【精品】《计算机图形学》总复习（可编辑.ppt

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1、计算机图形学总复习Ch1.asurveyofCS2GraphicsConceptnIn narrow sensen位图(bitmap)-图像Image，n矢量图(vectorgraph)GraphicnIn general,graphics can be any object which is able to give vision impression in mans vision system.It include various geometry graphics,views,pictures,patterns,and images.3n凡是能够在人的视觉系统中形成视觉印象的客观对象都称

2、为图形图形。n(1)自然景物n(2)照片和图片n(3)工程图、设计图和方框图n(4)人工美术绘画、雕塑品n(5)用数学方法描述的图形（包括几何图形、代数方程、分析表达式或列表所确定的图形）什么是图形？4Vectorgraph and bitmap(1).vectorgraph(1).vectorgraphAny curves are approached with many short linesAny curves are approached with many short lines(2).bitmap(2).bitmapEvery curve must be consist of se

3、veral pixelsEvery curve must be consist of several pixels5Relationshipwithothersubjects数字图像数字图像Digital Images数据模型数据模型Data Models图像生成 Image Rendering（计算机图形学计算机图形学 Computer Graphics）模型/特征的提取 Model/Feature Extraction（计算机视觉计算机视觉 Computer Vision,模式识别模式识别 Pattern Recognition）模型变换 Model Transformation（计算几何

4、计算几何 Computer Geometry）图像变换 Image Transformation（图像处理图像处理 Image Processing）研究内容（学科学科）8Computer Graphics Applicationsn图形用户界面(GUI)n计算机辅助设计与制造（CAD/CAM）n娱乐游戏及计算机动画(entertainment/game/animation)n计算机艺术(computer art)n地理信息系统(GIS)n科学技术与信息可视化(Visualization)n虚拟现实(Virtual Reality)n图形用户界面(GUI)n9Research Hotspotn

5、真实感显示Realistic Displayn变形技术 Morphing Technologyn数字城市 Digital Cityn识别技术 Recognize Technologyn基于图像的建模 Image Based Modelingn自然对象的建模 Nature Objects Modelingn离散数据建模 Discrete Data Modelingn网络漫游 Web 3Dn 10CRT(CathodeRayTube)nThebeamemitselectrons(cathode).nRayintensityiscontrolledbythegrid.nThefocusforcest

6、heelectronstowardsaconvergencepath.nDeflectorsforcetheraytopointataspecificscreenpoint.nTheraystunsoverthephosphor.Phosphoremitslights.nPhosphoremissiondeclinesveryfast(refreshmentrequired)Figure2-4ElectrostaticdeflectionoftheelectronbeaminaCRT111213当前研究动态n(1)造型技术n规则形体：欧氏几何方法n不规则形体：n分形几何方法、粒子系统、纹理映射

7、n实体造型n基于物理的造型n基于图像的造型14当前研究动态n(2)真实感图形绘制技术n光照明模型n绘制算法n快速算法n基于图像的绘制n（非真实感图形绘制技术）15当前研究动态n(3)人机交互技术n(4)与计算机网络技术的紧密结合与计算机网络技术的紧密结合n远程医疗与诊断n远程导航与维修n远程教育16研究热点nModelingn ngettingmodelsfromtherealworldgettingmodelsfromtherealworldnAnimationn nphysicallybasedmodelingphysicallybasedmodelingn nmotioncapturem

8、otioncapturenRenderingn nmorerealistic:image-basedrenderingmorerealistic:image-basedrenderingn nlessrealistic:impressionist,pen&inklessrealistic:impressionist,pen&ink17Ch2.IntroductiontoOpenGL/GLUT18WhatisOpenGL?nAsoftwareinterfacetographicshardwarenGraphicsrenderingAPI(LowLevel)nHigh-qualitycolorim

9、agescomposedofgeometricandimageprimitivesnWindowsystemindependentnOperatingsystemindependent19OpenGLandGLUTnGLUT(OpenGLUtilityToolkit)nAnauxiliarylibrarynAportablewindowingAPInEasiertoshowtheoutputofyourOpenGLapplicationnNotofficiallypartofOpenGLnHandles:nWindowcreation,nOSsystemcallsnMousebuttons,m

