圆的等面积正多边形逼近法 当用内接正多边形逼近圆时，其面积要小于圆的面积；而当用圆的外切正多边形逼近圆时，其面积则要大于圆的面积。为了使近似代替圆的正多边形和圆之间在面积上相等，只有使该正多边形和圆弧相交，称之为圆的等面积正多边形。

计算机图形学实验 1.一笔绘制金刚石 2.魔术三角形 3.北极星 4.绘制Bezier曲线 B样条曲线 5. 二维裁剪

内容索引:VC/C++源码,图形处理,图形　　一个计算机图形学相关的程序源代码，含二维线画图元、二维线填充图元、线段裁切、多边形裁切、二维图形变换、三维图形变换、凸多面体的建模、透视投影，隐藏面的消除及基本图形变换（平移、旋转、缩放）、曲线移动、曲线清除等。

SES # TOPICS KEY DATES Lec 00 Introduction and Course Overview Lec 01 Bezier Curves and Splines Assignment 0 Lec 02 Curves Properties and Conversion, Surface Representation Lec 03 Coordinates and Transformations Lec 04 Hierarchical Modeling Lec 05 Color Assignment 1 Lec 06 Basics of Computer Animation—Skinning/Enveloping Lec 07 Particle Systems and ODEs Lec 08 Particle Systems and ODE Solvers II, Mass Spring Modeling Assignment 2 Lec 09 Implicit Integration, Collision Detection Lec 10 Collision Detection and Response Quiz Lec 11 Ray Casting and Rendering Lec 12 Ray Casting II Lec 13 Ray Tracing Lec 14 Acceleration Structures for Ray Casting Assignment 3 Lec 15 Shading and Material Appearance Lec 16 Texture Mapping and Shaders Lec 17 Sampling, Aliasing, and Mipmaps Lec 18 Global Illumination and Monte Carlo Assignment 4 Lec 19 Image-Based Rendering and Lighting Lec 20 Output Devices Lec 21 Graphics Pipeline and Rasterization Lec 22 Graphics Pipeline and Rasterization II Lec 23 Real-time Shadows Lec 24 Graphics Hardware and Computer Games Assignment 5

本书从计算机与人对图形理解的差异入手K介绍了计算机处理图形的基本概念和方法K讨 论了点阵图形的基本算法Ð图形的几何变换及矩阵表示Ð图形的裁剪算法K并介绍了现在广泛 应用的图形交互技术与以此为基础的用户界面设计方法K还从几何直观入手导入了计算机图 形学中的曲线Ð曲面设计理论和几何造型方法K探讨了三维图形的消隐及真实感图形的生成技 术以及计算机动画技术。

本程序完全实现了计算机图形学课程中的程序设计，包括使用Opengl制作并旋转立体图；使用DDA算法、Bresenham算法、逐点比较法绘制直线、圆；实现二维和三维图形的变换，包括平移变换、缩放变换、错切变换、旋转变换等。

计算机图形学实用教程

2.7 光栅扫描显示系统和随机扫描显示系统的主要区别是什么？ 2.10 某彩色图形显示系统，CRT显示器的分辨率为800×600，能显示216种颜色，其帧缓冲器的容量应如何计算？ 2.11某彩色图形显示系统，CRT显示器的分辨率为1024×1024，它可以从217种颜色中选出215种来显示，其帧缓冲器的容量应如何计算？查色表的长度和宽度应为多少？ 2.12 假如某光栅扫描显示系统拟采用8英寸×12英寸的屏幕，其分辨率为每英寸100个像素。如果需显示2048种颜色，则缓冲器需要设计成多大容量？

