Continuous Penalty Forces

by Min Tang1, Dinesh Manocha2, Miguel A. Otaduy3 and Ruofeng Tong1.

1 - Zhejiang University, China

2 - University of North Carolina at Chapel Hill, USA

3 - URJC Madrid, Spain


Figure 1: Sticking and penetration problems: We highlight sticking and penetration problems in the Chain Benchmark (a)(14.3k triangles, 60fps) and the Rings Benchmark (b)(7.4k triangles, 35fps) with traditional penalty methods. Our novel continuous penalty force formulation can alleviate these problems based on continuous collision and force computation.


We present a simple algorithm to compute continuous penalty forces to determine collision response between rigid and deformable models bounded by triangle meshes. Our algorithm provides a well-behaved solution in contrast to the traditional stability and robustness problems of penalty methods, induced by force discontinuities. We trace contact features along their deforming trajectories and accumulate penalty forces along the penetration time intervals between the overlapping feature pairs. Moreover, we present a closed-form expression to compute the continuous and smooth collision response. Our method has very small additional overhead compared to previous penalty methods, while significantly improves the stability and robustness. We highlight its benefits on several benchmarks.



Paper  (PDF 834 KB)

Min Tang, Dinesh Manocha, Miguel A. Otaduy, and Ruofeng Tong, Continuous Penalty Forces, ACM Transactions on Graphics, 31(4), Article 107 (July 2012), 9 pages (Proc. of ACM SIGGRAPH). 2012.

  author = {Tang, Min and Manocha, Dinesh and Otaduy, Miguel A. and Tong, Ruofeng},
  title = {Continuous Penalty Forces},
  journal = {ACM Trans. Graph.},
  volume = {31},
  issue = {4},
  month = {July},
  year = {2012},
  pages = {107:1--107:9},


Video (25.2 MB)


Related Links

UNC dynamic model benchmark repository

VolCCD: Fast Continuous Collision Culling between Deforming Volume Meshes

Collision-Streams: Fast GPU-based Collision Detection for Deformable Models

Fast Continuous Collision Detection using Deforming Non-Penetration Filters

Interactive Continuous Collision Detection between Deformable Models using Connectivity-Based Culling

MCCD: Multi-Core Collision Detection between Deformable Models using Front-Based Decomposition

Fast Collision Detection for Deformable Models using Representative-Triangles

DeformCD: Collision Detection between Deforming Objects

Interactive Collision Detection between Deformable Models using Chromatic Decomposition

Fast Proximity Computation Among Deformable Models using Discrete Voronoi Diagrams

CULLIDE: Interactive Collision Detection between Complex Models using Graphics Hardware

RCULLIDE: Fast and Reliable Collision Culling using Graphics Processors

Quick-CULLIDE: Efficient Inter- and Intra-Object Collision Culling using Graphics Hardware

Collision Detection




We would like to thank Fran\c{c}ois Faure and the SOFA team for their support, and Jianfei Chen for useful discussions. This research is supported in part by NSFC (61170140), the National Basic Research Program of China (2011CB302205), the National Key Technology R&D Program of China (2012BAD35B01), NSFZC (Y1100069). Manocha is supported in part by ARO Contract W911NF-10-1-0506, NSF awards 0917040, 0904990, 1000579 and 1117127, and Intel. Otaduy is supported in part by the Spanish Ministry of Science and Innovation (TIN2009-07942) and by the European Research Council (ERC-2011-StG-280135 Animetrics). Tong is partly supported by NSFC (61170141).


CB #3175, Department of Computer Science
University of North Carolina
Chapel Hill, NC 27599-3175