Triage polygonization of rounded polyhedra

This paper describes a method for rounding and polygonizing edges and corners of polyhedral models to produce softer, more natural looking objects. The underlying rounded surface is assumed to be defined by aquasiconvolutional smoothingo, and the focus is on polygonizing the surface rapidly and efficiently. A binary space partitioning (BSP) tree is used to classify space in the vicinity of a polyhedron to identify the curved regions. Planar surfaces are extracted as single polygons, and extra polygons are introduced only at rounded edges and corners. The result is a highquality polygonization of the rounded polyhedron with none of the fragmentation problems of more general polygonization methods.

[1]  Bruce F. Naylor,et al.  Set operations on polyhedra using binary space partitioning trees , 1987, SIGGRAPH.

[2]  John M. Snyder,et al.  Interval analysis for computer graphics , 1992, SIGGRAPH.

[3]  B. Naylor.  A priori based techniques for determining visibility priority for 3-d scenes , 1981 .

[4]  Steve Colburn,et al.  Solid Modeling with Global Blending for Machining Dies and Patterns , 1990 .

[5]  William E. Lorensen,et al.  Marching cubes: A high resolution 3D surface construction algorithm , 1987, SIGGRAPH.

[6]  John Amanatides,et al.  Merging BSP trees yields polyhedral set operations , 1990, SIGGRAPH.

[7]  Jules Bloomenthal,et al.  Polygonization of implicit surfaces , 1988, Comput. Aided Geom. Des..

[8]  Russell H. Taylor,et al.  Superfaces: polygonal mesh simplification with bounded error , 1996, IEEE Computer Graphics and Applications.

[9]  Charles D. Hansen,et al.  Geometric optimization , 1993, Proceedings Visualization '93.

[10]  Josef Hoschek,et al.  Fundamentals of computer aided geometric design , 1996 .

[11]  Henry Fuchs,et al.  On visible surface generation by a priori tree structures , 1980, SIGGRAPH '80.

[12]  Bernd Hamann,et al.  Constructing Hierarchies for Triangle Meshes , 1998, IEEE Trans. Vis. Comput. Graph..

[13]  Burkhard Wuensche,et al.  A Survey and Analysis of Common Polygonization Methods and Optimization Techniques , 1997 .

[14]  Tom Duff,et al.  Interval arithmetic recursive subdivision for implicit functions and constructive solid geometry , 1992, SIGGRAPH.

[15]  Mark Hall,et al.  Adaptive polygonalization of implicitly defined surfaces , 1990, IEEE Computer Graphics and Applications.

[16]  Akio Koide,et al.  An Efficient Method of Triangulating Equi-Valued Surfaces by Using Tetrahedral Cells , 1991 .

[17]  Jules Bloomenthal,et al.  An Implicit Surface Polygonizer , 1994, Graphics Gems.