vs2008下 opengl实现，多边形扫描线填充算法。 用到glut库 鼠标左右键实现选点和填充

用MFC VC++实现的时钟源代码 // MFCFrame1View.cpp : implementation of the CMFCFrame1View class // #include "stdafx.h" #include "MFCFrame1.h" #include "MFCFrame1Doc.h" #include "MFCFrame1View.h" #include "PointDialog.h" #include "math.h" GLUquadricObj *objCylinder = gluNewQuadric(); #ifdef _DEBUG #define new DEBUG_NEW #undef THIS_FILE static char THIS_FILE[] = __FILE__; #endif ///////////////////////////////////////////////////////////////////////////// // CMFCFrame1View IMPLEMENT_DYNCREATE(CMFCFrame1View, CView) BEGIN_MESSAGE_MAP(CMFCFrame1View, CView) //{{AFX_MSG_MAP(CMFCFrame1View) ON_WM_CREATE() ON_WM_DESTROY() ON_WM_SIZE() ON_COMMAND(IDM_ZIXUAN, OnZixuan) ON_WM_TIMER() ON_COMMAND(IDM_ChangDirect, OnChangDirect) //}}AFX_MSG_MAP // Standard printing commands ON_COMMAND(ID_FILE_PRINT, CView::OnFilePrint) ON_COMMAND(ID_FILE_PRINT_DIRECT, CView::OnFilePrint) ON_COMMAND(ID_FILE_PRINT_PREVIEW, CView::OnFilePrintPreview) END_MESSAGE_MAP() ///////////////////////////////////////////////////////////////////////////// // CMFCFrame1View construction/destruction CMFCFrame1View::CMFCFrame1View() { // TODO: add construction code here this->m_GLPixelIndex = 0; this->m_hGLContext = NULL; Angle1=0.0; Angle2=30.0; Timer=0; x=0.0; z=0.0; juli=40.0; } CMFCFrame1View::~CMFCFrame1View() { } BOOL CMFCFrame1View::PreCreateWindow(CREATESTRUCT& cs) { // TODO: Modify the Window class or styles here by modifying // the CREATESTRUCT cs cs.style |= (WS_CLIPCHILDREN | WS_CLIPSIBLINGS); return CView::PreCreateWindow(cs); } ///////////////////////////////////////////////////////////////////////////// // CMFCFrame1View drawing ///////////////////////////////////////////////////////////////////////////// // CMFCFrame1View printing BOOL CMFCFrame1View::OnPreparePrinting(CPrintInfo* pInfo) { // default preparation return DoPreparePrinting(pInfo); } void CMFCFrame1View::OnBeginPrinting(CDC* /*pDC*/, CPrintInfo* /*pInfo*/) { // TODO: add extra initialization before printing } void CMFCFrame1View::OnEndPrinting(CDC* /*pDC*/, CPrintInfo* /*pInfo*/) { // TODO: add cleanup after printing } ///////////////////////////////////////////////////////////////////////////// // CMFCFrame1View diagnostics #ifdef _DEBUG void CMFCFrame1View::AssertValid() const { CView::AssertValid(); } void CMFCFrame1View::Dump(CDumpContext& dc) const { CView::Dump(dc); } CMFCFrame1Doc* CMFCFrame1View::GetDocument() // non-debug version is inline { ASSERT(m_pDocument->IsKindOf(RUNTIME_CLASS(CMFCFrame1Doc))); return (CMFCFrame1Doc*)m_pDocument; } #endif //_DEBUG ///////////////////////////////////////////////////////////////////////////// // CMFCFrame1View message handlers BOOL CMFCFrame1View::SetWindowPixelFormat(HDC hDC) { PIXELFORMATDESCRIPTOR pixelDesc= { sizeof(PIXELFORMATDESCRIPTOR), 