图形学实验报告2

1、实验二 图形变换与裁减一、实验目的：1、通过本次实验掌握二维图形和三维图形的基本变换算法，及变换矩阵的求法。2、掌握三维图形的投影方法。3、使用Cohen-Sutherland算法裁减二维线段或使用Sutherland-Hodgman算法对多边形进行裁减，验证算法的正确性。二、实验内容：（必做）1、编写一个通用的子程序（如：类或多个函数），其功能可以完成基本二维图形变换（平移、旋转、变比、反射）。通过调用此子程序，实现下列变换：（1）将一平行四边形做平移变换；（2）将平行四边形以原点为中心，以10o为间隔做360o旋转；（3）将一三角形在x和y方向均缩小为原来一半。绘制各种基本图形可以使用系统

2、函数。（必做）2、绘制立方体的平行投影效果图和一点透视效果图。在程序中给出立方体的顶点坐标。视点方向为从z轴正方向看原点，视线平行于z轴。投影面为XOY平面，投影中心位于z轴负轴某点，当改变投影中心位置时，查看一点透视效果的变化。绘制各种基本图形可以使用系统函数。（选做）3、用Cohen-Sutherland算法裁剪二维线段或用Sutherland-Hodgman算法裁剪多边形。要求：输入裁减窗口的四条边坐标，对于Cohen-Sutherland算法裁剪二维线段要输入线段的起点与终点x,y坐标，对于Sutherland-Hodgman算法裁剪多边形要输入多边形的顶点数及各顶点x,y坐标。禁止使

3、用裁减的系统函数。三、实验要求：实验前须规划程序界面和按钮的相关事件的编写代码。实验时进行代码的调试。四、实验代码1，图形的变换/ TransformView.cpp : implementation of the CTransformView class/#include "stdafx.h"#include "Transform.h"#include "TransformDoc.h"#include "TransformView.h"#include <math.h>#ifdef _DEBUG#de

4、fine new DEBUG_NEW#undef THIS_FILEstatic char THIS_FILE = _FILE_;#endif/ CTransformViewIMPLEMENT_DYNCREATE(CTransformView, CView)BEGIN_MESSAGE_MAP(CTransformView, CView)/AFX_MSG_MAP(CTransformView)ON_COMMAND(ID_MENU_TRANSFORM_TRANSLATE, OnMenuTransformTranslate)ON_COMMAND(ID_MENU_TRANSFORM_SCALE, On

5、MenuTransformScale)ON_COMMAND(ID_MENU_TRANSFORM_ROTATE, OnMenuTransformRotate)ON_WM_KEYDOWN()/AFX_MSG_MAP/ Standard printing commandsON_COMMAND(ID_FILE_PRINT, CView:OnFilePrint)ON_COMMAND(ID_FILE_PRINT_DIRECT, CView:OnFilePrint)ON_COMMAND(ID_FILE_PRINT_PREVIEW, CView:OnFilePrintPreview)END_MESSAGE_M

6、AP()/ CTransformView construction/destructionCTransformView:CTransformView()/ TODO: add construction code herePt0.x = 200; Pt0.y = 220;Pt1.x = 260; Pt1.y = 300;Pt2.x = 360; Pt2.y = 180;dAngle = 0.0;CTransformView:CTransformView()BOOL CTransformView:PreCreateWindow(CREATESTRUCT& cs)/ TODO: Modify

7、 the Window class or styles here by modifying/ the CREATESTRUCT csreturn CView:PreCreateWindow(cs);/ CTransformView drawingvoid CTransformView:OnDraw(CDC* pDC)CTransformDoc* pDoc = GetDocument();ASSERT_VALID(pDoc);/ TODO: add draw code for native data hereDrawTriangle(pDC);/ CTransformView printingB

