Robust adaptive floating-point geometric predicates
Proceedings of the twelfth annual symposium on Computational geometry
Interval arithmetic yields efficient dynamic filters for computational geometry
Discrete Applied Mathematics - Special issue 14th European workshop on computational geometry CG'98 Selected papers
Robust treatment of collisions, contact and friction for cloth animation
Proceedings of the 29th annual conference on Computer graphics and interactive techniques
A Fast Finite Element Solution for Cloth Modelling
PG '03 Proceedings of the 11th Pacific Conference on Computer Graphics and Applications
Adaptive meshing for cloth animation
Engineering with Computers
Cloth animation with adaptively refined meshes
ACSC '05 Proceedings of the Twenty-eighth Australasian conference on Computer Science - Volume 38
Real-Time Collision Detection (The Morgan Kaufmann Series in Interactive 3-D Technology) (The Morgan Kaufmann Series in Interactive 3D Technology)
Continuous collision detection for articulated models using Taylor models and temporal culling
ACM SIGGRAPH 2007 papers
A finite element method for animating large viscoplastic flow
ACM SIGGRAPH 2007 papers
Robust treatment of simultaneous collisions
ACM SIGGRAPH 2008 papers
Fast viscoelastic behavior with thin features
ACM SIGGRAPH 2008 papers
A mass spring model for hair simulation
ACM SIGGRAPH 2008 papers
Interval Arithmetic Using SSE-2
Reliable Implementation of Real Number Algorithms: Theory and Practice
Robust Topological Operations for Dynamic Explicit Surfaces
SIAM Journal on Scientific Computing
Fast continuous collision detection using deforming non-penetration filters
Proceedings of the 2010 ACM SIGGRAPH symposium on Interactive 3D Graphics and Games
Dynamic local remeshing for elastoplastic simulation
ACM SIGGRAPH 2010 papers
Speculative parallel asynchronous contact mechanics
ACM Transactions on Graphics (TOG) - Proceedings of ACM SIGGRAPH Asia 2012
Adaptive anisotropic remeshing for cloth simulation
ACM Transactions on Graphics (TOG) - Proceedings of ACM SIGGRAPH Asia 2012
Modeling friction and air effects between cloth and deformable bodies
ACM Transactions on Graphics (TOG) - SIGGRAPH 2013 Conference Proceedings
Folding and crumpling adaptive sheets
ACM Transactions on Graphics (TOG) - SIGGRAPH 2013 Conference Proceedings
Putting holes in holey geometry: topology change for arbitrary surfaces
ACM Transactions on Graphics (TOG) - SIGGRAPH 2013 Conference Proceedings
Technical Section: Adaptive cloth simulation using corotational finite elements
Computers and Graphics
Dynamic radial view based culling for continuous self-collision detection
Proceedings of the 18th meeting of the ACM SIGGRAPH Symposium on Interactive 3D Graphics and Games
Special Section on CAD/Graphics 2013: Canopy-frame interactions for umbrella simulation
Computers and Graphics
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Continuous collision detection (CCD) between deforming triangle mesh elements in 3D is a critical tool for many applications. The standard method involving a cubic polynomial solver is vulnerable to rounding error, requiring the use of ad hoc tolerances, and nevertheless is particularly fragile in (near-)planar cases. Even with per-simulation tuning, it may still cause problems by missing collisions or erroneously flagging non-collisions. We present a geometrically exact alternative guaranteed to produce the correct Boolean result (significant collision or not) as if calculated with exact arithmetic, even in degenerate scenarios. Our critical insight is that only the parity of the number of collisions is needed for robust simulation, and this parity can be calculated with simpler non-constructive predicates. In essence we analyze the roots of the nonlinear system of equations defining CCD through careful consideration of the boundary of the parameter domain. The use of new conservative culling and interval filters allows typical simulations to run as fast as with the non-robust version, but without need for tuning or worries about failure cases even in geometrically degenerate scenarios. We demonstrate the effectiveness of geometrically exact detection with a novel adaptive cloth simulation, the first to guarantee to remain intersection-free despite frequent curvature-driven remeshing.