPoint2.x, TempPoint2.y); glVertex2d(TempPoint0.x, TempPoint0.y); glVertex2d(TempPoint3.x, TempPoint3.y); glVertex2d(TempPoint1.x, TempPoint1.y); glVertex2d(TempPoint2.x, TempPoint2.y); glVertex2d(TempPoint1.x, TempPoint1.y); glVertex2d(TempPoint3.x, Te
12、mpPoint3.y); glVertex2d(TempPoint2.x, TempPoint2.y); glVertex2d(TempPoint3.x, TempPoint3.y); glEnd(); glColor3f(0.0f, 1.0f, 0.0f); glBegin(GL_LINES); glVertex2d(TempPoint0.x,TempPoint0.y); glVertex2d(0, 0); glVertex2d(TempPoint1.x,TempPoint1.y); glVertex2d(0, 0); glVertex2d(TempPoint2.x,TempPoint2.y
13、); glVertex2d(0, 0); glVertex2d(TempPoint3.x,TempPoint3.y); glVertex2d(0, 0); glEnd();（5）程序运行结果二关键算法步骤图（1）矩阵变换函数步骤图（2）三视图绘制算法步骤图三程序源代码#include stdafx.h#include#include#includeusing namespace std;const int MaxNum = 200;vectorFace10;/最大数，面数vectorint winWidth = 1000, winHeight = 600;/窗口宽高int PointNum =
14、 4, FaceNum = 4; /用户图形顶点,面数double Matrix44 = 1, 0, 0, 0 , 0, 1, 0, 0 , 0, 0, 1, 0 , 500, 300, 300, 1 ;/初始化为单位矩阵double XOZ44 = 1, 0, 0, 0 , 0, 0, 0, 0 , 0, 0, 1, 0 , 0, 0, 0, 1 ;/主视图变换矩阵double XOY44 = 1, 0, 0, 0 , 0, 0, -1, 0 , 0, 0, 0, 0 , 0, 0, -50, 1 ;/俯视图变换矩阵double YOZ44 = 0, 0, 0, 0 , -1, 0, 0,
15、0 , 0, 0, 1, 0 , -150, 0, 0, 1 ;/侧视图变换矩阵double DD= -400, NN = -200, MM = -360, LL = -500;/DD视点，平移到合适距离NN.MM.LLdouble YOY44 = 1, 0, 0, 0 , 0, 1, 0, 0 , 0, 0, 0, 1 / DD , LL, MM, 0, 1 + NN / DD ;/一点透视矩阵/定义图形顶点struct DefPoint double x, y, z, tag;PointMaxNum, TPointMaxNum, XOZPointMaxNum, XOYPointMaxNum
16、, YOZPointMaxNum,YOYPointMaxNum;/初始化自定义三维图形void ThPmidInit() PointNum = 4; Point0.x = 400, Point0.y = 0, Point0.z = 0, Point0.tag = 1; Point1.x = 400, Point1.y = 200, Point1.z = 0, Point1.tag = 1; Point2.x = 0, Point2.y = 200, Point2.z = 0, Point2.tag = 1; Point3.x = 200, Point3.y = 200, Point3.z =
17、200, Point3.tag = 1; FaceNum = 4; Face0.push_back(0); Face0.push_back(1); Face0.push_back(2); Face1.push_back(0); Face1.push_back(1); Face1.push_back(3); Face2.push_back(0); Face2.push_back(2); Face2.push_back(3); Face3.push_back(1); Face3.push_back(2); Face3.push_back(3);/取得变换后用户图形顶点void TransForm(
18、DefPoint NewPoint, DefPoint OldPoint, double Tran44) for (int i = 0; iPointNum; i+) double tx = OldPointi.x, ty = OldPointi.y, tz = OldPointi.z, ttag = OldPointi.tag; NewPointi.x = tx*Tran00 + ty*Tran10 + tz*Tran20 + ttag*Tran30; NewPointi.y = tx*Tran01 + ty*Tran11 + tz*Tran21 + ttag*Tran31; NewPoin
19、ti.z = tx*Tran02 + ty*Tran12 + tz*Tran22 + ttag*Tran32; NewPointi.tag = tx*Tran03 + ty*Tran13 + tz*Tran23 + ttag*Tran33; if (NewPointi.tag != 0 & NewPointi.tag != 1) NewPointi.x /= NewPointi.tag, NewPointi.y /= NewPointi.tag, NewPointi.z /= NewPointi.tag, NewPointi.tag = 1; /重新指定窗口宽高void ReShape(int
