2. 1 Displaced Subdivision Surfaces Aaron Lee Princeton University Henry Moreton Nvidia Hugues Hoppe Microsoft Research

3. 2 Triangle Meshes Interactive animation Adaptive rendering Compact storage Dataset provided by Cyberware

4. 3 Scalable Algorithms Multiresolution now well established subdivision surfaces mesh simplification

5. 4 Subdivision Surfaces Smooth with arbitrary topology No stitching of patches Easy Implementation Simple subdivision rules Level-of-detail rendering Uniform or adaptive subdivision

6. 5 Our Approach Control mesh Domain Surface Displaced Subdivision surface DSS = Smooth Domain  Scalar Disp Field

7. 6 Representation Overview Control mesh Piecewise-regular mesh of scalar displacement sampling pattern

8. 7 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. 8 Conversion Algorithm Control mesh creation Control mesh optimization Scalar displacement computation Attribute resampling

10. 9 Control Mesh Creation Mesh Simplification Original MeshInitial Control Mesh [Garland 97] Surface simplification using quadric error metrics Normal Cone Constraint

11. 10 Normal Cone Constraint allowable normals on Gauss sphere

12. 11 Tracking Correspondences Control Mesh Creation mesh simplification 11776 faces120 faces [Lee 98] Multiresolution Adaptive Parameterization of Surfaces

13. 12 Conversion Process 1. Obtain an initial control mesh by simplifying the original mesh. 2.Globally optimize the control mesh vertices. 3.Sample the displacement map and computr the signed displacement.

14. 13 Control Mesh Creation Mesh Simplification Original MeshInitial Control Mesh Normal Cone Constraint

15. 14 Control Mesh Optimization Initial Control MeshOptimized Control Mesh Global Optimization

16. 15 Scalar Displacement Computation Scalar Displacement Field Smooth Domain SurfaceDisplaced Subdivision Surface

17. 16 Attribute Resampling Original mesh DSS With Scalar Displacement Field DSS with Resampled Texture

18. 17 Applications Editing Animation Bump mapping Adaptive tessellation Compression

19. 18 Editing

20. 19 Animation Smooth Domain Surface (DSS) Polyhedral Domain Surface (e.g. Gumhold-Hüttner 99)

21. 20Animation

22. 21 Bump Mapping 134,656 faces 8,416 faces526 faces Explicit geometry Bump map [Blinn 78] Simulation of wrinkled surfaces

23. 22 Adaptive Tessellation Threshold4.01.3 #Triangles6,37622,190 L 2 error0.13 %0.05 %

24. 23 Compression Delta encoding with Linear Prediction Scalar Displacement field M0M0 M1M1 MkMk Quantizer Entropy Coder Quantizer Entropy Coder Quantizer Entropy Coder Bit Allocation

25. 24 Compression (Venus) OriginalSimplifiedDSSCompression Ratio Mesh Info #V=50002 #F=100000 #V=10002 #F=20000 #V=376 #F=748 (sub 4 times) 23 bits L 2 0.0014% 0.027%0.028% 12 bits L 2 0.014%0.03% 8 bits L 2 0.21% 0.15% [Venus Raw Data] 1,800,032 bytes Kbytes 3467517108 Kbytes 1403316115 Kbytes 69184410

26. 25 Compression (Dinosour)

27. 26 Conclusion DSS Representation: Unified representation Simple subdivision rules Analytic surface properties Applications Editing Animation Bump mapping Adaptive tessellation Compression

28. 27 Timings and Results Dataset Input size #triangles Armadillo 210,944 Venus 100,000 Bunny # Base domain triangles 69,451 Dinosaur 342,138 1306 748 526 1564 Simplification (mins) 61 28 19 115 Optimization (mins) 25 11 12 43 Scalar field creation (mins) 2.5 2 1.3 4.6

29. 28 over