
This Article  
 
Share  
Bibliographic References  
Add to:  
Digg Furl Spurl Blink Simpy Del.icio.us Y!MyWeb  
Search  
 
ASCII Text  x  
Wencheng Wang, Jing Li, Hanqiu Sun, Enhua Wu, "LayerBased Representation of Polyhedrons for Point Containment Tests," IEEE Transactions on Visualization and Computer Graphics, vol. 14, no. 1, pp. 7383, January/February, 2008.  
BibTex  x  
@article{ 10.1109/TVCG.2007.70407, author = {Wencheng Wang and Jing Li and Hanqiu Sun and Enhua Wu}, title = {LayerBased Representation of Polyhedrons for Point Containment Tests}, journal ={IEEE Transactions on Visualization and Computer Graphics}, volume = {14}, number = {1}, issn = {10772626}, year = {2008}, pages = {7383}, 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  JOUR JO  IEEE Transactions on Visualization and Computer Graphics TI  LayerBased Representation of Polyhedrons for Point Containment Tests IS  1 SN  10772626 SP73 EP83 EPD  7383 A1  Wencheng Wang, A1  Jing Li, A1  Hanqiu Sun, A1  Enhua Wu, PY  2008 KW  computational geometry KW  polyhedron KW  point containment KW  solid representation VL  14 JA  IEEE Transactions on Visualization and Computer Graphics ER   
Abstract—This paper presents the layerbased representation of polyhedrons and its use for pointinpolyhedron 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 layerbased 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 layerbased representation. Incorporating an octree structure for organizing polyhedrons, our approach can run at a speed comparable with BSPbased inclusion tests, and at the same time greatly reduce storage and preprocessing time in treating large polyhedrons. We have developed an efficient solution for pointinpolyhedron 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.
[1] J. Lane, B. Magedson, and M. Rarick, “An Efficient Point in Polyhedron Algorithm,” Computer Vision, Graphics, and Image Processing, vol. 26, pp. 118125, 1984.
[2] J. Linhart, “A Quick PointinPolyhedron Test,” Computers and Graphics, vol. 14, no. 3, pp. 445448, 1990.
[3] P.C.P. Carvalho and P.R. Cavalcanti, “Point in Polyhedron Testing Using Spherical Polygons,” Graphics Gems V, A.W. Paeth, ed. pp.4249, Morgan Kaufmann, 1995.
[4] F.R. Feito and J.C. Torres, “Inclusion Test for General Polyhedra,” Computers and Graphics, vol. 21, no. 1, pp. 2330, 1997.
[5] A.S. Glassner, “Space Subdivision for Fast Ray Tracing,” IEEE Computer Graphics and Applications, vol. 4, pp. 1522, 1984.
[6] D. Gordan and C. Shulong, “FronttoBack Display or BSP Trees,” IEEE Computer Graphics and Applications, vol. 11, no. 5, pp. 7986, Sept. 1991.
[7] M. Abrash, Michael Abrash's Graphics Programming Black Book, special ed. The Coriolis Group Inc., 1997.
[8] W. Wang, J. Li, and E. Wu, “2D PointinPolygon Test by Classifying Edges into Layers,” Computers and Graphics, vol. 29, no. 3, pp. 427439, 2005.
[9] P.L. Williams, “Visibility Ordering Meshed Polyhedra,” ACM Trans. Graphics, vol. 11, no. 2, pp. 103126, 1992.
[10] J.D. Foley, A.V. Dam, S.K. Feiner, and J.F. Hughes, Computer Graphics—Principles and Practice in C, second ed. AddisonWesley, pp. 9699, 1999.
[11] A.J. Rueda, F.R. Feito, and L.M. Ortega, “LayerBased Decomposition of Solids and Its Applications,” The Visual Computer, vol. 21, no. 6, pp. 406417, 2005.
[12] M. Berg, M. Kreveld, M. Overmars, and O. Schwarzkopf, “Chapter 2: Line Segment Intersection,” Computational Geometry, Algorithms and Applications, second ed. Springer, 2000.
[13] Y.E. Kalay, “Determining the Spatial Containment of a Point in General Polyhedra,” Computer Graphics and Image Processing, vol. 19, no. 4, pp. 303334, 1982.
[14] W. Horn and D.L. Taylor, “A Theorem to Determine the Spatial Containment of a Point in a Planar Polyhedron,” Computer Vision, Graphics, and Image Processing, vol. 45, no. 1, pp. 106116, 1989.
[15] C.J. Ogayar, R.J. Segura, and F.R. Feito, “Point in Solid Strategies,” Computers and Graphics, vol. 29, no. 4, pp. 616624, 2005.
[16] J. O'Rourque, Computational Geometry in C. p. 2, Cambridge Univ., 1993.
[17] F. Yamaguchi, S. Tsuda, and T. Nagasaki, “Applications of 4 $\times$ 4 Determinant Method and the Polygon Engine,” The Visual Computer, vol. 4, no. 4, pp. 176187, 1988.
[18] M. Dietzfelbinger, A. Karlin, K. Mehlhorn, F.M. Heide, H. Rohnert, and R.E. Tarjan, “Dynamic Perfect Hashing: Upper and Lower Bounds,” SIAM J. Computing, vol. 23, pp. 738761, 1994.
[19] A. Glassner, An Introduction to Ray Tracing. pp.217220, Academic Press, 1989.
[20] P. Brunet and I. Navazo, “Solid Representation and Operation Using Extended Octrees,” ACM Trans. Graphics, vol. 9, no. 2, pp.170197, 1990.
[21] A. Watt, 3D Computer Graphics, third ed. pp. 5154, AddisonWesley, 2000.
[22] B. Payne and A. Toga, “Distance Field Manipulation of Surface Models,” IEEE Computer Graphics and Applications, vol. 12, no. 1, pp. 6571, Jan. 1992.
[23] S.F. Frisken, R.N. Perry, A.P. Rockwood, and T.R. Jones, “Adaptively Sampled Distance Fields: A General Representation of Shape for Computer Graphics,” Proc. ACM SIGGRAPH '00, pp.249254, 2000.
[24] C. Sigg, R. Peikert, and M. Gross, “Signed Distance Transform Using Graphics Hardware,” Proc. 14th IEEE Visualization Conf. (VIS '03), pp. 8390, 2003.
[25] J.A. Bærentzen and H. Aanæs, “Signed Distance Computation Using the Angle Weighted PseudoNormal,” IEEE Trans. Visualization and Computer Graphics, vol. 11, no. 3, pp. 243253, May/June 2005.
[26] A.J. Ruedo, F.R. Feito, and M.L. Rivero, “A TriangleBased Representation for Polygons and Its Applications,” Computers and Graphics, vol. 26, no. 5, pp. 805814, 2002.