Table Of Content

ARAYCASTINGVISIBILITYALGORITHMFORCUBIC SURFACES By I§INGURSESBUYUKLiMANLI ADISSERTATIONPRESENTEDTOTHEGRADUATESCHOOL OFTHEUNIVERSITYOFFLORIDAINPARTIALFULFILLMENT OFTHEREQUIREMENTSFORTHEDEGREEOF DOCTOROFPHILOSOPHY UNIVERSITYOFFLORIDA 1991 ACKNOWLEDGEMENTS Iwouldliketoexpressmyappreciationtomyadvisorandsupervisorycommittee chairman,Dr.JohnStaudhammer,fortheguidanceandencouragementheprovided me onthis project. Iamalso gratefulto the othermembers ofmysupervisory committee.Dr.JamesKeesling,Dr.SteveThebaut,Dr.PanosLivadas,andDr.Carl Crane,fortheircommitment. IalsowishtothankthemembersoftheComputer GraphicsResearchGroup,especiallyKrisIskandarandHasanIncirlioglu,fortheir helpandsuggestions. IwanttothanktoDr.MuratBalabanforhisencouragement andthehelpheprovided. Lastbutnotleast,Ithankmyhusband,mybestfriend, Temel,forhishelp,support,andlovethroughoutthisdissertation. Thisdissertation isdedicatedtomyparents,YurdanurandMuzafferGiirses. ii TABLEOFCONTENTS ACKNOWLEDGEMENTS " ABSTRACT v 1INTRODUCTION 1 LIResearchMotivationandObjective 2 1.2DissertationOverview 4 2REVIEWOFBASICCONCEPTSUSED 5 2.1ImageSynthesis 5 2.L1VisibilityDetermination 8 2.L2RayCasting 10 2.2CurvedSurfaces 17 3 PROBLEM DEFINITION AND REVIEW OF EXISTING ALGORITHMS 28 3.1ProblemDefinition 28 3.2LiteratureReview 30 3.2.1NumericalTechniques 31 3.2.2SubdivisionTechniques 33 3.2.3ParallelProcessingTechniques 35 4THEPROPOSEDALGORITHM 37 4.1PreprocessingSteps 38 4.1.1SelectionofaBoundingVolume 38 4.1.2ConstructionofaBoundingBoxTree 41 4.1.3DeterminationofBoundaryEdges 42 4.1.4LocationofSilhouetteEdges 43 4.1.5CalculationofSurfaceNormal 45 4.2Newton'sMethod 48 4.3Algorithm 53 4.4LightingModel 57 4.5ResultsandDiscussion 60 4.5.1ComplexityandPerformanceAnalysis 61 4.5.2SimulationResults 64 iii 5THEPARALLELIMPLEMENTATIONOFTHEALGORITHM 66 5.1Coherence 69 5.2ForwardDifferencingTechnique 70 5.3PipelinedandParallelArchitecture 76 5.4ResultsandDiscussion 77 5.4.1ComplexityandPerformanceAnalysis 80 5.4.2SimulationResults 88 6CONCLUSION 90 6.1Summary 90 6.2FutureWork 93 BIBLIOGRAPHY 95 BIOGRAPHICALSKETCH 101 iv I AbstractofDissertationPresentedtotheGraduateSchool oftheUniversityofFloridainPartialFulfillmentofthe RequirementsfortheDegreeofDoctorofPhilosophy ARAYCASTINGVISIBILITYALGORITHMFORCUBICSURFACES By I§mGiirsesBiiyiiklimanli May1991 Chairman:Dr.JohnStaudhammer MajorDepartment:ComputerandInformationSciences Analgorithmforraycastingparametricsurfacesisdevelopedforvisibility calculation. Thenewalgorithmsolvestheray/surfaceintersectiondirectlyusing Newtoniterationandutilizes ray-to-raycoherence. Thecomputationrequiredis reduced using bounding boxes as bounding volumes, coherence, and forward differencingmethods. Aparallelimplementationofthealgorithmisalsopresented takingadvantageoftheparallelismofraycastingtofurtherreducethealgorithm's computationalrequirements. Thefinalparametricsurface intersectionalgorithm givesagoodcombinationofspeedandaccuracy. Thealgorithmseemstobewell suitedforhardwareimplementation. Algorithmsaswellasvariousarchitecturesarereviewedandsomeofthemare alsocomparedtothenewalgorithmtoproveitsefficiency. Asystemsimulatoris developed to verify the algorithm and the functional behavior of the system architecture. V CHAPTER1 INTRODUCTION Computergraphicsproducespicturesgeneratedbyacomputerprogrammed andoperatedbyhumanbeings. Onlytheimaginationoftheuserandthecapability of the hardware limits the form they can take: animation, simulation, graphs, recreations,portraits,architecture,drawings,paintings,orjustsimplelines. Because computergraphicsisawayofmakingthoughtsandideasvisible,theserevolutionary imagesarebecomingtheuniversallanguageofourtime[WARD89]. Thedesignandmanufactureofaircraft,turbomachinery,andautomobiles, and recentapplications inthe advertisingand animationindustrieshavebecome driving forces behind research into techniques for surface design. Curves and surfaceshavingfree-formshapessuchasfaces,clothes,shoes,clouds,mountains,car bodies,airplanes,areimportantintheconstructionofthree-dimensionalobjectsfor imagesynthesisincomputergraphics. Thevastmajorityofcurvedsurfacesmaybe definedwitharelativelyfewnumbersbyusingpiecewisecontinuoussurfacepatches [BART87]. However, the display of these surfaces, the rendering, on a high-definitiondisplayrequiresthecomputationofcoloringonapixel-by-pixelbasis. Clearlythiscanbeacomputationallyintensivetask,eventhoughthecolorvariations areoftenslight. 