Computing minimum length paths of a given homotopy class
Computational Geometry: Theory and Applications
Optimal workpiece setups for 4-axis numerical control machining based on machinability
Computers in Industry - special issue ASI'94 selection of papers presented at the advanced summer institute “computer integrated manufacturing and industrial automation” Patras, Greece, 26 June—1 July 1994
Multidimensional binary search trees used for associative searching
Communications of the ACM
Particle-based fluid simulation for interactive applications
Proceedings of the 2003 ACM SIGGRAPH/Eurographics symposium on Computer animation
A theorem on polygon cutting with applications
SFCS '82 Proceedings of the 23rd Annual Symposium on Foundations of Computer Science
Real time physics: class notes
ACM SIGGRAPH 2008 classes
Gpu gems 3
Testing an axis of rotation for 3D workpiece draining
2009 SIAM/ACM Joint Conference on Geometric and Physical Modeling
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Given a triangular mesh defining the geometry of a 3D workpiece filled with water, we propose an algorithm to test whether, for an arbitrary given axis, the workpiece will be completely drained under gravity when the rotation axis is set parallel to the ground and the workpiece is rotated around the axis. Observing that all water traps contain a concave vertex, we solve our problem by constructing and analyzing a directed ''draining graph'' whose nodes correspond to concave vertices of the geometry and whose edges are set according to the transition of trapped water when we rotate the workpiece around the given axis. Our algorithm to test whether or not a given rotation axis drains the workpiece outputs a result in about a second for models with more than 100,000 triangles after a few seconds of preprocessing.