10、ovement,keyboard,etcnCallbacks20HowtoinstallGLUT?nDownloadGLUTnhttp:/www.opengl.org/resources/libraries/glut.htmlnCopythefilestofollowingfolders:nglut.h VC/include/gl/nglut32.libVC/lib/nglut32.dllwindows/system32/nHeaderFiles:n#includen#includenIncludeglutautomaticallyincludesotherheaderfiles21Sampl

11、eProgram#include#includevoidmain(intargc,char*argv)int mode=GLUT_RGB|GLUT_DOUBLE;glutInitDisplayMode(mode);glutInitWindowSize(500,500);glutCreateWindow(“Simple”);init();glutDisplayFunc(display);glutKeyboardFunc(key);glutMainLoop();22OpenGLInitializationnSetupwhateverstateyouregoingtousenDontneedthis

12、muchdetailunlessworkingin3Dvoidinit(void)glClearColor(0.0,0.0,0.0,0.0);glViewport(0,0,width,height);glMatrixMode(GL_PROJECTION);glLoadIdentity();glOrtho(-10,10,-10,10,-10,20);glMatrixMode(GL_MODELVIEW);glLoadIdentity();glEnable(GL_LIGHT0);glEnable(GL_LIGHTING);glEnable(GL_DEPTH_TEST);23GLUTCallbackf

13、unctionsnEvent-driven:ProgramsthatusewindowsnInput/OutputnWaituntilaneventhappensandthenexecutesomepre-definedfunctionsaccordingtotheusersinputnEventskeypress,mousebuttonpressandrelease,windowresize,etc.n nYour OpenGL program will be in infinite loopYour OpenGL program will be in infinite loop24GLUT

14、CallbackFunctionsnCallbackfunction:RoutinetocallwhenaneventhappensnWindowresizeorredrawnUserinput(mouse,keyboard)nAnimation(rendermanyframes)n“Register”callbackswithGLUTnglutDisplayFunc(my_display_func);nglutIdleFunc(my_idle_func);nglutKeyboardFunc(my_key_events_func);nglutMouseFunc(my_mouse_events_

15、func);25EventQueueKeyboardMouseWindow.MainLoop()Eventqueuewindow_callback().Mouse_callback().Keypress_callback().26OpenGLGeometricPrimitivesnThegeometryisspecifiedbyvertices.nTherearetenprimitivetypes:31AnExamplevoid drawParallelogram(GLfloat color)glBegin(GL_QUADS);glColor3fv(color);glVertex2f(0.0,

16、0.0);glVertex2f(1.0,0.0);glVertex2f(1.5,1.118);glVertex2f(0.5,1.118);glEnd();32Ch3.GeometricPrimitives几何图元绘制33Whatisrastering?nTherasterdisplaytechnologyrequirestobrakedowngraphicprimitivesintopixelswithintheraster.nThisprocessiscalledrastering(栅格化栅格化).nscanconversion（扫描转换）This is usually done by th

17、e graphics hardware.However,it is useful to understand how this process works in order to be able to achieve good graphics performance.34扫描转换n将图形数字化为一组像素强度值，并存放在帧缓存中。这个数字化过程称为扫描转换(scan conversion)n n基本图元的扫描转换就是计算出落在基本图元上或充分靠近它的一串像素，并以此像素近似替代基本图元上对应位置在屏幕上显示的过程。35Line-DrawingAlgorithmsn1)DDAalgorithmn

18、2)Bresenhamalgorithm36DDAalgorithm(p94)nThedigital differential analyzer(DDA，数字微分分析法)isascan-conversionlinealgorithmbasedoncalculatingdifferencesbasedontheslopeoftheline.37DDAalgorithmnAlinecanbedescribedbytheequationy=mx+bnWithoutlossofgenerality,wecanassume0m1.Otherwisewecanmirrororinterchangethec

19、oordinatesasneeded.nNow,weneedtocomputetheseriesofpoints(xk,yk),k=0,nthatbestdescribestheline.38DDAalgorithmnSince0mabs(dx)f fabs(dy)abs(dy)steps=steps=f fabs(dx);abs(dx);elsesteps=abs(dy);elsesteps=abs(dy);xIncrement=(floatxIncrement=(float)(dx)/step(dx)/steps s;yIncrement=(floatyIncrement=(float)(