8、OOL CTransformView:OnPreparePrinting(CPrintInfo* pInfo)/ default preparationreturn DoPreparePrinting(pInfo);void CTransformView:OnBeginPrinting(CDC* /*pDC*/, CPrintInfo* /*pInfo*/)/ TODO: add extra initialization before printingvoid CTransformView:OnEndPrinting(CDC* /*pDC*/, CPrintInfo* /*pInfo*/)/

9、TODO: add cleanup after printing/ CTransformView diagnostics#ifdef _DEBUGvoid CTransformView:AssertValid() constCView:AssertValid();void CTransformView:Dump(CDumpContext& dc) constCView:Dump(dc);CTransformDoc* CTransformView:GetDocument() / non-debug version is inlineASSERT(m_pDocument->IsKin

10、dOf(RUNTIME_CLASS(CTransformDoc);return (CTransformDoc*)m_pDocument;#endif /_DEBUG/ CTransformView message handlersvoid CTransformView:DrawTriangle(CDC *pDC)pDC->MoveTo(Pt0);pDC->LineTo(Pt1);pDC->LineTo(Pt2);pDC->LineTo(Pt0);void CTransformView:OnMenuTransformTranslate() / TODO: Add your

11、 command handler code hereint nX = 50; int nY = 80; /平移的X坐标和Y坐标for(int i=0; i<3; i+)Pti.x += nX;Pti.y += nY;RedrawWindow();void CTransformView:OnMenuTransformScale() / TODO: Add your command handler code herefloat dScaleX = 2.0; float dScaleY = 0.5;for(int i=0; i<3; i+)Pti.x *= dScaleX;Pti.y *

12、= dScaleY;RedrawWindow();#define PI 3.1415926void CTransformView:OnMenuTransformRotate() / TODO: Add your command handler code herefloat dRadiusAngle = 30.0 * PI /180.0;for(int i=0; i<3; i+)Pti.x = Pti.x * cos(dRadiusAngle) - Pti.y * sin(dRadiusAngle);Pti.y = Pti.x * sin(dRadiusAngle) + Pti.y * c

13、os(dRadiusAngle);RedrawWindow();void CTransformView:OnKeyDown(UINT nChar, UINT nRepCnt, UINT nFlags) / TODO: Add your message handler code here and/or call defaultint i=0;CPoint TmpPt = Pt0;switch (nChar)case VK_UP:/上for(i=0; i<3; i+)Pti.y -= 5;break;case VK_DOWN:/下for(i=0; i<3; i+)Pti.y += 5;

14、break;case VK_LEFT:/左for(i=0; i<3; i+)Pti.x -= 5;break;case VK_RIGHT:/右for(i=0; i<3; i+)Pti.x += 5;break;case 0X5A:/Z的ASCII码Pt1 = Pt1 - Pt0;Pt2 = Pt2 - Pt0;Pt0.x = Pt0.y = 0;for(i=1; i<3; i+)Pti.x *= 0.5;Pti.y *= 0.5;Pt0 = TmpPt;Pt1 = Pt1 + Pt0;Pt2 = Pt2 + Pt0;break;case 0X58:/X的ASCII码Pt1 =

15、 Pt1 - Pt0;Pt2 = Pt2 - Pt0;Pt0.x = Pt0.y = 0;for(i=1; i<3; i+)Pti.x *= 2.0;Pti.y *= 2.0;Pt0 = TmpPt;Pt1 = Pt1 + Pt0;Pt2 = Pt2 + Pt0;break;case 0X52 : /R的ASCII码dAngle = -1.0;float dRadiusAngle = dAngle * PI /180.0;Pt1 = Pt1 - Pt0;Pt2 = Pt2 - Pt0;Pt0.x = Pt0.y = 0;for(int i=1; i<3; i+)/由于CPoint的

16、x和y坐标值都为正值，所以如果计算出是负值来时，就直接赋0Pti.x = (float)Pti.x * cos(dRadiusAngle) - (float)Pti.y * sin(dRadiusAngle);Pti.y = (float)Pti.x * sin(dRadiusAngle) + (float)Pti.y * cos(dRadiusAngle);Pt0 = TmpPt;Pt1 = Pt1 + Pt0;Pt2 = Pt2 + Pt0;break;RedrawWindow();CView:OnKeyDown(nChar, nRepCnt, nFlags);2、中心投影#include