20、 w, int h) winWidth = w; winHeight = h; glViewport(0, 0, w, h); glMatrixMode(GL_PROJECTION); glLoadIdentity(); gluOrtho2D(0.0, winWidth, 0.0, winHeight);/绘制指定图形void OnDraw(DefPoint TempPoint) glBegin(GL_LINES); for (int i = 0; iFaceNum; i+) int size = Facei.size(); for (int j = 0; jsize; j+) glVerte
21、x2d(TempPointFaceij.x, TempPointFaceij.z); glVertex2d(TempPointFacei(j + 1) % size.x, TempPointFacei(j + 1) % size.z); glEnd();/绘制指定图形void OnDraw_O(DefPoint TempPoint) glColor3f(1.0f, 0.0f, 0.0f); glBegin(GL_LINES); glVertex2d(TempPoint0.x, TempPoint0.y); glVertex2d(TempPoint1.x, TempPoint1.y); glVe
22、rtex2d(TempPoint0.x, TempPoint0.y); glVertex2d(TempPoint2.x, TempPoint2.y); glVertex2d(TempPoint0.x, TempPoint0.y); glVertex2d(TempPoint3.x, TempPoint3.y); glVertex2d(TempPoint1.x, TempPoint1.y); glVertex2d(TempPoint2.x, TempPoint2.y); glVertex2d(TempPoint1.x, TempPoint1.y); glVertex2d(TempPoint3.x,
23、 TempPoint3.y); glVertex2d(TempPoint2.x, TempPoint2.y); glVertex2d(TempPoint3.x, TempPoint3.y); glEnd(); glColor3f(0.0f, 1.0f, 0.0f); glBegin(GL_LINES); glVertex2d(TempPoint0.x, TempPoint0.y); glVertex2d(0, 0); glVertex2d(TempPoint1.x, TempPoint1.y); glVertex2d(0, 0); glVertex2d(TempPoint2.x, TempPo
24、int2.y); glVertex2d(0, 0); glVertex2d(TempPoint3.x, TempPoint3.y); glVertex2d(0, 0); glEnd();/绘制坐标系void OnCoordinate() glColor3f(0.0f, 0.0f, 0.0f); glBegin(GL_LINES); glVertex2d(winWidth / 2, 0); glVertex2d(winWidth / 2, winHeight); glVertex2d(0, winHeight / 2); glVertex2d(winWidth, winHeight / 2);
25、/标识Z轴 glVertex2d(winWidth / 2 + 5, winHeight - 15); glVertex2d(winWidth / 2 + 15, winHeight - 15); glVertex2d(winWidth / 2 + 5, winHeight - 25); glVertex2d(winWidth / 2 + 15, winHeight - 15); glVertex2d(winWidth / 2 + 5, winHeight - 25); glVertex2d(winWidth / 2 + 15, winHeight - 25); glVertex2d(winW
26、idth / 2 - 5, winHeight - 5); glVertex2d(winWidth / 2, winHeight); glVertex2d(winWidth / 2 + 5, winHeight - 5); glVertex2d(winWidth / 2, winHeight); /标识Y轴 glVertex2d(winWidth / 2 + 25, 0 + 15); glVertex2d(winWidth / 2 + 20, 0 + 10); glVertex2d(winWidth / 2 + 15, 0 + 15); glVertex2d(winWidth / 2 + 20
27、, 0 + 10); glVertex2d(winWidth / 2 + 20, 0 + 10); glVertex2d(winWidth / 2 + 20, 0 + 5); glVertex2d(winWidth / 2 - 5, 0 + 5); glVertex2d(winWidth / 2, 0); glVertex2d(winWidth / 2 + 5, 0 + 5); glVertex2d(winWidth / 2, 0); /标识Y轴 glVertex2d(0 + 25, winHeight / 2 + 15); glVertex2d(0 + 20, winHeight / 2 + 10); glVertex2d(0 + 15, winHeight / 2 + 15); glVertex2d(0 + 20, winHeight / 2 + 10); glVertex2d(0 + 20, winHeight / 2 + 10); glVertex2d(0 + 20, winHeight / 2 + 5); glVertex2d(0 + 5, winHeigh
