A unified approach for simplifying polygonal and spline models

We present a new approach for simplifying models composed of polygons or spline patches. Given an input model, the algorithm computes a new representation of the model in terms of triangular Bezier patches. It performs a series of geometric operations, consisting of patch merging and swapping diagonals, and makes use of batch connectivity information to generate C-LODs (curved levels-of-detail). Each C-LOD is represented using cubic triangular Bezier patches. The C-LODs provide a compact representation for storing the model. The algorithm tries to minimize the surface deviation error and maintains continuity at patch boundaries. Given the CLODs, the algorithm can generate their polygonal approximations using static and dynamic tessellation schemes. It has been implemented and we highlight its performance on a number of polygonal and spline models.

[1]  Dinesh Manocha,et al.  Simplifying polygonal models using successive mappings , 1997, Proceedings. Visualization '97 (Cat. No. 97CB36155).

[2]  C XiaJulie,et al.  Adaptive Real-Time Level-of-Detail-Based Rendering for Polygonal Models , 1997 .

[3]  C. D. Boor,et al.  Good approximation by splines with variable knots. II , 1974 .

[4]  Paul Dierckx,et al.  Curve and surface fitting with splines , 1994, Monographs on numerical analysis.

[5]  William J. Schroeder.  A topology modifying progressive decimation algorithm , 1997, Proceedings. Visualization '97 (Cat. No. 97CB36155).

[6]  Dinesh Manocha,et al.  A unified approach for simplifying polygonal and spline models , 1998 .

[7]  Tony DeRose,et al.  Multiresolution analysis for surfaces of arbitrary topological type , 1997, TOGS.

[8]  Dinesh Manocha,et al.  Simplification Culling of Static and Dynamic Scene Graphs , 1998 .

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

[10]  Dinesh Manocha,et al.  Accelerated walkthrough of large spline models , 1997, SI3D.

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

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

[13]  Charles T. Loop,et al.  Smooth spline surfaces over irregular meshes , 1994, SIGGRAPH.

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

[15]  Hugues Hoppe,et al.  View-dependent refinement of progressive meshes , 1997, SIGGRAPH.

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

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

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

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

[20]  Tony DeRose,et al.  Generalized B-spline surfaces of arbitrary topology , 1990, SIGGRAPH.

[21]  Gerald Farin,et al.  Curves and surfaces for computer aided geometric design , 1990 .

[22]  Dinesh Manocha,et al.  Appearance-preserving simplification , 1998, SIGGRAPH.

[23]  Chandrajit L. Bajaj,et al.  Error-bounded reduction of triangle meshes with multivariate data , 1996, Electronic Imaging.

[24]  Matthias Eck,et al.  Automatic reconstruction of B-spline surfaces of arbitrary topological type , 1996, SIGGRAPH.

[25]  Jihad El-Sana,et al.  Controlled simplification of genus for polygonal models , 1997, Proceedings. Visualization '97 (Cat. No. 97CB36155).

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

[27]  Anselmo Lastra,et al.  Interactive display of large-scale NURBS models , 1995, I3D '95.

[28]  Ramon F. Sarraga,et al.  Computer modeling of surfaces with arbitrary shapes , 1990, IEEE Computer Graphics and Applications.