Publication 2008 Issue No. 1 - January/February Abstract - Layer-Based Representation of Polyhedrons for Point Containment Tests
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Layer-Based Representation of Polyhedrons for Point Containment Tests
January/February 2008 (vol. 14 no. 1)
pp. 73-83
 ASCII Text x Wencheng Wang, Jing Li, Hanqiu Sun, Enhua Wu, "Layer-Based Representation of Polyhedrons for Point Containment Tests," IEEE Transactions on Visualization and Computer Graphics, vol. 14, no. 1, pp. 73-83, January/February, 2008.
 BibTex x @article{ 10.1109/TVCG.2007.70407,author = {Wencheng Wang and Jing Li and Hanqiu Sun and Enhua Wu},title = {Layer-Based Representation of Polyhedrons for Point Containment Tests},journal ={IEEE Transactions on Visualization and Computer Graphics},volume = {14},number = {1},issn = {1077-2626},year = {2008},pages = {73-83},doi = {http://doi.ieeecomputersociety.org/10.1109/TVCG.2007.70407},publisher = {IEEE Computer Society},address = {Los Alamitos, CA, USA},}
 RefWorks Procite/RefMan/Endnote x TY - JOURJO - IEEE Transactions on Visualization and Computer GraphicsTI - Layer-Based Representation of Polyhedrons for Point Containment TestsIS - 1SN - 1077-2626SP73EP83EPD - 73-83A1 - Wencheng Wang, A1 - Jing Li, A1 - Hanqiu Sun, A1 - Enhua Wu, PY - 2008KW - computational geometryKW - polyhedronKW - point containmentKW - solid representationVL - 14JA - IEEE Transactions on Visualization and Computer GraphicsER -

Abstract—This paper presents the layer-based representation of polyhedrons and its use for point-in-polyhedron tests. In the representation, the facets and edges of a polyhedron are sequentially arranged, and so the binary search algorithm is efficiently used to speed up inclusion tests. In comparison with conventional representation for polyhedrons, the layer-based representation we propose greatly reduces the storage requirement because it represents much information implicitly, though it still has a storage complexity O(n). It is simple to implement, and robust for inclusion tests because many singularities are erased in constructing the layer-based representation. Incorporating an octree structure for organizing polyhedrons, our approach can run at a speed comparable with BSP-based inclusion tests, and at the same time greatly reduce storage and preprocessing time in treating large polyhedrons. We have developed an efficient solution for point-in-polyhedron tests with the time complexity varying between O(n) and O(log n), depending on the polyhedron shape and the constructed representation, and less than O(log^3 n) in most cases. The time complexity of preprocess is between O(n) and O(n^2), varying with polyhedrons, where n is the edge number of a polyhedron.

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Index Terms:
computational geometry, polyhedron, point containment, solid representation
Citation:
Wencheng Wang, Jing Li, Hanqiu Sun, Enhua Wu, "Layer-Based Representation of Polyhedrons for Point Containment Tests," IEEE Transactions on Visualization and Computer Graphics, vol. 14, no. 1, pp. 73-83, Jan.-Feb. 2008, doi:10.1109/TVCG.2007.70407