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Fast Collision Detection for Deformable Models using Representative-Triangles. Sean Curtis 1 , Rasmus Tamstorf 2 , & Dinesh Manocha 1 I3D 2008 February 15, 2008.

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## Fast Collision Detection for Deformable Models using Representative-Triangles

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**Fast Collision Detection for Deformable Models using**Representative-Triangles Sean Curtis1, Rasmus Tamstorf 2, & Dinesh Manocha1 I3D 2008 February 15, 2008 1 University of North Carolina at Chapel Hill 2 Walt Disney Animation Studios**Faster Collision Detection**• Seven layers of cloth and body with 50K triangles. • 3.3X collision detection speed-up with Representative Triangles.**Previous Work**• General surveys • Ericson 2004; Lin and Manocha 2003; Teschner et al. 2005.**Previous Work**• Triangle-pair Culling • BVH - BV types • Sphere, Swept-sphere, AABB, OBB, k-DOP, hybrid, etc. • Bradshaw and O’Sullivan. 2004; Gottschalk et al. 1996; Hubbard 1993; Klosowski et al. 1998; van den Bergen 1997; etc.**Previous Work**• Triangle-pair Culling • BVH Management • Restructuring, rebuilding, lazy construction, etc. • Larsson and Akenine-Möller 2006; Otaduy et al. 2007, Yoon et al. 2007; Zachmann and Weller 2006.**Previous Work**• Triangle-pair Culling • BVH Management • Restructuring, rebuilding, lazy construction, etc. • Larsson and Akenine-Möller 2006; Otaduy et al. 2007, Yoon et al. 2007; Zachmann and Weller 2006. • Specialized culling techniques • Normal cones, GPU-based culling, etc. • Govindaraju et al. 2005; Provot 1997; Sud et al. 2006.**Previous Work**• Feature-based Collision Detection • Voronoi regions (convex and non-convex) • Ehmann and Lin 2001; Lin and Canny 1991; Mirtich 1998.**Previous Work**• Feature-based Collision Detection • Voronoi regions (convex and non-convex) • Ehmann and Lin 2001; Lin and Canny 1991; Mirtich 1998. • Feature BVs • Hutter and Fuhrmann 2007.**Previous Work**• Continuous Collision Detection • Reduction of elementary tests • Govindaraju et al. 2005; Hutter and Fuhrmann 2007; Tang et al. 2007; Wong 2005, etc.**Continuous Collision Detection (CCD)**• Time of collision. t = i t = i+1**Continuous Collision Detection (CCD)**• Time of collision. t = i t = i+Δt t = i+1**Continuous Collision Detection (CCD)**• Time of collision. • Test between features (vertices, edges and faces.) Vertex-Face Edge-Edge**Triangles vs. Features**• Triangles used for culling.**Triangles vs. Features**• Triangles used for culling. • CD operates on features.**Triangles vs. Features**• Triangles used for culling. • CD operates on features. • This leads to: • Less efficient culling • Elementary test duplication**Culling Efficiency**• Features usually occupy significantly less space than their corresponding triangles.**Culling Efficiency**• Features usually occupy significantly less space than their corresponding triangles. • Based on triangle BVs: • 15 elementary tests**Culling Efficiency**• Features can occupy significantly less space than their corresponding triangles. • Based on triangle BVs: • 15 elementary tests • Based on feature BVs: • 1 EE test**Culling Efficiency**• Features can occupy significantly less space than their corresponding triangles. • Based on triangle BVs: • 15 elementary tests • Based on feature BVs: • 1 EE test**Culling Efficiency**• Features can occupy significantly less space than their corresponding triangles. • Based on triangle BVs: • 15 elementary tests • Based on feature BVs: • 2 EE tests**Culling Efficiency**• Features can occupy significantly less space than their corresponding triangles. • Based on triangle BVs: • 15 elementary tests • Based on feature BVs: • 2 EE tests**Culling Efficiency**• Features can occupy significantly less space than their corresponding triangles. • Based on triangle BVs: • 15 elementary tests • Based on feature BVs: • 2 EE tests**Culling Efficiency**• Features can occupy significantly less space than their corresponding triangles. • Based on triangle BVs: • 15 elementary tests • Based on feature BVs: • 2 EE tests**Culling Efficiency**• Features can occupy significantly less space than their