11Model ConstructionAdam FinkelsteinPrinceton UniversityC0S 426, Fall 20012Modeling• How do we ...o Represent 3D objects in a computer?o Construct such representationsquickly and/or automatically with a computer?o Manipulate 3D objects with a computer?LorensenH&B Figure 10.83bFowlerH&B Figure 10.793Modeling• How do we ...o Represent 3D objects in a computer?o Construct such representationsquickly and/or automatically with a computer?o Manipulate 3D objects with a computer?LorensenH&B Figure 10.83bFowlerH&B Figure 10.794Model Construction• Interactive modeling toolso CAD programso Subdivision surface editors :)• Scanning toolso CAT, MRI, las er, magnetic, robotic arm, etc.• Computer visiono Stereo, motion, etc.• Procedural generationo Sweeps, fractals, grammars5Interactive Modeling Tools• User constructs objects with drawing programo Menu commands, direct manipulation, etc.o CSG, parametric surfaces, quadrics, etc.Cosmoworlds, SGI6Interactive Modeling Tools• Example: Mechanical CADH&B Figure 9.927Model 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, grammars8Scanning tools• Acquire geometry of objects with active sensorso CAT/MRIo Laser range scannero Magnetic sensoro Robotic armo etc.Stanford Graphics Laboratory9Scanning tools• Acquire geometry of objects with active sensorso CAT/MRIo Laser range scannero Magnetic sensoro Robotic armo etc.Depth ColorXp (Xc,Yc)10Laser Range ScanningStanford Graphics Laboratory• Example: 70 scanso Volumetric reconstruction11Scanning tools• Acquire geometry of objects with active sensorso CAT/MRIo Laser range scannero Magnetic sensoro Robotic armo etc.12Scanning tools• Acquire geometry of objects with active sensorso CAT/MRIo Laser range scannero Magnetic sensoro Robotic armo etc.313Model 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, grammars14Computer Vision• Infer 3D geometry from imageso Stereoo Motiono Constraintso etc.15Computer Vision• Infer 3D geometry from imageso Stereoo Motiono Constraintso etc.16Computer Vision• Infer 3D geometry from imageso Stereoo Motiono Constraintso etc.Debevec9617Model 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, grammars18Procedural 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 models419Procedural Modeling• Sweeps• Fractals• Grammars20Example: 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 379-387.21Example: Seashells• Sweep generating curve around helico-spiral axisFowler et al. Figure 1ziiriiiizzrrλλ==∆Θ+Θ=Θ+++111Helico-spiral definition:22Example: Seashells• Connect adjacent points to form polygonal meshFowler et al. Figure 623Example: Seashells• Model is parameterized:o Helico-spiral: z0, λz, r0, λr, Νθ, ∆θo Generating curve: shape, Nc, λcFowler et al. Figure 124Example: Seashells• Generate different shells by varying parametersFowler et al. Figure 2Different helico-spirals525Example: Seashells• Generate different shells by varying parametersFowler et al. Figure 3Different generating curves26Example: SeashellsFowler et al. Figures 4,5,7Generate many interesting shellswithasimpleproceduralmodel!Generate many interesting shellswithasimpleproceduralmodel!27Procedural Modeling• Sweeps• Fractals• Grammars28Fractals• Defining property:o Self-similar with infinite resolutionH&B Figure 10.100Mandelbrot Set29Fractals• Useful for describing natural 3D phenomenono Terraino Plantso Cloudso Watero Featherso Furo etc.H&B Figure 10.8030Fractal Generation• Deterministically self-similar fractalso Parts are scaled copies of original• Statistically self-similar fractalso Parts have s ame statistical properties as original631Deterministic Fractal Generation• General procedure:o Initiator: start with a shapeo Generator: replace subparts with scaled copy of originalH&B Figure 10.6832Deterministic Fractal Generation• Apply generator repeatedlyH&B Figure 10.69Koch Curve33Deterministic Fractal GenerationMandelbrot Figure X• Useful for creating interesting shapes!34Deterministic Fractal GenerationMandelbrot Figure 46• Useful for creating interesting shapes!35Deterministic Fractal GenerationH&B Figures 75 & 109• Useful for creating interesting shapes!36Fractal Generation• Deterministically self-similar fractalso Parts are scaled copies of original• Statistically self-similar fractalso Parts have s ame statistical properties as original737Statistical Fractal Generation• General procedure:o Initiator: start with a shapeo Generator: replace subparts with a self-similarrandom patternRandom Midpoint Displacement38Statistical Fractal Generation• Example: terrainH&B Figure 10.83b39Statistical Fractal GenerationH&B Figure 10.83a• Useful for creating mountains40Statistical Fractal GenerationH&B Figure 10.82• Useful for creating 3D plants41Statistical Fractal GenerationH&B Figure 10.79• Useful for creating 3D plants42Procedural Modeling• Sweeps• Fractals• Grammars843Grammars• Generate description of geometric modelby applying production rulesSABABa|aBAb|bSABABa|aBAb|babbabbaababaab...44Grammars• Useful for creating plantsTree Branch Tree | LeafBranch Cylinder | [ Tree ]C[CL]C[C[CL][CL]]C[[CL][CL]]C[*]C[*][*]45GrammarsH&B Figure 10.77• Useful for creating plants46Summary• Interactive modeling toolso CAD programso Subdivision surface editors :)• Scanning toolso CAT, MRI, Laser, magnetic, robotic arm, etc.• Computer visiono Stereo, motion, etc.• Procedural
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