20、dy)/steps;(dy)/steps;For(k=0;ksteps;k+)For(k=0;k1,swapthecoordinatesaxes.414242Advantage and Disadvantage for DDAFFAdvantage优点:-消除乘法.FFDisadvantage缺点:-浮点数相加积累误差，对长线段而言，引起像素点位置与理想位置的偏移.-需要圆整操作和浮点计算，消耗时间。42DDAalgorithmnTheDDAalgorithmeasilycanbeextendedtoothergraphicsprimitives,suchascircles,ellipses,

21、etc.nDDA is Good,but Still Not Fast Enough!nFloatingpointmultiplygonefromy=mx+bnButloopstillhasafloatingpointaddnAndaround()nWE CAN DO BETTER!nBestperformance:Onlyintegeradds/subtractsinsideloopnTheBresenhamalgorithmallowsustodojustthat.43Bresenhamalgorithm(p95)nAgain,weassumewithoutlossofgenerality

22、thattheslopeis0m1;hence,thelineislocatedinthefirstoctant.nIdeannomatterwhattheslopeis,weincreaseonecoordinatebyone(x-coordinate)similartotheDDAalgorithm.nTheothercoordinate(y-coordinate)iseitherincreasedbyoneaswellorleftunchanged,dependingonthedistancetothenextgridpoint.44BresenhamalgorithmnInordert

23、odecidewhichpointtopick,weintroduceanerrorEwhichisproportionaltothedifferencebetweentheexactpointonthestraightlineandthecenterbetweenthetwopossiblegridpointsontheraster.nThesignofEcanthenbeusedasacriterionforthedecision.nEitherpoint1orpoint2isdrawn,dependingonwhichisclosertothestraightline.dupperyxk

24、xk+1=xk+1dlowerykyk+1linepath45Bresenhamalgorithmdupperyxkxk+1=xk+1dlowerykyk+1linepath46BresenhamalgorithmnIfwescaleEusingx,thenwecaneliminatem.47BresenhamalgorithmnCanEkbecaculatedrecursively?Yes!48BresenhamalgorithmNote:ONLYintegeroperationsareused!Bresenham Algorithm/(x1,y1),(x2,y2),x1 x2x=x1;y=

25、y1;dx=x2-x1;dy=y2-y1;e=2*dy-dx;setPixel(x,y);while(x x2)x=x+1;if(e 0)e=e+2*dy;else e=e+2*dy-2*dx;y=y+1;setPixel(x,y);49BresenhamalgorithmxkEkplot(xk,yk)dx=5,dy=4,2*dy=8,2*dy-2*dx=-2E0=2*dy-dx=3 if(e 0)e=e+2*dy;else e=e+2*dy-2*dx;y=y+1;xkEkplot(xk,yk)03(0,0)11(1,1)2-1(2,2)37(3,2)45(4,3)53(5,4)50Midpo

26、intCircleAlgorithm(Hearn&Baker,Section3-9,P103)nExtensionofBresenhamideasnCircleequation:x2+y2=r2nDefineacirclefunction:f(x,y)=x2+y2-r2nf(x,y)=0(x,y)isoncirclenf(x,y)0(x,y)isoutsidecircle51MidpointCircleAlgorithmnAssumethatwevejustplotted(xk,yk)nSteppinginx,nextpixeliseither:n(xk+1,yk)-the“top”casen

27、(xk+1,yk-1)-the“bottom”casenLookatmidpoint:ykxkxk+1xk+2yk-152MidpointCircleChoicesnInside:f(x,y)0chooselowerpixel53MidpointCircleChoicesnEvaluatefatmidpoint(xk+1,yk-1/2)nDefinePredictor:Pk=f(xk+1,yk-1/2)Pk0outside(choosebottompixel)nPk=(xk+1)2+(yk-1/2)2-r2=xk2+2xk+5/4+yk2-yk-r2n!AsforBresenham,tryto

