1Greg HumphreysCS445: Intro GraphicsUniversity of Virginia, Fall 2003Modeling Grab BagGreg HumphreysUniversity of VirginiaCS 445, Fall 2003Choose• Acquisition• Seashells• Fractals• Volumes• Constructive Solid GeometryModel Construction• Interactive modeling toolsD CAD programsD Subdivision surface editors :)• Scanning toolsD CAT, MRI, laser, magnetic, robotic arm, etc.• Computer visionD Stereo, motion, etc.Interactive Modeling Tools• User constructs objects with drawing programD Menu commands, direct manipulation, etc.D CSG, parametric surfaces, quadrics, etc.Cosmoworlds, SGI2Interactive Modeling Tools• Example: Mechanical CADH&B Figure 9.9Model Construction• Interactive modeling toolsD CAD programsD Subdivision surface editors :)• Scanning toolsD Laser, magnetic, robotic arm, etc.• Computer visionD Stereo, motion, etc.Scanning tools• Acquire geometry of objects with active sensorsD CAT/MRID Laser range scannerD Magnetic sensorD Robotic armD etc.Stanford Graphics LaboratoryLorensenScanning tools• Acquire geometry of objects with active sensorsD CAT/MRID Laser range scannerD Magnetic sensorD Robotic armD etc.Depth ColorXp (Xc,Yc)3Laser Range ScanningStanford Graphics Laboratory• Example: 70 scansD Volumetric reconstructionScanning tools• Acquire geometry of objects with active sensorsD CAT/MRID Laser range scannerD Magnetic sensorD Robotic armD etc.Scanning tools• Acquire geometry of objects with active sensorsD CAT/MRID Laser range scannerD Magnetic sensorD Robotic armD etc.Computer Vision• Infer 3D geometry from imagesD StereoD MotionD ConstraintsD etc.4Computer Vision• Infer 3D geometry from imagesD StereoD MotionD ConstraintsD etc.Computer Vision• Infer 3D geometry from imagesD StereoD MotionD ConstraintsD etc.Debevec96Procedural Modeling• Goal: D Describe 3D models algorithmically• Best for models resulting from ...D Repeating processesD Self-similar processesD Random processes• Advantages:D Automatic generationD Concise representationD Parameterized classes of modelsExample: 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 379-387.5Example: 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:D Helico-spiral: z0, λz, r0, λr, Νθ, ∆θD Generating curve: shape, Nc, λcFowler et al. Figure 1Example: Seashells• Generate different shells by varying parametersFowler et al. Figure 2Different helico-spirals6Example: 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!Fractals• Defining property:D Self-similar with infinite resolutionH&B Figure 10.100Mandelbrot SetFractals• Useful for describing natural 3D phenomenonD TerrainD PlantsD CloudsD WaterD FeathersD FurD etc.H&B Figure 10.807Fractal Generation• Deterministically self-similar fractalsD Parts are scaled copies of original• Statistically self-similar fractalsD Parts have same statistical properties as originalDeterministic Fractal Generation• General procedure:D Initiator: start with a shapeD 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!8Deterministic 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 fractalsD Parts are scaled copies of original• Statistically self-similar fractalsD Parts have same statistical properties as originalStatistical Fractal Generation• General procedure:D Initiator: start with a shapeD Generator: replace subparts with a self-similar random patternRandom Midpoint Displacement9Statistical 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 plants10Solid Modeling• Represent solid interiors of objects D Surface may not be described explicitlyVisible Human(National Library of Medicine)SUNY Stony BrookMotivation 1• Some acquisition methods generate solidsD Example: CAT scanStanford UniversityMotivation 2• Some applications require solidsD Example: CAD/CAMIntergraph CorporationSolid Modeling Representations• What makes a good solid representation?D AccurateD ConciseD Affine invariantD Easy acquisitionD Guaranteed validityD Efficient boolean operationsD Efficient displayLorensen11Voxels• Partition space into uniform grid D Grid cells are called a voxels (like pixels)• Store properties of solid object with each voxelD OccupancyD ColorD DensityD TemperatureD etc.FvDFH Figure 12.20Voxel Acquisition• Scanning devices D MRID CAT• SimulationD FEM SUNY Stoney BrookStanford UniversityVoxel Storage•O(n3) storage for nxnxn gridD 1 billion voxels for 1000x1000x1000Voxel Boolean Operations• Compare objects voxel by voxelD Trivial∪=∩=12Voxel Display• Isosurface renderingD Render surfaces bounding volumetric regions of constant value (e.g., density)Isosurface VisualizationPrinceton UniversityVoxel Display• SlicingD Draw 2D image resulting from intersecting voxelswith a planeVisible Human(National Library of Medicine)Voxel Display• Ray castingD Integrate density along rays through pixelsEngine BlockStanford UniversityVoxels• AdvantagesD Simple, intuitive, unambiguousD Same complexity for all objects D Natural acquisition for some applicationsD Trivial boolean operations• DisadvantagesD ApproximateD Not affine invariantD Large storage requirementsD Expensive display13Quadtrees & Octrees• Refine resolution of voxels hierarchicallyD More concise and efficient for non-uniform objectsUniform Voxels QuadtreeFvDFH Figure 12.21Quadtree Boolean
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