17、 "stdafx.h"#include "中心投影.h"#include "中心投影Doc.h"#include "中心投影View.h"#ifdef _DEBUG#define new DEBUG_NEW#undef THIS_FILEstatic char THIS_FILE = _FILE_;#endif#include "math.h"#include "dlg.h"#include "dlgangl.h"#include "point.

18、h"# include < time.h > /时间处理函数原型及数据结构point p10, tp10;int xx;/ CMyViewIMPLEMENT_DYNCREATE(CMyView, CView)BEGIN_MESSAGE_MAP(CMyView, CView)/AFX_MSG_MAP(CMyView)ON_COMMAND(IDC_dai, Ondai)ON_COMMAND(IDD_anypoint, Onanypoint)ON_COMMAND(IDD_any2, Onany2)ON_COMMAND(IDD_anyPmap, OnanyPmap)/AFX_MS

19、G_MAPEND_MESSAGE_MAP()/ CMyView construction/destructionCMyView:CMyView()/ TODO: add construction code hereCMyView:CMyView()BOOL CMyView:PreCreateWindow(CREATESTRUCT& cs)/ TODO: Modify the Window class or styles here by modifying/ the CREATESTRUCT csreturn CView:PreCreateWindow(cs);/ CMyView dra

20、wingvoid CMyView:OnDraw(CDC* pDC)CMyDoc* pDoc = GetDocument();ASSERT_VALID(pDoc);/ TODO: add draw code for native data here/*edge Ed12;face fc6;int a=200;volum v;v.num=12; v.en0=0; v.en1=1; v.en2=2;v.en3=3; v.en4=4; v.en5=5;v.en6=6; v.en7=7; v.en8=8;v.en9=9; v.en10=10; v.en11=11; / pDC->LineTo(10

21、0,100); p0.x=a; p0.y=a; p0.z=a; p1.x=100+a; p1.y=a; p1.z=a; p2.x=100+a; p2.y=100+a; p2.z=a; p3.x=a; p3.y=100+a; p3.z=a; p4.x=a; p4.y=a; p4.z=100+a; p5.x=100+a; p5.y=a; p5.z=100+a; p6.x=100+a; p6.y=100+a; p6.z=100+a; p7.x=a; p7.y=100+a; p7.z=100+a;/ pDC->LineTo(p6.x+100,p6.y); Ed0.sn=0;Ed0.en=1; E

22、d1.sn=1;Ed1.en=2; Ed2.sn=2;Ed2.en=3; Ed3.sn=3;Ed3.en=0; Ed4.sn=4;Ed4.en=5; Ed5.sn=5;Ed5.en=6; Ed6.sn=6;Ed6.en=7; Ed7.sn=7;Ed7.en=4; Ed8.sn=0;Ed8.en=4; Ed9.sn=1;Ed9.en=5; Ed10.sn=2;Ed10.en=6; Ed11.sn=3;Ed11.en=7; double seta=-3.14/6,fai=-3.14/8;double sseta,cseta,sfai,cfai; CString s; sseta=sin(seta)

23、; cseta=cos(seta); sfai=sin(fai); cfai=cos(fai); s.Format("%.2f %.2f %.2f %.2f ",sseta,cseta,sfai,cfai); pDC->TextOut(100,100,s);float xe,ye,ze,x,y,z;int i,j,k,D=600, d=200;long tx,ty; for(i=0;i<8;i+) xe=pi.x*cseta-pi.y*sseta; ye=pi.x*sseta*cfai+ pi.y*cseta*cfai -pi.z*sfai; ze=D-(pi.

