A pyramidal data structure for triangle-based surface description

A hierarchical model for approximating 2-1/2-dimensional surfaces is described. This model, called a Delaunay pyramid, is a method for compression of spatial data and representation of a surface at successively finer levels of detail. A Delaunay pyramid is based on a sequence of Delaunay triangulations of suitably defined subsets of the set of data points. A triangle-oriented encoding structure for a Delaunay pyramid is presented, and its storage complexity is evaluated. An algorithm for constructing a Delaunay pyramid is described, and a method for solving the point location and evaluation on such a model is discussed.<<ETX>>

[1]  A. R. Forrest,et al.  On coons and other methods for the representation of curved surfaces , 1972, Comput. Graph. Image Process..

[2]  David H. Douglas,et al.  Detection of Surface-Specific Points by Local Parallel Processing of Discrete Terrain Elevation Data , 1975 .

[3]  C. Lawson.  Software for C1 Surface Interpolation , 1977 .

[4]  David G. Kirkpatrick,et al.  Fast Detection of Polyhedral Intersections , 1982, ICALP.

[5]  Donald Meagher,et al.  Geometric modeling using octree encoding , 1982, Comput. Graph. Image Process..

[6]  Leonidas J. Guibas,et al.  Primitives for the manipulation of general subdivisions and the computation of Voronoi diagrams , 1983, STOC.

[7]  David G. Kirkpatrick,et al.  Optimal Search in Planar Subdivisions , 1983, SIAM J. Comput..

[8]  Hanan Samet,et al.  The Quadtree and Related Hierarchical Data Structures , 1984, CSUR.

[9]  Leila De Floriani,et al.  A hierarchical structure for surface approximation , 1984, Comput. Graph..

[10]  Donald P. Greenberg,et al.  Improved Computational Methods for Ray Tracing , 1984, TOGS.

[11]  Leila De Floriani,et al.  Delaunay-based representation of surfaces defined over arbitrarily shaped domains , 1985, Comput. Vis. Graph. Image Process..

[12]  Francis J. M. Schmitt,et al.  An adaptive subdivision method for surface-fitting from sampled data , 1986, SIGGRAPH.

[13]  Jean-Daniel Boissonnat,et al.  The hierarchical representation of objects: the Delaunay tree , 1986, SCG '86.

[14]  Schmitt Francis,et al.  Adaptative Polyhedral Approximation Of Digitized Surfaces , 1986, Other Conferences.

[15]  Alan H. Barr,et al.  Accurate triangulations of deformed, intersecting surfaces , 1987, SIGGRAPH.

[16]  Olivier D. Faugeras,et al.  An object centered hierarchical representation for 3D objects: The prism tree , 1987, Comput. Vis. Graph. Image Process..

[17]  Leila De Floriani,et al.  Constrained Delaunay triangulation for multiresolution surface description , 1988, [1988 Proceedings] 9th International Conference on Pattern Recognition.