1, PFD_DRAW_TO_WINDOW|PFD_SUPPORT_OPENGL| PFD_DOUBLEBUFFER|PFD_SUPPORT_GDI, PFD_TYPE_RGBA, 24, 0,0,0,0,0,0, 0, 0, 0, 0,0,0,0, 32, 0, 0, PFD_MAIN_PLANE, 0, 0,0,0 }; this->m_GLPixelIndex = ChoosePixelFormat(hDC,&pixelDesc); if(this->m_GLPixelIndex==0) { this->m_GLPixelIndex = 1; if(DescribePixelFormat(hDC,this->m_GLPixelIndex,sizeof(PIXELFORMATDESCRIPTOR),&pixelDesc)==0) { return FALSE; } } if(SetPixelFormat(hDC,this->m_GLPixelIndex,&pixelDesc)==FALSE) { return FALSE; } return TRUE; } int CMFCFrame1View::OnCreate(LPCREATESTRUCT lpCreateStruct) { if (CView::OnCreate(lpCreateStruct) == -1) return -1; // TODO: Add your specialized creation code here HWND hWnd = this->GetSafeHwnd(); HDC hDC = ::GetDC(hWnd); if(this->SetWindowPixelFormat(hDC)==FALSE) { return 0; } if(this->CreateViewGLContext(hDC)==FALSE) { return 0; } return 0; } BOOL CMFCFrame1View::CreateViewGLContext(HDC hDC) { this->m_hGLContext = wglCreateContext(hDC); if(this->m_hGLContext==NULL) {//创建失败 return FALSE; } if(wglMakeCurrent(hDC,this->m_hGLContext)==FALSE) {//选为当前RC失败 return FALSE; } return TRUE; } void CMFCFrame1View::OnDestroy() { CView::OnDestroy(); // TODO: Add your message handler code here if(wglGetCurrentContext()!=NULL) { wglMakeCurrent(NULL,NULL); } if(this->m_hGLContext!=NULL) { wglDeleteContext(this->m_hGLContext); this->m_hGLContext = NULL; } } void CMFCFrame1View::OnSize(UINT nType, int cx, int cy) { CView::OnSize(nType, cx, cy); // TODO: Add your message handler code here GLsizei width,height; GLdouble aspect; width = cx; height = cy; if(cy==0) { aspect = (GLdouble)width; } else { aspect = (GLdouble)width/(GLdouble)height; } glViewport(0,0,width,height); glMatrixMode(GL_PROJECTION); glLoadIdentity(); gluPerspective(40.0,aspect,5.0,1000.0); } void CMFCFrame1View::OnDraw(CDC* pDC) { CMFCFrame1Doc* pDoc = GetDocument(); ASSERT_VALID(pDoc); // TODO: add draw code for native data here CPaintDC dc(this); glClearColor(1.0,1.0,1.0,1.0); glClear(GL_COLOR_BUFFER_BIT); glMatrixMode(GL_MODELVIEW); glLoadIdentity(); gluLookAt(0.0,0.0,10.0,0.0,0.0,0.0,0.0,1.0,0.0); glRotatef(-90.0,1.0,0.0,0.0);/*返回原坐标*/ glTranslatef(-3.0,0.0,0.0); SwapBuffers(dc.m_ps.hdc); glDrawBuffer (GL_BACK); glFlush(); } void CMFCFrame1View::OnZixuan() { // TODO: Add your command handler code here Timer=1; SetTimer(1,100,NULL); } void CMFCFrame1View::OnTimer(UINT nIDEvent) { // TODO: Add your message handler code here and/or call default CPaintDC dc(this); if (Timer==1) { Angle1=Angle1-1; Angle2=Angle2-1; glClearColor(1.0,1.0,1.0,1.0); glClear(GL_COLOR_BUFFER_BIT); glMatrixMode(GL_MODELVIEW);/**/ glLoadIdentity(); gluLookAt(0.0,20.0,0.000000001,0.0,0.0,0.0,0.0,1.0,0.0); glPushMatrix(); glColor3f(0.7,0.7,0.7); glTranslatef(0.0,0.0,1.1); glRotatef(-90.0,1.0,0.0,0.0); glutSolidCone(5.0,0.0,60.0,60.0); /*底盘*/ glPopMatrix(); glPushMatrix(); glColor3f(0.0,0.0,0.0); glTranslatef(3.9,0.99,1.0); /*刻度*/ glRotatef(90.0,0.0,1.0,0.0); gluCylinder(objCylinder, 0.05, 0.05, 0.8, 9999, 9); glPopMatrix(); glPushMatrix(); glColor3f(0.0,0.0,0.0); glTranslatef(-4.7,0.99,1.0); /*刻度*/ glRotatef(90.0,0.0,1.0,0.0); gluCylinder(objCylinder,0.05, 0.05, 0.8, 9999, 9); glPopMatrix(); glPushMatrix(); glColor3f(0.0,0.0,0.0); glTranslatef(0.0,0.99,-2.9); /*刻度*/ glRotatef(180.0,0.0,1.0,0.0); gluCylinder(objCylinder,0.05, 0.05, 0.8, 9999, 9); glPopMatrix(); glPushMatrix(); glColor3f(0.0,0.0,0.0); glTranslatef(0.0,0.99,5.8); /*刻度*/ glRotatef(180.0,0.0,1.0,0.0); gluCylinder(objCylinder,0.05, 0.05,0.8, 9999, 9); glPopMatrix(); glPushMatrix(); glColor3f(0.0,1.0,0.0); glRotatef(45.0,0.0,1.0,0.0); glTranslatef(-0.67,0.99,0.7); /*时针*/ glRotatef(Angle1/129600,0.0,1.0,0.0); gluCylinder(objCylinder, 0.07, 0.02, 2.5, 9999, 9); glPopMatrix(); glPushMatrix(); glColor3f(1.0,0.0,0.0); glTranslatef(0.0,0.99,1.0); /*分针*/ glRotatef(Angle2/360,0.0,1.0,0.0); gluCylinder(objCylinder, 0.05, 0.02, 3.5, 9999, 9); glPopMatrix(); glPushMatrix(); glColor3f(0.0,0.0,0.5); glTranslatef(0.0,0.99,1.0); /*秒针*/ glRotatef(Angle1,0.0,1.0,0.0); gluCylinder(objCylinder, 0.07, 0.02, 4.5, 9999, 9); glPopMatrix(); SwapBuffers(dc.m_ps.hdc); glDrawBuffer (GL_BACK); glFlush(); } else if(Timer==2) { glClearColor(1.0,1.0,1.0,1.0); glClear(GL_COLOR_BUFFER_BIT); if (juli>12.0) { glMatrixMode(GL_MODELVIEW);/*建立了从世界坐标系到观察坐标系的转换矩阵*/ glLoadIdentity(); gluLookAt(0.0,8.0,juli,0.0,0.0,0.0,0.0,1.0,0.0); juli=juli-0.1; glPushMatrix(); glColor3f(0.0,0.0,0.0); glRotatef(-90.0,1.0,0.0,0.0); glutWireCone(40.0,0.0,30.0,30.0); /*画高度为0的圆锥*/ glPopMatrix(); glPushMatrix(); glColor3f(1.0,0.0,1.0); glLineWidth(4.0); glTranslatef(4.0,1.0,0.0); glutWireOctahedron(); /*画八面体*/ glLineWidth(1.0); glPopMatrix(); glPushMatrix(); glColor3f(1.0,0.0,1.0); glTranslatef(0.0,1.1,0.0); glRotatef(Angle2,0.0,1.0,0.0); gluCylinder(objCylinder, 1.0, 1.0, 10.0, 9999, 9); /*画壶*/ glPopMatrix(); } else if(juli<=12.0) { Angle2=Angle2+0.01; if (Angle2==360.0) Angle2=0.0; glMatrixMode(GL_MODELVIEW);/*建立了从世界坐标系到观察坐标系的转换矩阵*/ glLoadIdentity(); x=12.0*sin(Angle2); z=12.0*cos(Angle2); gluLookAt(x,5.0,z,0.0,0.0,0.0,0.0,1.0,0.0); glPushMatrix(); glColor3f(0.0,0.0,0.0); glRotatef(-90.0,1.0,0.0,0.0); glutWireCone(40.0,0.0,30.0,30.0); /*画高度为0的圆锥*/ glPopMatrix(); glPushMatrix(); glColor3f(1.0,0.0,1.0); glLineWidth(4.0); glTranslatef(4.0,1.0,0.0); glutWireOctahedron(); /*画八面体*/ glLineWidth(1.0); glPopMatrix(); glPushMatrix(); glColor3f(1.0,0.0,1.0); glTranslatef(0.0,1.1,0.0); gluCylinder(objCylinder, 1.0, 1.0, 10.0, 9999, 9); /*画壶*/ glPopMatrix(); } SwapBuffers(dc.m_ps.hdc); glDrawBuffer (GL_BACK); glFlush(); } CView::OnTimer(nIDEvent); } void CMFCFrame1View::OnChangDirect() { // TODO: Add your command handler code here Timer=2; SetTimer(1,100 ,NULL); }