The multi-LREP decomposition of solids and its application to a point-in-polyhedron inclusion test

This paper presents a scheme for decomposing polyhedra called multi-LREP. The scheme is based on the L-REP decomposition, which classifies the triangular faces of a polyhedron into a set of layered tetrahedra. In the multi-LREP these layered tetrahedra are grouped into regions of a space subdivision. The paper also describes an efficient method for constructing the L-REP decomposition and how the multi-LREP can be applied to speed up two L-REP applications: the point-in-polyhedron inclusion test and the ray-scene intersection. An experimental comparison with other point-in-polyhedron tests is presented as well.

[1]  Francisco R. Feito-Higueruela,et al.  A triangle-based representation for polygons and its applications , 2002, Comput. Graph..

[2]  Tomas Akenine-Möller,et al.  Real-time rendering , 1997 .

[3]  Tomas Akenine-Möller,et al.  Real-time rendering, 2nd Edition , 2002 .

[4]  Eric Haines,et al.  Point in Polygon Strategies , 1994, Graphics Gems.

[5]  Francisco R. Feito-Higueruela,et al.  Layer-based decomposition of solids and its applications , 2005, The Visual Computer.

[6]  Andrew S. Glassner,et al.  Space subdivision for fast ray tracing , 1984, IEEE Computer Graphics and Applications.

[7]  Paul S. Heckbert,et al.  Graphics gems IV , 1994 .

[8]  Mark de Berg,et al.  Computational geometry: algorithms and applications , 1997 .

[9]  Rafael Jesús Segura,et al.  Point in solid strategies , 2005, Comput. Graph..

[10]  Wencheng Wang,et al.  Layer-Based Representation of Polyhedrons for Point Containment Tests , 2008, IEEE Transactions on Visualization and Computer Graphics.

[11]  Francisco R. Feito-Higueruela,et al.  The multi-L-REP decomposition and its application to a point-in-polygon inclusion test , 2006, Comput. Graph..

[12]  Gino van den Bergen.  Efficient Collision Detection of Complex Deformable Models using AABB Trees , 1997, J. Graphics, GPU, & Game Tools.

[13]  Hanan Samet,et al.  Foundations of multidimensional and metric data structures , 2006, Morgan Kaufmann series in data management systems.

[14]  Francisco R. Feito-Higueruela,et al.  Inclusion test for general polyhedra , 1997, Comput. Graph..