1 / 2 Oneofthemorewidelyusedmethodsforfinelyrenderingobjectsonadisplay screenisraycasting. Asthenameimplies,theprocedurecallsforcalculatingthe lightpropertiesofarayoflightwhichtravelsfromthesurfaceelementsinapixel totheobserver. Raycastingisapowerfulyetsimpleapproachtoimagegeneration. This method hasbecome one ofthe important tools fromwhich highly realistic imagesaregenerated. Butitalsohasdisadvantages. Themajordrawbackofthis procedureisthegreatamountoftimetocomputeray/surfaceintersections. Inthis dissertation,thisproblemisattackedandanewraycastingvisibilityalgorithmis devised. Thisalgorithmhasbeencomparedwithsomealgorithmsthatarewidely used. Theresultsshowthatitsexecutiontimeisabitbetterthantheothers. Ithas uniqueproperties:itisshort,elegantandhassomeinterestingapplications. 1.1ResearchMotivationandObjective Thisdissertationwasmotivatedbythelackofefficientraycastingalgorithms for curved surfaces. This work especially deals with ray casting of parametric surfaces. Theparametricmethodofsurfacerepresentationisveryconvenientfor approximationanddesignofcurvedsurfaces. Inparticular,Beziersurfacepatches andB-Splinesurfacesareextensivelyused incomputergraphicsandCAD. The research has focused onefficient and fastalgorithm designwith the objective of determiningtheray/objectintersectionsasfastaspossible. Theresearchhasalso addressed both the efficiency and speed of existing algorithms and analyzed 3 deficienciesofthosealgorithms. Thisprocessledtoanewapproachtoresolvethose deficiencies. Asthefirstpartoftheresearch,theNewton-Raphsonmethodisreformulated forBeziersurfacestoreducethecomplexityoftheray/objectintersections. Since everyraycastingalgorithmisbynatureanobject-orientedone,thischaracteristic madethedesignandimplementationattractivebyapplyingobject-orientedconcepts andideas. For applications that require fast transformation such as ray casting and renderingofcomplexshadedimages,aparallel,pipelinedmultiprocessorarchitecture canbeusedtoachievehighreal-timeperformanceforimagesynthesis. Aparallel architectureoffersanincreaseinspeedthatgrowsalmostlinearlywiththenumber ofprocessorsused. Toextractthemaximumefficiencyfromaparallelarchitecture, key bottlenecks must be identified and an architecture that is best suited to overcomingthosebottlenecksmustbeimplemented. Sincethecalculationforaray castthroughapixelinthescreenisindependentofthecalculationforotherrays cast,thisprocesscanbeimplementedinparallel. Therefore,asasecondpartofthis research,aVLSI-orientedreal-timealgorithmisdevelopedthatcombinesefficiency, simplicity,speed,andparallelism. Usinganincrementaltechnique,thecomputation fortheintersectionsofaraywithsurfacesisreduced. Thealgorithmisdesignedin awaythateachintersectionprocessorcanbeplacedinaVLSIchip. Inapractical display system several of these chips may be used to calculate surface-ray intersectionsatpixelsorgroupsofpixels. 4 1.2DissertationOverview Thisdissertationisconcernedwiththedesignofanefficientalgorithmfor displaypurposes. Itisorganizedintosixchapters. Chapter 1 isanintroductory chapter-thatcoversobjectivesandbackground aboutthedissertationsubject. In chapter2areviewispresentedofthebasicconceptsuseddevisingthealgorithm. Chapter3definestheproblemandgivesareviewofexistingalgorithms. Chapter4 discussesthedetailsofthealgorithmanditscomplexityandperformanceanalysis. Chapter5describesthetechniquestoreducethecomputationrequiredandparallel implementationofthealgorithmandcomplexityandperformanceanalysisresultsare given. Finally,chapter6summarizestheresultsalongwithsuggestionsforfuture work. Insummary,themajorcontributionsofthisworkarethedesignofanefficient ray/objectintersectionalgorithm,andimprovementsonthisalgorithmtomakeit suitableforparallelhardwareimplementation. CHAPTER2 REVIEWOFBASICCONCEPTSUSED 2.1ImageSynthesis Imagesynthesisisthesubfieldofcomputergraphicsthatisconcernedwiththe productionofpicturesdefinedbynumbersandprocedures. Iftheimageistoappear truetoaphysical object, theprocessmaybe costly, complexand may requirea tremendousamountofcomputingpower. Thereisatradeoffpresentinallimage synthesisapplicationsbetweenrealismandtheamountofrequiredcomputations. Theimagesynthesisisusuallyaccomplishedwithaseriesofprocesses,termed theimagesynthesispipeline. Basedonasimulationoflightpropagationinthereal world, the image synthesis pipeline consists of several steps: creating data representations,geometryprocessing(modelingtransformation,viewingoperation), rasterization(visible-surfacedetermination,scanconversion,shading),anddisplaying theresult. Geometryprocessingisindependentofthedisplaydevice,whereasthe rasterizationpipelinetakestransformed,clippedprimitivesandproducespixels. The displayprocessthatmapsamodeltoanimageonscreeniscalledrendering,andits implementationinsoftwareand/orhardwareisreferredtoastherenderingpipeline. Thisstandardgraphicsrendering,theimagesynthesispipeline,isshowninFigure2.1. 5