24、x*sseta*sfai+ pi.y*cseta*sfai +pi.z*cfai); tpi.x=d*xe/ze;/pi.x; tpi.y=d*ye/ze; /pi.y; int esn,een,ent; for(i=0;i<12;i+) /v.num; i+) esn=Edv.eni.sn; een=Edv.eni.en; tx=tpesn.x; ty=tpesn.y; s.Format("*%d %d %d %d ",esn,een, tx,ty); pDC->TextOut(200+j*30,200+j*20,s); pDC->MoveTo(tx,t

25、y); /要求int tx=tpeen.x; ty=tpeen.y; pDC->LineTo(tx,ty); */ / CMyView diagnostics#ifdef _DEBUGvoid CMyView:AssertValid() constCView:AssertValid();void CMyView:Dump(CDumpContext& dc) constCView:Dump(dc);CMyDoc* CMyView:GetDocument() / non-debug version is inlineASSERT(m_pDocument->IsKindOf(RU

26、NTIME_CLASS(CMyDoc);return (CMyDoc*)m_pDocument;#endif /_DEBUG/ CMyView message handlers/操作步骤: 1. 改变d的大小： 可见z轴向外， / 2。 改变y的大小 ，确定y或x方向/ 3。旋转seita=30, 确定绕z轴转/ 4。旋转fai=90, 确定绕x轴转/ 5. 一起转，看结果void CMyView:MatrixM(array3 Ao,array3 A1,array3 A2) int i,j; / Ao11=A111*A211+A112*A221+ A113*A231+A114*A241; /

27、Ao12=A111*A212+A112*A222+ A113*A232+A114*A242; for(i=1;i<5;i+) for( j=1;j<5;j+) Aoij=A1i1*A21j+A1i2*A22j+ A1i3*A23j+A1i4*A24j;void CMyView:printa(array3 A,int w) int i,j;CString s; CDC *pDC=GetDC(); for(i=1;i<5;i+) s.Format("i:%d, %.3lf ,%.3lf, %.3lf ,%.3lf n",i, Ai1,Ai2,Ai3,Ai4);

28、 pDC->TextOut(50,i*30+w,s); void CMyView:readp() /物心在原点double a=0; p0.x=a-50; p0.y=a-50; p0.z=a-50; p1.x=50+a; p1.y=a-50; p1.z=a-50; p2.x=50+a; p2.y=100+a; p2.z=a-50; p3.x=a-50; p3.y=100+a; p3.z=a-50; p4.x=a-50; p4.y=a-50; p4.z=50+a; p5.x=50+a; p5.y=a-50; p5.z=50+a; p6.x=50+a; p6.y=100+a; p6.z=50

29、+a; p7.x=a-50; p7.y=100+a; p7.z=50+a; void CMyView:Ondai() / TODO: Add your command handler code heredlg dd;dd.DoModal(); /启动对话框CDC *pDC=GetDC();edge Ed12;/face fc6;int a=0;int b=0,yy=0;pDC->SetViewportOrg(200,200);volum v;v.num=12; /体用线来构成，下面是初始化v.en0=0; v.en1=1; v.en2=2;v.en3=3; v.en4=4; v.en5=

30、5;v.en6=6; v.en7=7; v.en8=8;v.en9=9; v.en10=10; v.en11=11; readp();/ pDC->LineTo(p6.x+100,p6.y); /线的初始化 Ed0.sn=0;Ed0.en=1; Ed1.sn=1;Ed1.en=2; Ed2.sn=2;Ed2.en=3; Ed3.sn=3;Ed3.en=0; Ed4.sn=4;Ed4.en=5; Ed5.sn=5;Ed5.en=6; Ed6.sn=6;Ed6.en=7; Ed7.sn=7;Ed7.en=4; Ed8.sn=0;Ed8.en=4; Ed9.sn=1;Ed9.en=5; Ed1

