1Procedural ModelingAdam FinkelsteinPrinceton UniversityCOS 426, Spring 2003Modeling• How do we ...o Represent 3D objects in a computer?o Construct such representations quickly and/or automatically with a computer?o Manipulate 3D objects with a computer?H&B Figure 10.83bFowlerH&B Figure 10.79Modeling• How do we ...o Represent 3D objects in a computer?o Construct such representations quickly and/or automatically with a computer?o Manipulate 3D objects with a computer?H&B Figure 10.83bFowlerH&B Figure 10.79Model Construction• Interactive modeling toolso CAD programso Subdivision surface editors :)• Scanning toolso CAT, MRI, laser, magnetic, robotic arm, etc.• Computer visiono Stereo, motion, etc.• Procedural generationo Sweeps, fractals, grammarsInteractive Modeling Tools• User constructs objects with drawing programo Menu commands, direct manipulation, etc.o CSG, parametric surfaces, quadrics, etc.Cosmoworlds, SGIInteractive Modeling Tools• Example: Mechanical CADH&B Figure 9.92Model Construction• Interactive modeling toolso CAD programso Subdivision surface editors :)• Scanning toolso Laser, magnetic, robotic arm, etc.• Computer visiono Stereo, motion, etc.• Procedural generationo Sweeps, fractals, grammarsScanning tools• Acquire geometry of objects with active sensorso CAT/MRIo Laser range scannero Magnetic sensoro Robotic armo etc.Stanford Graphics LaboratoryLorensenScanning tools• Acquire geometry of objects with active sensorso CAT/MRIo Laser range scannero Magnetic sensoro Robotic armo etc.DepthColorXp (Xc,Yc)Laser Range ScanningStanford Graphics Laboratory• Example: 70 scanso Volumetric reconstructionScanning tools• Acquire geometry of objects with active sensorso CAT/MRIo Laser range scannero Magnetic sensoro Robotic armo etc.Scanning tools• Acquire geometry of objects with active sensorso CAT/MRIo Laser range scannero Magnetic sensoro Robotic armo etc.3Model Construction• Interactive modeling toolso CAD programso Subdivision surface editors :)• Scanning toolso Laser, magnetic, robotic arm, etc.• Computer visiono Stereo, motion, etc.• Procedural generationo Sweeps, fractals, grammarsComputer Vision• Infer 3D geometry from imageso Stereoo Motiono Constraintso etc.Computer Vision• Infer 3D geometry from imageso Stereoo Motiono Constraintso etc.Computer Vision• Infer 3D geometry from imageso Stereoo Motiono Constraintso etc.Debevec96Model Construction• Interactive modeling toolso CAD programso Subdivision surface editors :)• Scanning toolso Laser, magnetic, robotic arm, etc.• Computer visiono Stereo, motion, etc.• Procedural generationo Sweeps, fractals, grammarsProcedural Modeling• Goal: o Describe 3D models algorithmically• Best for models resulting from ...o Repeating processeso Self-similar processeso Random processes• Advantages:o Automatic generationo Concise representationo Parameterized classes of models4Procedural Modeling•Sweeps• Fractals• GrammarsExample: Seashells• Create 3D polygonal surface models of seashellsFowler et al. Figure 7“Modeling Seashells,” Deborah Fowler, Hans Meinhardt, and Przemyslaw Prusinkiewicz,Computer Graphics (SIGGRAPH 92), Chicago, Illinois, July, 1992, p 379-387.“Modeling Seashells,” Deborah Fowler, Hans Meinhardt, and Przemyslaw Prusinkiewicz,Computer Graphics (SIGGRAPH 92), Chicago, Illinois, July, 1992, p 379-387.Example: Seashells• Sweep generating curve around helico-spiral axisFowler et al. Figure 1ziiriiiizzrrλλ==∆Θ+Θ=Θ+++111Helico-spiral definition:Example: Seashells• Connect adjacent points to form polygonal meshFowler et al. Figure 6Example: Seashells• Model is parameterized:o Helico-spiral: z0, λz, r0, λr,Νθ, ∆θo Generating curve: shape, Nc, λcFowler et al. Figure 1Example: Seashells• Generate different shells by varying parametersFowler et al. Figure 2Different helico-spirals5Example: Seashells• Generate different shells by varying parametersFowler et al. Figure 3Different generating curvesExample: SeashellsFowler et al. Figures 4,5,7Generate many interesting shellswith a simple procedural model!Generate many interesting shellswith a simple procedural model!Procedural Modeling•Sweeps• Fractals• GrammarsFractals• Defining property:o Self-similar with infinite resolutionH&B Figure 10.100Mandelbrot SetFractals• Useful for describing natural 3D phenomenono Terraino Plantso Cloudso Watero Featherso Furo etc.H&B Figure 10.80Fractal Generation• Deterministically self-similar fractalso Parts are scaled copies of original• Statistically self-similar fractalso Parts have same statistical properties as original6Deterministic Fractal Generation• General procedure:o Initiator: start with a shapeo Generator: replace subparts with scaled copy of originalH&B Figure 10.68Deterministic Fractal Generation• Apply generator repeatedlyH&B Figure 10.69Koch CurveDeterministic Fractal GenerationMandelbrot Figure X• Useful for creating interesting shapes!Deterministic Fractal GenerationMandelbrot Figure 46• Useful for creating interesting shapes!Deterministic Fractal GenerationH&B Figures 75 & 109• Useful for creating interesting shapes!Fractal Generation• Deterministically self-similar fractalso Parts are scaled copies of original• Statistically self-similar fractalso Parts have same statistical properties as original7Statistical Fractal Generation• General procedure:o Initiator: start with a shapeo Generator: replace subparts with a self-similar random patternRandom Midpoint DisplacementStatistical Fractal Generation• Example: terrainH&B Figure 10.83bStatistical Fractal GenerationH&B Figure 10.83a• Useful for creating mountainsStatistical Fractal GenerationH&B Figure 10.82• Useful for creating 3D plantsStatistical Fractal GenerationH&B Figure 10.79• Useful for creating 3D plantsProcedural Modeling•Sweeps• Fractals• Grammars8Grammars• Generate description of geometric model by applying production rulesSABA Ba | aB Ab | bSABA Ba | aB Ab | babbabbaababaab...Grammars• Useful for creating plantsTree Branch Tree | Leaf Branch Cylinder | [ Tree ]C[CL]C[C[CL][CL]]C[[CL][CL]]C[*]C[*][*]GrammarsH&B Figure 10.77• Useful for creating plantsSummary• Interactive modeling toolso CAD programso Subdivision surface editors :)• Scanning toolso CAT, MRI, Laser, magnetic, robotic arm, etc.• Computer visiono Stereo, motion, etc.• Procedural generationo Sweeps, fractals,
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