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Shape Modeling with Point-Sampled Geometry

Shape Modeling with Point-Sampled Geometry. Mark Pauly. Leif Kobbelt. Richard Keiser. Markus Gross. ETH Zürich. ETH Zürich. ETH Zürich. RWTH Aachen.  - Efficient rendering  - Sharp features  - Intuitive editing.  - Boolean operations  - Changes of topology

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Shape Modeling with Point-Sampled Geometry

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

  2.  - Efficient rendering  - Sharp features  - Intuitive editing  - Boolean operations  - Changes of topology  - Extreme deformations Motivation • Surface representations • Explicit surfaces (B-reps) • Polygonal meshes • Subdivision surfaces • NURBS • Implicit surfaces • Level sets • Radial basis functions • Algebraic surfaces

  3.  - Efficient rendering  - Sharp features  - Intuitive editing Motivation • Surface representations • Explicit surfaces (B-reps) • Polygonal meshes • Subdivision surfaces • NURBS  - Boolean operations  - Changes of topology  - Extreme deformations • Implicit surfaces • Level sets • Radial basis functions • Algebraic surfaces

  4. Motivation • Surface representations • Explicit surfaces (B-reps) • Polygonal meshes • Subdivision surfaces • NURBS • Hybrid Representation • Explicit cloud of point samples • Implicit dynamic surface model • Implicit surfaces • Level sets • Radial basis functions • Algebraic surfaces

  5. Outline • Implicit surface model • Moving least squares approximation • Interactive shape modeling • Boolean operations • Free-form deformation • Demo • Results & Conclusions

  6. Surface Model • Goal: Define continuous surface from a set of discrete point samples continuous surface S interpolating or approximating P discrete set of point samples P = { pi, ci, mi, ... }

  7. 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. Boolean Operations + - -

  9. 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. 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. Boolean Operations • Classification: • given a smooth, closed surface S and point p. Is p inside or outside of the volume V bounded by S? • find closest point q on S

  12. Boolean Operations • Classification: • given a smooth, closed surface S and point p. Is p inside or outside of the volume V bounded by S? • find closest point q on S • classify p as • inside V, if (p-q)·n < 0 • outside V, if (p-q)·n > 0

  13. Boolean Operations • Classification: • represent smooth surface S by point cloud Pm

  14. Boolean Operations • Classification: • represent smooth surface S by point cloud Pm • find closest point q in P • classify p as • inside V, if (p-q)·n < 0 • outside V, if (p-q)·n > 0

  15. Boolean Operations • Classification: • piecewise constant surface approximation leads to false classification close to the surface

  16. Boolean Operations • Classification: • piecewise constant surface approximation leads to false classification close to the surface

  17. Boolean Operations • Classification: • piecewise constant surface approximation leads to false classification close to the surface

  18. Boolean Operations • Classification: • piecewise constant surface approximation leads to false classification close to the surface

  19. Boolean Operations • Classification: • piecewise constant surface approximation leads to false classification close to the surface

  20. Boolean Operations • Classification: • use MLS projection of p for correct classification

  21. Boolean Operations • Sampling the intersection curve classification A B sampling the intersection curve A  B

  22. Boolean Operations • Sampling the intersection curve • identify pairs of closest points

  23. Boolean Operations • Sampling the intersection curve • identify pairs of closest points

  24. Boolean Operations • Sampling the intersection curve • identify pairs of closest points • find closest point on intersection of tangent spaces

  25. Boolean Operations • Sampling the intersection curve • identify pairs of closest points • find closest point on intersection of tangent spaces • re-project point on both surfaces

  26. Boolean Operations • Sampling the intersection curve • identify pairs of closest points • find closest point on intersection of tangent spaces • re-project point on both surfaces • iterate

  27. Boolean Operations • Demo – Part 1 • Dinosaur: 56,194 samples • Max Planck: 52,809 samples

  28. Free-form Deformation • Smooth deformation field F:R3R3 that warps 3D space • Can be applied directly to point samples

  29. 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 rigid part deformable part control handle

  30. Robust free-form deformation requires dynamic adaptation of the sampling density 10,000 points 271,743 points Dynamic Sampling • Large deformations lead to strong distortions

  31. 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. Free-form Deformation • Demo – Part 2

  33. Results • Combination of free-form deformation with collision detection, boolean operations, particle-based blending, embossing and texturing

  34. Results • Interactive modeling with scanned data: noise removal, free-form deformation, cut-and-paste editing, interactive texture mapping

  35. Results • The Octopus: Free-form deformation with dynamic sampling

  36. 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. Future Work • Physics-based modeling • Haptic interfaces • Robust handling of singularities for boolean operations • More complex surfaces, e.g. hairy or furry models

  38. Acknowledgements • Tim Weyrich, Matthias Zwicker • European Graduate Program on Combinatorics, Geometry, and Computation • Check out: www.pointshop3d.com

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