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Continuous collision detection for deformable objects using permissible clusters

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Abstract

In this paper, we propose a new data structure to perform continuous collision detection (CCD) for deformable triangular meshes. The critical component of this data structure is permissible clusters. At the preprocessing phase, the triangular meshes are divided into permissible clusters. Then, the features of the triangular meshes are assigned to the permissible clusters. At the runtime phase, the potentially colliding feature pairs are collected and they are processed only once in the elementary processing. Our method has been integrated with a normal cone-based method and compared with other CCD methods. Experimental results show that our method improves the overall performance of CCD for deformable objects.

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Acknowledgments

We thank the reviewers for their constructive and invaluable comments. The animation data of Cloth and Balls were obtained from the UNC Gamma Group. This work was supported in part by the National Science Council Taiwan under contract number NSC 102-2221-E-009-103-MY2 and Hong Kong RGC GRF grants (PolyU 5101/11E, PolyU 5100/12E and PolyU 5100/13E).

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Authors and Affiliations

  1. National Chiao Tung University, Hsinchu, Taiwan, ROC

    Sai-Keung Wong

  2. Hong Kong Polytechnic University, Kowloon, Hong Kong

    George Baciu

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  1. Sai-Keung Wong
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  2. George Baciu
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Correspondence to Sai-Keung Wong.

Appendix A: Properties of the permissible clusters

Appendix A: Properties of the permissible clusters

We give a proof for the properties of the permissible clusters (see Sect. 4.1). Assume that the clusters are free of collision before the simulation time interval.

  1. 1.

    Type I: a single triangle is free of collision on its own. This is because the edges of the triangles are connected to each other and the vertices of the triangle are adjacent to the triangle.

  2. 2.

    Type II: if two non-adjacent features of the cluster collide with each other, then the two triangles of the cluster must be coplanar and their normal vectors point to the opposite directions. The cluster does not have a valid continuous normal cone.

  3. 3.

    Type III: a Type III cluster is a 2-manifold mesh with boundary. The triangles of the cluster share a common vertex at the center and each triangle is adjacent to another two triangles. If the cluster collides with itself, there must be an external vertex colliding with the supporting plane of a triangle of the cluster. In this case, there are two or more than two disjointed subspaces which are formed by the half spaces of the supporting planes of the triangles. The cluster does not have a valid continuous normal cone. One of the subspace may be empty. An example is illustrated in Fig. 8.

  4. 4.

    Type IV: it is unnecessary to check a Type IV cluster as all the internal edges of the cluster are connected at the common vertex.

Fig. 8
figure 8

A Type III cluster. It collides with itself when it deforms in three cases. Its contour is drawn on the \(xy\)-plane for the three cases. a The initial shape of the cluster; b a vertex \(p_2\) collides with a triangle (\(p_0\), \(p_8\), \(p_7\)); c an edge \(p_0p_7\) collides with an edge \(p_2p_3\); d a triangle (\(p_0\), \(p_3\), \(p_2\)) with another triangle (\(p_0\), \(p_7\), \(p_6\)). There are three colliding edge–edge pairs

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Wong, SK., Baciu, G. Continuous collision detection for deformable objects using permissible clusters. Vis Comput 31, 377–389 (2015). https://doi.org/10.1007/s00371-014-0933-6

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  • DOI: https://doi.org/10.1007/s00371-014-0933-6

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