Controlled simplification of genus for polygonal models

Genus-reducing simplifications are important in constructing multiresolution hierarchies for level-of-detail-based rendering, especially for datasets that have several relatively small holes, tunnels, and cavities. We present a genus-reducing simplification approach that is complementary to the existing work on genus-preserving simplifications. We propose a simplification framework in which genus-reducing and genus-preserving simplifications alternate to yield much better multiresolution hierarchies than would have been possible by using either one of them. In our approach we first identify the holes and the concavities by extending the concept of /spl alpha/-hulls to polygonal meshes under the L/sub /spl infin// distance metric and then generate valid triangulations to fill them.

[1]  Henry Fuchs,et al.  Optimal surface reconstruction from planar contours , 1977, CACM.

[2]  William E. Lorensen,et al.  Decimation of triangle meshes , 1992, SIGGRAPH.

[3]  David Salesin,et al.  Hierarchical image caching for accelerated walkthroughs of complex environments , 1996, SIGGRAPH.

[4]  Chandrajit L. Bajaj,et al.  Sampling and reconstructing manifolds using alpha-shapes , 1997, CCCG.

[5]  D. Manocha,et al.  Fast Polygon Triangulation Based on Seidel's Algorithm , 1995 .

[6]  Shenchang Eric Chen,et al.  QuickTime VR: an image-based approach to virtual environment navigation , 1995, SIGGRAPH.

[7]  Gavin S. P. Miller,et al.  Hierarchical Z-buffer visibility , 1993, SIGGRAPH.

[8]  David G. Kirkpatrick,et al.  On the shape of a set of points in the plane , 1983, IEEE Trans. Inf. Theory.

[9]  Jihad El-Sana,et al.  Adaptive Real-Time Level-of-Detail-Based Rendering for Polygonal Models , 1997, IEEE Trans. Vis. Comput. Graph..

[10]  Amitabh Varshney,et al.  Navigating static environments using image-space simplification and morphing , 1997, SI3D.

[11]  Leonard McMillan,et al.  Plenoptic Modeling: An Image-Based Rendering System , 2023 .

[12]  Jarek Rossignac,et al.  Multi-resolution 3D approximations for rendering complex scenes , 1993, Modeling in Computer Graphics.

[13]  Lance Williams,et al.  View Interpolation for Image Synthesis , 1993, SIGGRAPH.

[14]  Greg Turk,et al.  Re-tiling polygonal surfaces , 1992, SIGGRAPH.

[15]  Bernard Chazelle,et al.  An optimal algorithm for intersecting three-dimensional convex polyhedra , 1989, 30th Annual Symposium on Foundations of Computer Science.

[16]  Bernd Hamann,et al.  A data reduction scheme for triangulated surfaces , 1994, Comput. Aided Geom. Des..

[17]  John M. Airey,et al.  Increasing update rates in the building walkthrough system with automatic model-space subdivision and potentially visible set calculations , 1990 .

[18]  Kenneth L. Clarkson,et al.  A fast las vegas algorithm for triangulating a simple polygon , 1989, Discret. Comput. Geom..

[19]  Franklin C. Crow,et al.  A more flexible image generation environment , 1982, SIGGRAPH.

[20]  John F. Canny,et al.  An efficient approach to removing geometric degeneracies , 1992, SCG '92.

[21]  Ned Greene,et al.  Hierarchical polygon tiling with coverage masks , 1996, SIGGRAPH.

[22]  Dinesh Manocha,et al.  Visibility culling using hierarchical occlusion maps , 1997, SIGGRAPH.

[23]  James H. Clark,et al.  Hierarchical geometric models for visible surface algorithms , 1976, CACM.

[24]  Peter Shirley,et al.  Visual navigation of large environments using textured clusters , 1995, I3D '95.

[25]  Herbert Edelsbrunner,et al.  Weighted alpha shapes , 1992 .

[26]  John Rohlf,et al.  IRIS performer: a high performance multiprocessing toolkit for real-time 3D graphics , 1994, SIGGRAPH.

[27]  Hugues Hoppe,et al.  Progressive meshes , 1996, SIGGRAPH.

[28]  David P. Luebke,et al.  Portals and mirrors: simple, fast evaluation of potentially visible sets , 1995, I3D '95.

[29]  Carlo H. Séquin,et al.  Visibility preprocessing for interactive walkthroughs , 1991, SIGGRAPH.

[30]  Amitabh Varshney,et al.  Controlled Topology Simplification , 1996, IEEE Trans. Vis. Comput. Graph..

[31]  Dinesh Manocha,et al.  Simplification envelopes , 1996, SIGGRAPH.

[32]  Herbert Edelsbrunner,et al.  Three-dimensional alpha shapes , 1994, ACM Trans. Graph..

[33]  David E. Muller,et al.  Finding the Intersection of two Convex Polyhedra , 1978, Theor. Comput. Sci..

[34]  Chandrajit L. Bajaj,et al.  Generation of configuration space obstacles: the case of a moving sphere , 1988, IEEE J. Robotics Autom..

[35]  Carlo H. Séquin,et al.  Adaptive display algorithm for interactive frame rates during visualization of complex virtual environments , 1993, SIGGRAPH.