1. Pauly, Keiser, Kobbelt, Gross: Shape Modeling with Point-Sampled GeometrySIGGRAPH 2003 Shape Modeling with Point-Sampled Geometry Mark Pauly Richard Keiser Leif Kobbelt Markus Gross ETH Zürich RWTH Aachen

2. Pauly, Keiser, Kobbelt, Gross: Shape Modeling with Point-Sampled GeometrySIGGRAPH 2003 Motivation Surface representations –Explicit surfaces (B-reps) Polygonal meshes Subdivision surfaces NURBS –Implicit surfaces Level sets Radial basis functions Algebraic surfaces - Efficient rendering - Sharp features - Intuitive editing - Boolean operations - Changes of topology - Extreme deformations

3. Pauly, Keiser, Kobbelt, Gross: Shape Modeling with Point-Sampled GeometrySIGGRAPH 2003 Motivation Surface representations –Explicit surfaces (B-reps) Polygonal meshes Subdivision surfaces NURBS –Implicit surfaces Level sets Radial basis functions Algebraic surfaces  - Boolean operations  - Changes of topology  - Extreme deformations  - Efficient rendering  - Sharp features  - Intuitive editing

4. Pauly, Keiser, Kobbelt, Gross: Shape Modeling with Point-Sampled GeometrySIGGRAPH 2003 Motivation Surface representations –Explicit surfaces (B-reps) Polygonal meshes Subdivision surfaces NURBS –Implicit surfaces Level sets Radial basis functions Algebraic surfaces –Hybrid Representation Explicit cloud of point samples Implicit dynamic surface model

5. Pauly, Keiser, Kobbelt, Gross: Shape Modeling with Point-Sampled GeometrySIGGRAPH 2003 Outline Implicit surface model –Moving least squares approximation Interactive shape modeling –Boolean operations –Free-form deformation Demo Results & Conclusions

6. Pauly, Keiser, Kobbelt, Gross: Shape Modeling with Point-Sampled GeometrySIGGRAPH 2003 Surface Model Goal: Define continuous surface from a set of discrete point samples discrete set of point samples P = { p i, c i, m i,... } continuous surface S interpolating or approximating P

7. Pauly, Keiser, Kobbelt, Gross: Shape Modeling with Point-Sampled GeometrySIGGRAPH 2003 Surface Model Moving least squares (MLS) approximation (Levin, Alexa et al.) –Surface defined as stationary set of projection operator  P  implicit surface model –Weighted least squares optimization Gaussian kernel function –local, smooth –mesh-less, adaptive

8. Pauly, Keiser, Kobbelt, Gross: Shape Modeling with Point-Sampled GeometrySIGGRAPH 2003 Boolean Operations +--

9. Pauly, Keiser, Kobbelt, Gross: Shape Modeling with Point-Sampled GeometrySIGGRAPH 2003 Boolean Operations Classification –Inside-outside test using signed distance function induced by MLS projection Sampling –Compute exact intersection of two MLS surfaces to sample the intersection curve Rendering –Accurate depiction of sharp corners and creases using point-based rendering

10. Pauly, Keiser, Kobbelt, Gross: Shape Modeling with Point-Sampled GeometrySIGGRAPH 2003 Boolean Operations Classification: –given a smooth, closed surface S and point p. Is p inside or outside of the volume V bounded by S?

11. Pauly, Keiser, Kobbelt, Gross: Shape Modeling with Point-Sampled GeometrySIGGRAPH 2003 Boolean Operations Classification: –given a smooth, closed surface S and point p. Is p inside or outside of the volume V bounded by S? 1.find closest point q on S

12. Pauly, Keiser, Kobbelt, Gross: Shape Modeling with Point-Sampled GeometrySIGGRAPH 2003 Classification: –given a smooth, closed surface S and point p. Is p inside or outside of the volume V bounded by S? 1.find closest point q on S 2.classify p as –inside V, if (p-q)·n < 0 –outside V, if (p-q)·n > 0 Boolean Operations

13. Pauly, Keiser, Kobbelt, Gross: Shape Modeling with Point-Sampled GeometrySIGGRAPH 2003 Boolean Operations Classification: –represent smooth surface S by point cloud P m

14. Pauly, Keiser, Kobbelt, Gross: Shape Modeling with Point-Sampled GeometrySIGGRAPH 2003 Boolean Operations Classification: –represent smooth surface S by point cloud P m 1.find closest point q in P 2.classify p as –inside V, if (p-q)·n < 0 –outside V, if (p-q)·n > 0

15. Pauly, Keiser, Kobbelt, Gross: Shape Modeling with Point-Sampled GeometrySIGGRAPH 2003 Boolean Operations Classification: –piecewise constant surface approximation leads to false classification close to the surface

16. Pauly, Keiser, Kobbelt, Gross: Shape Modeling with Point-Sampled GeometrySIGGRAPH 2003 Boolean Operations Classification: –piecewise constant surface approximation leads to false classification close to the surface

17. Pauly, Keiser, Kobbelt, Gross: Shape Modeling with Point-Sampled GeometrySIGGRAPH 2003 Boolean Operations Classification: –piecewise constant surface approximation leads to false classification close to the surface

