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Displaced Subdivision Surfaces

Displaced Subdivision Surfaces. Aaron Lee Princeton University. Hugues Hoppe Microsoft Research. Henry Moreton Nvidia. Triangle Meshes. Interactive animation Adaptive rendering Compact storage Transmission. Dataset provided by Cyberware. mesh simplification. Scalable Algorithms.

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Displaced Subdivision Surfaces

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  1. Displaced Subdivision Surfaces Aaron Lee Princeton University Hugues Hoppe Microsoft Research Henry Moreton Nvidia

  2. Triangle Meshes • Interactive animation • Adaptive rendering • Compact storage • Transmission Dataset provided by Cyberware

  3. mesh simplification Scalable Algorithms • Multiresolution now well established subdivision surfaces

  4. Subdivision Surfaces • Smooth (C1) with arbitrary topology • No stitching of patches • Easy Implementation • Simple subdivision rules • Level-of-detail rendering • Uniform or adaptive subdivision

  5. Displacement Mapping • Scalar/Vector displacement • Cook 84 • RenderMan • Mesh approximation • Krishnamurthy-Levoy 96, … • Hardware implementation • Gumhold-Hüttner 99, …

  6. Our Approach DSS = Smooth Domain  Scalar Disp Field Displaced Subdivision surface Control mesh Domain Surface

  7. Representation Overview Piecewise-regular mesh of scalar displacement sampling pattern Control mesh

  8. Advantages of DSS • Intrinsic parameterization • Governed by a subdivision surface • No storage necessary • Significant computation efficiency • Capture detail as scalar displacement • Unified representation • Same sampling pattern and subdivision rules for geometry and scalar displacement field

  9. Analytic Properties • C1 continuous everywhere except at extraordinary vertices • Surface normals are easy to evaluate

  10. Evaluation of derivatives

  11. Conversion Algorithm • Control mesh creation • Control mesh optimization • Scalar displacement computation • Attribute resampling

  12. Control Mesh Creation Mesh Simplification Normal Cone Constraint Original Mesh Initial Control Mesh [Garland 97] Surface simplification using quadric error metrics

  13. Normal Cone Constraint allowable normals on Gauss sphere

  14. Tracking Correspondences • Control Mesh Creation • mesh simplification 11776 faces 120 faces [Lee 98] Multiresolution Adaptive Parameterization of Surfaces

  15. Control Mesh Creation Mesh Simplification Normal Cone Constraint Original Mesh Initial Control Mesh

  16. Control Mesh Optimization Global Optimization Initial Control Mesh Optimized Control Mesh [Hoppe 94] Piecewise smooth surface reconstruction

  17. Scalar Displacement Computation Scalar Displacement Field Smooth Domain Surface Displaced Subdivision Surface [Gottschalk, Lin and Manocha 96] OBB-tree

  18. Attribute Resampling DSS With Scalar Displacement Field DSS with Resampled Texture Original mesh

  19. Applications • Editing • Animation • Bump mapping • Adaptive tessellation • Compression

  20. Editing

  21. Animation Polyhedral Domain Surface (e.g. Gumhold-Hüttner 99) Smooth Domain Surface (DSS)

  22. Bump Mapping • Explicit geometry Bump map 134,656 faces 8,416 faces 526 faces [Blinn 78] Simulation of wrinkled surfaces

  23. Adaptive Tessellation

  24. VIDEO

  25. Compression Scalar Displacement field Quantizer Entropy Coder M0 Quantizer Entropy Coder Delta encoding with Linear Prediction M1 Bit Allocation Quantizer Entropy Coder Mk

  26. Compression (Venus) [Venus Raw Data] 1,800,032 bytes IBM VRML Compressed Binary Format (Draft 4 Implementation)

  27. Conclusion • DSS Representation: • Unified representation • Simple subdivision rules • Analytic surface properties • Applications • Editing • Animation • Bump mapping • Adaptive tessellation • Compression

  28. Q & A

  29. Timings and Results Scalar field creation Simplification Input size # Base Optimization Dataset #triangles domain (mins) (mins) (mins) triangles Armadillo 1306 210,944 61 25 2.5 Venus 748 28 11 2 100,000 1.3 Bunny 69,451 526 19 12 4.6 43 342,138 1564 115 Dinosaur

  30. DSS Vs Normal Meshes • + Single level displacement map • Hardware implementation • Easy conversion to bump map • + Displacements strictly scalar • No extraordinary vector displacements • Less compression • Multilevel displacement map

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