Contour Edge Analysis for Polyhedron Projections

Given a polyhedron (in 3-space) and a view point, an edge of the polyhedron is called contour edge, if one of the two incident facets is directed towards the view point, and the other incident facet is directed away from the view point. Algorithms on polyhedra can exploit the fact that the number of contour edges is usually much smaller than the overall number of edges. The main goal of this paper is to provide evidence for (and quantify) the claim, that the number of contour edges is small in many situations.

[1]  Arthur Appel,et al.  The notion of quantitative invisibility and the machine rendering of solids , 1967, ACM National Conference.

[2]  Robert A. Schumacker,et al.  A Characterization of Ten Hidden-Surface Algorithms , 1974, CSUR.

[3]  C. William Gear,et al.  Raster-scan hidden surface algorithm techniques , 1977, SIGGRAPH '77.

[4]  F M Richards,et al.  Areas, volumes, packing and protein structure. , 1977, Annual review of biophysics and bioengineering.

[5]  P. Gruber.  Approximation of convex bodies , 1983 .

[6]  Carlo H. Séquin,et al.  Visible Feature Return at Object Resolution , 1985, IEEE Computer Graphics and Applications.

[7]  Otto Nurmi.  A fast line-sweep algorithm for hidden line elimination , 1985, BIT Comput. Sci. Sect..

[8]  Tony DeRose,et al.  Surface reconstruction from unorganized points , 1992, SIGGRAPH.

[9]  Tony DeRose,et al.  Mesh optimization , 1993, SIGGRAPH.

[10]  Barbara Wolfers,et al.  Surface Reconstruction Between Simple Polygons via Angle Criteria , 1994, J. Symb. Comput..

[11]  Tony DeRose,et al.  Piecewise smooth surface reconstruction , 1994, SIGGRAPH.

[12]  Emo Welzl.  Gram's Equation - A Probabilistic Proof , 1994, Results and Trends in Theoretical Computer Science.

[13]  Susan E. Dorward.  A survey of object-space hidden surface removal , 1994, Int. J. Comput. Geom. Appl..

[14]  Tony DeRose,et al.  Multiresolution analysis of arbitrary meshes , 1995, SIGGRAPH.

[15]  Reinhard Klein,et al.  Large mesh generation from boundary models with parametric face representation , 1995, SMA '95.

[16]  Mark H. Overmars.  Designing the Computational Geometry Algorithms Library CGAL , 1996, WACG.

[17]  Geert-Jan Giezeman,et al.  The CGAL Kernel: A Basis for Geometric Computation , 1996, WACG.