18. Pauly, Keiser, Kobbelt, Gross: Shape Modeling with Point-Sampled GeometrySIGGRAPH 2003 Boolean Operations Classification: –piecewise constant surface approximation leads to false classification close to the surface

19. Pauly, Keiser, Kobbelt, Gross: Shape Modeling with Point-Sampled GeometrySIGGRAPH 2003 Boolean Operations Classification: –piecewise constant surface approximation leads to false classification close to the surface

20. Pauly, Keiser, Kobbelt, Gross: Shape Modeling with Point-Sampled GeometrySIGGRAPH 2003 Boolean Operations Classification: –use MLS projection of p for correct classification

21. Pauly, Keiser, Kobbelt, Gross: Shape Modeling with Point-Sampled GeometrySIGGRAPH 2003 Sampling the intersection curve Boolean Operations A classification sampling the intersection curve B A  B

22. Pauly, Keiser, Kobbelt, Gross: Shape Modeling with Point-Sampled GeometrySIGGRAPH 2003 Sampling the intersection curve 1.identify pairs of closest points Boolean Operations

23. Pauly, Keiser, Kobbelt, Gross: Shape Modeling with Point-Sampled GeometrySIGGRAPH 2003 Sampling the intersection curve 1.identify pairs of closest points Boolean Operations

24. Pauly, Keiser, Kobbelt, Gross: Shape Modeling with Point-Sampled GeometrySIGGRAPH 2003 Sampling the intersection curve 1.identify pairs of closest points 2.find closest point on intersection of tangent spaces Boolean Operations

25. Pauly, Keiser, Kobbelt, Gross: Shape Modeling with Point-Sampled GeometrySIGGRAPH 2003 Sampling the intersection curve 1.identify pairs of closest points 2.find closest point on intersection of tangent spaces 3.re-project point on both surfaces Boolean Operations

26. Pauly, Keiser, Kobbelt, Gross: Shape Modeling with Point-Sampled GeometrySIGGRAPH 2003 Sampling the intersection curve 1.identify pairs of closest points 2.find closest point on intersection of tangent spaces 3.re-project point on both surfaces 4.iterate Boolean Operations

27. Pauly, Keiser, Kobbelt, Gross: Shape Modeling with Point-Sampled GeometrySIGGRAPH 2003 Boolean Operations Demo – Part 1 –Dinosaur: 56,194 samples –Max Planck: 52,809 samples

28. Pauly, Keiser, Kobbelt, Gross: Shape Modeling with Point-Sampled GeometrySIGGRAPH 2003 Free-form Deformation Smooth deformation field F:R 3  R 3 that warps 3D space Can be applied directly to point samples

29. Pauly, Keiser, Kobbelt, Gross: Shape Modeling with Point-Sampled GeometrySIGGRAPH 2003 Free-form Deformation Intuitive editing using painting metaphor –Define rigid surface part and handle using interactive painting tool –Displace handle using translation and/or rotation –Create smooth blend towards rigid part control handle rigid part deformable part

30. Pauly, Keiser, Kobbelt, Gross: Shape Modeling with Point-Sampled GeometrySIGGRAPH 2003 Dynamic Sampling Large deformations lead to strong distortions 10,000 points271,743 points Robust free-form deformation requires dynamic adaptation of the sampling density

31. Pauly, Keiser, Kobbelt, Gross: Shape Modeling with Point-Sampled GeometrySIGGRAPH 2003 Dynamic Sampling Dynamic insertion of point samples: –measure local surface stretch –split samples that exceed stretch threshold –regularize distribution by relaxation –interpolate scalar attributes

32. Pauly, Keiser, Kobbelt, Gross: Shape Modeling with Point-Sampled GeometrySIGGRAPH 2003 Free-form Deformation Demo – Part 2

33. Pauly, Keiser, Kobbelt, Gross: Shape Modeling with Point-Sampled GeometrySIGGRAPH 2003 Results Combination of free-form deformation with collision detection, boolean operations, particle-based blending, embossing and texturing

34. Pauly, Keiser, Kobbelt, Gross: Shape Modeling with Point-Sampled GeometrySIGGRAPH 2003 Results Interactive modeling with scanned data: noise removal, free-form deformation, cut-and-paste editing, interactive texture mapping

35. Pauly, Keiser, Kobbelt, Gross: Shape Modeling with Point-Sampled GeometrySIGGRAPH 2003 Results The Octopus: Free-form deformation with dynamic sampling

36. Pauly, Keiser, Kobbelt, Gross: Shape Modeling with Point-Sampled GeometrySIGGRAPH 2003 Conclusions Point cloud: Explicit representation –Minimal consistency constraints allow efficient dynamic re-sampling –Modeling of sharp features –Fast rendering MLS approximation: Implicit surface model –Fast inside/outside tests for boolean classification and collision detection

37. Pauly, Keiser, Kobbelt, Gross: Shape Modeling with Point-Sampled GeometrySIGGRAPH 2003 Future Work Physics-based modeling Haptic interfaces Robust handling of singularities for boolean operations More complex surfaces, e.g. hairy or furry models

38. Pauly, Keiser, Kobbelt, Gross: Shape Modeling with Point-Sampled GeometrySIGGRAPH 2003 Tim Weyrich, Matthias Zwicker European Graduate Program on Combinatorics, Geometry, and Computation Check out: www.pointshop3d.com Acknowledgements