High-performance Penetration Depth Computation for Haptic Rendering

Transcription

1 High-performance Penetration Depth Computation for Haptic Rendering Young J. Kim Ewha Womans University

2 Issues of Interpenetration Position and orientation of the haptic probe, governed by the user through the haptic device probe Interpenetration in haptic simulation is unavoidable object

3 Penalty-based Response Penetration depth (PD) is required for computing penalty-based contact response probe F=k PD object

4 Previous Work on PD Convex polytopes -[Cameron and Culley86], [Dobkin93], [Agarwal00], [Bergen01], [Kim et al. 04] Non-convex polyhedra -[Kim02],[Redon and Lin06], [Lien08a,b], [Hachenberger09] Polygon soups [Je et al. 12] Distance fields -[Fisher and Lin01], [Hoff02], [Sud06] Pointwise PD - [Tang et al. 09] Generalized PD [Ong and Gilbert96], [Ong96], [Zhang07], [Tang et al. 12] Volumetric PD - [Wellner and Zachmann09]

5 Challenges Penetration depth (PD) Is very expensive to compute accurately May not handle arbitrary geometry and topology Current practice Hacks Slow, inconsistent, geometrically unstable

6 Goal Recent research results Pointwise Translational Generalized Recent results on 6DoF haptic rendering

7 M. Tang, M. Lee, Y. J. Kim, Interactive Hausdorff Distance Computation for General Polygonal Models, SIGGRAPH 2009 Pointwise Penetration Depth

8 Pointwise Penetration Depth Defined as deepest interpenetrating points

9 One-sided Hausdorff Distance WHC, April 14 th 2013 Felix Hausdorff ( )

10 One-sided Hausdorff Distance WHC, April 14 th 2013 Felix Hausdorff ( )

11 Two-sided Hausdorff Distance WHC, April 14 th 2013 Felix Hausdorff ( )

12 Shape Deviation Measure Hausdorff distance quantifies deviation between two geometric models Large Hausdorff Distance Value Small Hausdorff Distance Value

13 Pointwise Penetration Depth 1. Find intersection surfaces and 2. Penetration depth = Penetration Depth

14 Pointwise Penetration Depth Demo (40K Bunny vs 40K Bunny)

15 Benchmark: Pointwise PD Model complexity 50K tri Avg. Performance 3.88ms/pair

16 Benchmark: Pointwise PD Model complexity 3.5K tri Avg. performance 0.95ms/pair

17 C. Je, M. Tang, Y. Lee, M. Lee, Y. J. Kim, PolyDepth: Real-time Penetration Depth Computation using Iterative Contact-space Projection, ACM Transactions on Graphics 2012 Translational Penetration Depth

18 (Translational) Penetration Depth [Dobkin 93] Minimum translational distance to separate overlapping objects A B Penetration Depth

19 Configuration Space workspace configuration space 19

20 Translational Configuration Space workspace configuration space Translational C-space = Minkowski Sums 20

21 Minkowski Sum P Q { p q p P, q Q} P Q { p q p P, q Q} Q P P Q

22 Example Video credit: D. Halperin 22

23 PD VS Minkowski Sum Penetration Depth P Q

24 Combinatorial Explosion Complexity of Minkowski Sum O(m 3 n 3 ) with m and n triangles

25 PD Estimation Penetration Depth o Boundary of Minkowski Sums

26 Out-Projection = Continuous Collision Detection q Out-Projection f q 0 o Boundary of Minkowski Sums

27 Continuous Collision Detection Source codes are available (2-manifold) (polygonsoups) (articulated) (for motion planning)

28 In-Projection = LCP (Linear Complementarity Problem) q 2 In-Projection o Boundary of Minkowski Sums

29 PolyDepth: Iterative Optimization WHC, April 14 th 2013 Out-Projection q f q 1 q 2 q 0 In-Projection Penetration Depth o Boundary of Minkowski Sums

30 PolyDepth Performance Spoon: 1.3K triangles Cup: 8.4K triangles Time: 1~7 msec

31 PolyDepth Performance Bunny: 40K triangles Dragon: 174K triangles Time: 2~15 msec

32 Comparison against Exact Solution Accuracy Performance

33 M. Tang, Y. J. Kim, Interactive Generalized Penetration Depth Computation for Rigid and Articulated Models using Object Norm, Ewha Technical Report 2012 Generalized Penetration Depth

34 Generalized Penetration Depth Minimal rigid motion to separate overlapping objects Translational PD Generalized PD

35 Definition of Generalized PD Defined in 6D configuration space PD g interior, min q, o q, q A(o) ( q) q o o Contact space

36 Distance metric Object norm The average squared displacement q 1 1 q, q x q x q V x x q 0 o

37 PolyDepth++ Algorithm 1. Free-configuration selection q f Contact Space o

38 PolyDepth++ Algorithm 2. Contact-space projection q f q 0 Contact Space o

39 PolyDepth++ Algorithm 3. Constrained optimization q q 0 1 LLCS Contact Space o

40 PolyDepth++ Algorithm 4. Re-projection q q 0 1 LLCS Contact Space q 2 o

41 PolyDepth++ Algorithm 5. Iteration until finding a locally-optimal solution Contact Space o

42 i WHC, April 14 th 2013 PolyDepth++ for Articulated Model Object norm for a link 1 V i ' 2 i i i d x x q x q x qq n 1, ' i i 0 xq i ' J i Li 1 Li xq i

43 PolyDepth++ for Articulated Model Constrained optimization in higher dimension Minimize q n 1 i 0 subject to: C q q 0 m q c i

44 Generalized PD Performance WHC, April 14 th 2013

45 Software Implementations Source codes are available (translational PD) (Hausdorff distance and pointwise PD)

46 Y. Li, S. Zhang, Y. J. Kim, Six-degree-of-freedom Haptic Rendering using Translational and Generalized Penetration Depth Computation, IEEE WHC 2013 HAPTIC APPLICATIONS

47 Penalty-based Haptic Rendering using Translational and Generalized PD df 1 n 1 1 p 1 d o o o ' n f 2 2 x o ' o p 22 d 2 Translational PD Generalized PD

48 Penalty-based Haptic Rendering using Translational and Generalized PD f 1 f p 1 o f 2 o p 2 Translational PD Generalized PD

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50 Performance For More Details, This Tues, 1:10PM Oral Session V

51 Summary Pointwise PD Translational PD Generalized PD 6DoF haptic rendering with translational and generalized PD

52 Future Work Parallel haptic rendering Asynchronous contact handling GPU-based parallelization Haptic rendering for Articulated models Massive models

53 High Performance GPU-based Collision Queries WHC, April 14 th 2013 Real-time Collision Culling of a Million Bodies on GPUs ACM Trans on Graphics 2010 Real-time Adaptive Signed Distance Fields for Rigid and Deformable Models on GPUs

54 Acknowledgements Min Tang, Xinyu Zhang, Minkyoung Lee, Yi Li (Ewha) Fuchang Liu (NTU) Changsoo Je (Sogang) KEIT/MKE (IT core research) NRF

55 Thank you for listening!