1、實驗3：關于任意直線的對稱變換實驗類型：驗證、設計所需時間：3學時主要實驗內容及要求：對于任意直線的二維圖形對稱變化的實驗，要求輸入的直線是任意直線，直線的端點只能由鍵盤輸入或者鼠標拾取，要做對稱變換的圖形也是一個任意圖形（至少應是一個任意多邊形）。對稱變換，先分析如何使用一系列簡單變換來構造題目要求的復合變換。本體要實現的變換可以用如下一組變換組合來實現： 將直線任一點移至與坐標原點重合 將平移后的直線繞原點旋轉至與某一坐標軸重合 將題目要求的對稱變換轉為實現已知圖形關于上述坐標軸的對稱變換 按逆序求上述、變換的逆變換 將上述矩陣依次相乘得到最終的復合變換矩陣 則某一多邊形關于任意直線的對稱

2、變換就轉變為將該多邊形的各頂點與上述求得的復合變換進行矩陣乘法，求得變換后的新多邊形的各個頂點坐標。根據上述流程，編程實現，并測試程序功能。源代碼：#include<iostream>#include<gl/glut.h>using namespace std;void Initial(void)glClearColor(1.0f,1.0f,1.0f,1.0f);glMatrixMode(GL_PROJECTION);gluOrtho2D(0.0,200.0,0.0,150.0);class CPointpublic: int x;int y;CPoint()CPoin

3、t(int x1,int y1)x=x1; y=y1; static CPoint ZeroMoveToXY(CPoint p, CPoint XY);/原始坐標向屏幕坐標XY的平移static CPoint ToZero(CPoint p);/關于原點對稱 static CPoint XYMoveToZero(CPoint p, CPoint XY);/XY坐標向屏幕坐標的平移static CPoint Charge_AllLine(CPoint p, CPoint line_start, CPoint line_end);/關于Ax+By+C = 0對稱;CPoint CPoint:Zer

4、oMoveToXY(CPoint p, CPoint XY)/原始坐標向屏幕坐標XY的平移CPoint result;int change33 = 1,0,0,0,1,0,-XY.x,-XY.y,1;int p13 = 0,0,0;for (int j = 0;j < 3;j+)p1j=p.x * change0j + p.y * change1j + change2j;result.x = p10;result.y = p11;return result;CPoint CPoint:ToZero(CPoint p)/關于原點對稱CPoint result;int change33 =

5、-1,0,0,0,-1,0,0,0,1;int p13 = 0,0,0;for (int j = 0;j < 3;j+)p1j=p.x * change0j + p.y * change1j + change2j;result.x = p10;result.y = p11;return result;CPoint CPoint:XYMoveToZero(CPoint p, CPoint XY)/XY坐標向屏幕坐標的平移CPoint result;int change33 = 1,0,0,0,1,0,XY.x,XY.y,1;int p13 = 0,0,0;for (int j = 0;j

6、< 3;j+)p1j=p.x * change0j + p.y * change1j + change2j;result.x = p10;result.y = p11;return result;CPoint CPoint:Charge_AllLine(CPoint p, CPoint line_start, CPoint line_end)/關于Ax+By+C = 0對稱double A,B,C;if(line_start.x = line_end.x)A = 1;B = 0;C = -line_start.x;else if(line_start.y = line_end.y)A =

7、 0;B = 1;C = -line_start.y;else A = 1000/(line_end.x - line_start.x);B = -1000/(line_end.y - line_start.y);C = 1000*(-line_start.x/(line_end.x-line_start.x)+line_start.y/(line_end.y - line_start.y);CPoint result;float Y_f = (-A*B*p.x + A*A*p.y - B*C)/(B*B+A*A);float X_f = (-A*B*p.y + B*B*p.x - A*C)/

8、(B*B+A*A);CPoint xy,m1,m2;xy.x=X_f;xy.y = Y_f;m1 = CPoint:ZeroMoveToXY(p, xy);m2 = CPoint:ToZero(m1);result = XYMoveToZero(m2, xy);return result;void Display(void)glClear(GL_COLOR_BUFFER_BIT);glColor3f(1.0f,0.0f,0.0f);glBegin(GL_LINES);int n,x,y,i; cout<<"請輸入對稱圖形的頂點數："<<endl; c

9、in>>n; CPoint *p=new CPointn; for(i=0;i<n;i+) cout<<"請輸入第"<<i+1<<"個頂點坐標"<<endl; cin>>x>>y; pi.x=x; pi.y=y; if(i=0|i=1) glVertex2i(pi.x,pi.y); else if(i=n-1) glVertex2i(pi-1.x,pi-1.y); glVertex2i(pi.x,pi.y); glVertex2i(pi.x,pi.y); glVer

10、tex2i(p0.x,p0.y); else glVertex2i(pi-1.x,pi-1.y); glVertex2i(pi.x,pi.y); cout<<"請輸入對稱直線的兩個頂點："<<endl;CPoint *p2=new CPoint2;for(i=0;i<2;i+)cout<<"請輸入第"<<i+1<<"個頂點坐標"<<endl; cin>>x>>y; p2i.x=x; p2i.y=y;glVertex2i(p2i.x,p

11、2i.y); for(i=0;i<n;i+)pi=CPoint:Charge_AllLine(pi, p20, p21);if(i=0|i=1) glVertex2i(pi.x,pi.y); else if(i=n-1) glVertex2i(pi-1.x,pi-1.y); glVertex2i(pi.x,pi.y); glVertex2i(pi.x,pi.y); glVertex2i(p0.x,p0.y); else glVertex2i(pi-1.x,pi-1.y); glVertex2i(pi.x,pi.y); glEnd(); glFlush();int main(int argc,char*argv)glutInit(&argc,argv);glutInitDisplayMode(