corresponding triangles. • Based on triangle BVs: • 15 elementary tests • Based on feature BVs: • 2 EE tests**Culling Efficiency**• Features can occupy significantly less space than their corresponding triangles. • Based on triangle BVs: • 15 elementary tests • Based on feature BVs: • 2 EE tests**Culling Efficiency**• Features can occupy significantly less space than their corresponding triangles. • Based on triangle BVs: • 15 elementary tests • Based on feature BVs: • 2 EE tests**Culling Efficiency**• Features can occupy significantly less space than their corresponding triangles. • Based on triangle BVs: • 15 elementary tests • Based on feature BVs: • 2 EE tests • 0 VF tests**Culling Efficiency**• Features can occupy significantly less space than their corresponding triangles. • Based on triangle BVs: • 15 elementary tests • Based on feature BVs: • 2 EE tests • 0 VF tests**Culling Efficiency**• Features can occupy significantly less space than their corresponding triangles. • Based on triangle BVs: • 15 elementary tests • Based on feature BVs: • 2 EE tests • 0 VF tests**Culling Efficiency**• Features can occupy significantly less space than their corresponding triangles. • Based on triangle BVs: • 15 elementary tests • Based on feature BVs: • 2 EE tests • 1 VF test**Culling Efficiency**• Features can occupy significantly less space than their corresponding triangles. • Based on triangle BVs: • 15 elementary tests • Based on feature BVs: • 2 EE tests • 1 VF test**Culling Efficiency**• Features can occupy significantly less space than their corresponding triangles. • Based on triangle BVs: • 15 elementary tests • Based on feature BVs: • 2 EE tests • 1 VF test**Elementary Test Duplication**• The intersecting vertex is shared by six triangles.**Elementary Test Duplication**• The intersecting vertex is shared by six triangles. • The VF test could be spawned by six different triangle pairs.**Representative Triangles (R-Tris)**• R-Tris definition • R-Tris usage • R-Tris properties • Computing R-Tris (assignment)**R-Tri Definition**• An augmented triangle that “represents” some subset of its features and their corresponding feature BVs.**R-Tri DefinitionFeature Assignment**• The pattern in which each feature is assigned to an R-Tri is an assignment scheme.**R-Tri DefinitionFeature Assignment**• The pattern in which each feature is assigned to an R-Tri is an assignment scheme. • Assignment scheme • Not unique. • Every feature is assigned to one and only one triangle, incident to the feature.**R-Tri Usage**• Given a pair of R-Tris that are potentially colliding: • Find corresponding feature pairs.**R-Tri Usage**• Given a pair of R-Tris that are potentially colliding: • Find corresponding feature pairs. • Test feature BVs.**R-Tri Usage**• Given a pair of R-Tris that are potentially colliding: • Find corresponding feature pairs. • Test feature BVs.**R-Tri Usage**• Given a pair of R-Tris that are potentially colliding: • Find corresponding feature pairs. • Test feature BVs.**R-Tri Usage**• Given a pair of R-Tris that are potentially colliding: • Find corresponding feature pairs. • Test feature BVs.**R-Tri Usage**• Given a pair of R-Tris that are potentially colliding: • Find corresponding feature pairs. • Test feature BVs. • Spawn elementary tests.**R-Tri Usage**• Given a pair of R-Tris that are potentially colliding: • Find corresponding feature pairs. • Test feature BVs. • Spawn elementary tests. • Improves culling and eliminates duplicates.**R-Tris Properties**• General • Compatible with any triangle-pair culling algorithm (including grids, BVHs, sweep & prune, GPU occlusion queries, etc.)**R-Tris Properties**• Complete • R-Tris will find all collisions, guaranteed.**R-Tris Properties**• Compact • R-Tris need no additional memory. (However, O(|E|) data can be cached to potentially boost performance.)**R-Tris Properties**• Connectivity-based • Representation is a function of topology. For meshes which only undergo deformation, assignment is a pre-processing step.**Computing R-Tris Assignment Schema**• How are features assigned to R-Tris? • Does it matter? • How many elementary tests are performed per contact?

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