31、0.sn=2;Ed10.en=6; Ed11.sn=3;Ed11.en=7; int e=50; /画坐标 pDC->MoveTo(0+e,0+e); pDC->LineTo(300+e,0+e); pDC->TextOut(300+e,0+e,'x'); pDC->MoveTo(0+e ,0+e); pDC->LineTo(0+e,299+e); pDC->TextOut(0+e,299+e,'y'); pDC->MoveTo(e-1 ,e-1); pDC->LineTo(e+1,e+1); /0点 pDC-&g

32、t;TextOut(e+3,e+3,'0'); / pDC->TextOut(300,5,'x');/float seita=-3.14/6,fai=-3.14/8;float sita,fai; sita=(float)3.14*dd.m_seita/180; fai=(float)3.14*dd.m_fai/180;float ssita,csita,sfai,cfai; CString s; ssita=sin(sita); csita=cos(sita); sfai=sin(fai); cfai=cos(fai); s.Format("%

33、.2f %.2f %.2f %.2f ",ssita,csita,sfai,cfai); pDC->TextOut(100,100,s);float xe,ye,ze,xet,yet,zet,x,y,z;int i,j,k;/,D=400, d=200; /控制视点和投影平面long tx,ty; D=400, d=200; array3 Ao,A1,A2; A111=cfai ; A112=sfai ; A113=0; A114=0; A121=-sfai ; A122=cfai ; A123=0; A124=0; A131=0 ; A132=0 ; A133=1; A134

34、=0; A141=0 ; A142=0 ; A143=0; A144=1; /printa(A1,0); A211=1 ; A212=0 ; A213=0; A214=0; A221=0 ; A222=csita ; A223=ssita; A224=0; A231=0 ; A232=-ssita ; A233=csita; A234=0; A241=0 ; A242=0 ; A243=0; A244=1; /printa(A2,130); / sita for x fai for z /旋转公式：下面是两种旋转的合成 MatrixM(Ao,A1,A2); / printa(Ao,250);

35、AfxMessageBox("stop"); for(i=0;i<12;i+) / z(45)? /* if(sita>0.001 && fai>0.001) /s.Format("i=%d,%.3lf %.3lf",i,sita,fai); AfxMessageBox(s); xe= pi.x*Ao11+pi.y*Ao21+pi.z*Ao31; ye= pi.x*Ao12+pi.y*Ao22+pi.z*Ao32; ze= pi.x*Ao13+pi.y*Ao23+pi.z*Ao33-D; else */ if(fai&g

36、t;0.001) xet= pi.x*cfai -pi.y*sfai; /for z(fai) yet= pi.x*sfai+pi.y*cfai; zet=pi.z; else xet=pi.x; yet=pi.y;zet=pi.z; if( sita>0.001) xe=xet; /pi.x ; /ok for x(sita) ye=-yet* csita -zet*ssita ; ze=(yet*ssita+zet*csita); else xe=xet; ye=yet;ze=zet; ze=ze-D; /* if(sita>0.001) /换次序 xet= pi.x*csit

37、a -pi.y*ssita; /for z(sita) yet= pi.x*ssita+pi.y*csita; zet=pi.z; else xet=pi.x; yet=pi.y;zet=pi.z; if( fai>0.001) xe=xet; /pi.x ; /ok for x(fai) ye=-yet* cfai -zet*sfai ; ze=(yet*sfai+zet*cfai); else xe=xet; ye=yet;ze=zet; ze=ze-D; */ /* xe= pi.x*cfai -pi.y*csita*sfai +pi.z*sfai*ssita; ye= pi.x*

38、sfai+pi.y* csita*cfai+ pi.z* ssita*cfai; ze= pi.y*ssita+pi.z*csita-D; /ok */ /* xe=pi.x*csita-pi.y*ssita; ye=pi.x*ssita*cfai+ pi.y*csita*cfai -pi.z*sfai; ze=D-(pi.x*ssita*sfai+ pi.y*csita*sfai +pi.z*cfai); */ /* 88 /anyp xe=-pi.x*ssita+pi.y*csita; ye=-pi.x*csita*cfai- pi.y*ssita*cfai +pi.z*sfai; ze=

