Pyramidal simplicial complexes

We propose a new mo{le] for Iepreseuting a liypersurface describing a scalar field in ally dimension at ,Iifferellt levels of detail. The model is based on a smluence of domain decompositions into simplicial complexes and integrates the modeling characteristics of simplicial complexes wit.11 tile versatility of a multilevel descriptiml. we I)leseIlt a (ha structure an(i algorithms for efficiently encoding a]k[l nmlli}>ulating such model The proposed (Iata structlwe is slwcifk for applications in which a “~loll-to~~ol{~gical” lelJlesrlltatioll is required. Such applications include vollunetric data visualization and geometric [Iuery processing.

[1]  J. Wilhelms,et al.  Octrees for faster isosurface generation , 1992, TOGS.

[2]  Theodosios Pavlidis,et al.  Hierarchical triangulation using cartographic coherence , 1992, CVGIP Graph. Model. Image Process..

[3]  V. T. Rajan Optimality of the Delaunay triangulation in ℝd , 1994, Discret. Comput. Geom..

[4]  L. De Floriani A pyramidal data structure for triangle-based surface description , 1989, IEEE Computer Graphics and Applications.

[5]  Herbert Edelsbrunner,et al.  An acyclicity theorem for cell complexes ind dimension , 1990, Comb..

[6]  Leila De Floriani,et al.  A Hierarchical Triangle-Based Model for Terrain Description , 1992, Spatio-Temporal Reasoning.

[7]  H. Edelsbrunner,et al.  Tetrahedrizing Point Sets in Three Dimensions , 1988, ISSAC.

[8]  Jane Wilhelms,et al.  Octrees for faster isosurface generation , 1992, TOGS.

[9]  Michela Bertolotto,et al.  Hierarchical Hypersurface Modeling , 1994, IGIS.

[10]  Jane Wilhelms,et al.  A coherent projection approach for direct volume rendering , 1991, SIGGRAPH.

[11]  WilhelmsJane,et al.  A coherent projection approach for direct volume rendering , 1991 .

[12]  D. F. Watson Computing the n-Dimensional Delaunay Tesselation with Application to Voronoi Polytopes , 1981, Comput. J..

[13]  Leila De Floriani A pyramidal data structure for triangle-based surface description , 1989, IEEE Computer Graphics and Applications.

[14]  Barry Joe,et al.  Construction of three-dimensional Delaunay triangulations using local transformations , 1991, Comput. Aided Geom. Des..

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

[16]  Michael P. Garrity Raytracing irregular volume data , 1990, SIGGRAPH 1990.

[17]  V. T. Rajan,et al.  Optimality of the Delaunay triangulation in Rd , 1991, SCG '91.

[18]  Leila De Floriani,et al.  Extracting contour lines from a hierarchical surface model , 1993, Comput. Graph. Forum.

[19]  Peter L. Williams Interactive splatting of nonrectilinear volumes , 1992, Proceedings Visualization '92.