28、getarecurrencerelationforP.54MidpointCircleChoicesnTopCase:(xk+1=xk+1,yk+1=yk)55MidpointCircleChoicesnBottomCase:(xk+1=xk+1,yk+1=yk-1)56MidpointCircleAlgorithmnInitialPk:57MidpointCircleAlgorithmnInitialPk:P0=1-rnTopCase:(xk+1=xk+1,yk+1=yk)Pk+1=PK+2xk+1+1nBottomCase:(xk+1=xk+1,yk+1=yk-1)Pk+1=PK+2(xk

29、+1-yk+1)+1ykxkxk+1xk+2yk-1585959voidvoidMidPoint_Circle(intMidPoint_Circle(intx0,intx0,inty0,doubley0,doubleradius)radius)intx,y,h;intx,y,h;x=0;y=int(radius);h=1-int(radius);x=0;y=int(radius);h=1-int(radius);Set8Pixel(x0,y0,x,y);/CirclePlotPoints(x0,y0,x,y);/CirclePlotPointswhile(xy)while(xy)x+;x+;i

30、f(h0)if(h0)h+=2*x+1;h+=2*x+1;elsey-;h+=2*(x-y)+1;elsey-;h+=2*(x-y)+1;Set8Pixel(x0,y0,x,y);(x0,y0,x,y);59CirclesnotcenteredonoriginnNewSet8Pixel()Function:60Ch4.AttributesofGeometricPrimitives几何图元的属性611.AreaFillAlgorithms(区域填充算法)(Hearn&Baker,Section3-14/15,P123;Section4-10/11/12/13,P196)62Scan-lineme

31、thods(扫描线填充算法)nWorksrowbyrowfromtoptobottomnApixelinsidethecurrentscanlineisonlydrawnifitislocatedinsidethepolygon.逐点判断法逐点判断法nGreedyapproachveryslow!63CoherencenEdgeCoherence(边的连贯性)n某条边与当前扫描线相交，也可能与下一条扫描线相交nScan-lineCoherence(扫描线的连贯性)n当前扫描线与各边的交点顺序与下一条扫描线与各边的交点顺序可能相同或类似nSpanCoherence(区间的连贯性)n同一区间上的像

32、素取同一颜色属性64Scan-linemethods:ExampleExample:Scanliney=2:-intersectionwithpolygonatx=1,8-wecansubdividethescanlineinto3sections:x8:outsidethepolygon65Scan-linemethods:ExampleExample:Scanliney=4:-intersectionwithpolygonatx=1,4,6,8-wecansubdividethescanlineinto5sections:x1:outsidethepolygon1x4:insidethep

33、olygon4x8:outsidethepolygon66Scan-linemethodsnThesimpleorderededgelistalgorithm(有序边表算法)nMethod:preprocessing+scanconversion67OrderedEdgeListAlgorithmnPreprocessing(1)Determineforeveryedgeofthepolygontheintersectionswiththescanlinesatthepixelcenters;ignorehorizontaledges.(2)Storeeveryintersection(x,y

34、)inalist.(3)Sortlistfromtoptobottom,lefttoright.68OrderedEdgeListAlgorithmnScanconversion(1)Considerpairsofsubsequentintersections(x1,y1)and(x2,y2)inthelist,i.e.listelement1and2,listelement3and4,)(2)Duetothepreprocessingstep,weknowthatforeveryscanliney:y=y1=y2,x1x2(3)Drawallpixelsalongthescanlineyfo

35、rwhich:x1x=360.0)theta-=360.0;nglutPostRedisplay();n115#defineDEG_TO_RAD1.0/57.29578#includeGLfloattheta=0.0voidmydisplay()glClear(GL_COLOR_BUFFER_BIT);glBegin(GL_POLYGON);glVertex2f(cos(DEG_TO_RAD*theta),sin(DEG_TO_RAD*theta);glVertex2f(-sin(DEG_TO_RAD*theta),cos(DEG_TO_RAD*theta);glVertex2f(-cos(DEG_TO_RAD*theta),-sin(DEG_TO_RAD*theta);glVertex2f(sin(DEG_TO_RAD*theta),-cos(DEG_TO_RAD*theta);glEnd();glFlush();116