39、-pi.x*csita*sfai- pi.y*ssita*sfai -pi.z*cfai+D; */ tpi.x=d*xe/ze; /pi.x; /透视 tpi.y=d*ye/ze; /pi.y; int esn,een,ent; /e为了移动出来看得清楚 for(i=0;i<12;i+) /v.num; i+) esn=Edv.eni.sn; een=Edv.eni.en; tx=tpesn.x; ty=tpesn.y; / s.Format("i:%d,No:%d %d x:%d y:%d ",i,esn,esn, tx,ty);/ pDC->TextOut

40、(200+i*30,200+i*20,s); pDC->MoveTo(tx+e,ty+e); /要求int tx=tpeen.x; ty=tpeen.y;/ s.Format("i:%d,No:%d %d x:%d y:%d ",i,een,een, tx,ty);/ pDC->TextOut(300+i*30,300+i*20,s); pDC->LineTo(tx+e,ty+e); / AfxMessageBox("OK"); /* /饶annypoing rotolvoid print(CDC *pDC, CPoint p) pDC

41、->MoveTo(p0); for(int i=0;i<3;i+) pDC->LineTo(pi); pDC->LineTo(p0);void CMyView:Onanypoint() int tx=0,ty=20; dlgangl dg; /dg.DoModal(); float q=90*3.14159/180,y1,y2; /cosq=0;sinq=1; / q=dg.m_ang; /q=q*3.14159/180; CDC *pDC=GetDC(); pDC->SetWindowOrg(-200,-200);/pDC->SetViewportOrg(

42、+200,+200); CPoint p3= CPoint (100,100),CPoint(200,100),CPoint(150,150),pt3; pDC->MoveTo(0,0);pDC->LineTo(1,1); pDC->TextOut(2,2,"0") ; pDC->MoveTo(tx,ty);pDC->LineTo(tx+1,ty+1); pDC->TextOut(tx+2,ty+2,"T") ; print(pDC,p); for(int i=0;i<3;i+) y1=tx*(1-cos(q)+

43、ty*sin(q); y2=tx*sin(q)+ty*(1-cos(q); pti.x=pi.x*cos(q)-pi.y*sin(q)+y1 ; pti.y=pi.x*sin(q)+pi.y*cos(q)-y2 ; print(pDC,pt); void CMyView:Onany2() int tx=0,ty=20; dlgangl dg; /dg.DoModal(); float q=90*3.14159/180; /cosq=0;sinq=1; / q=dg.m_ang; /q=q*3.14159/180; CDC *pDC=GetDC(); pDC->SetWindowOrg(-

44、200,-200); CPoint p3= CPoint (100,100),CPoint(200,100),CPoint(150,150),pt3; pDC->MoveTo(0,0);pDC->LineTo(1,1); pDC->TextOut(2,2,"0") ; pDC->MoveTo(tx,ty);pDC->LineTo(tx+1,ty+1); pDC->TextOut(tx+2,ty+2,"T"); print(pDC,p); for(int i=0;i<3;i+) pti.x=pi.x*cos(q)-

45、pi.y*sin(q)+tx*(1-cos(q)-ty*sin(q) ; pti.y=pi.x*sin(q)+pi.y*cos(q)+tx*sin(q)+ty*(1-cos(q) ; print(pDC,pt); /* /任意点出发的正投影/void CMyView:OnanyPmap() CDC *pDC=GetDC();edge Ed12; point pt10;int yy=0;dlg dd;dd.DoModal(); /启动对话框int dx=dd.m_x,dy=dd.m_y,dz=dd.m_z;pDC->SetViewportOrg(200,200);volum V;V.num=12; /体用线来构成，下面是初始化V.en0=0; V.en1=1; V.en2=2;V.en3=3; V.en4=4; V.en5=5;V.en6=6; V.en7=7;