Delaunay-based representation of surfaces defined over arbitrarily shaped domains

A method for constructing surface models from a discrete set of arbitrarily distributed data is described. The surface is represented as a network of planar, triangular faces with vertices at the data points, which is built up on a Delaunay triangulation of the data point projections on thex−y plane. In the paper, the problem of triangulating arbitrarily shaped domains is considered. A new definition of Delaunay triangulation of a set of points constrained by a polygonal boundary is introduced, and some of its basic properties are briefly discussed. A new incremental algorithm for constructing a Delaunay triangulation of an arbitrarily shaped domain is described. This method is also demonstrated to be well suited to generate surface approximations at predefined levels of accuracy, which are based on significant subsets of selected data points.

[1]  J. Bramble,et al.  Triangular elements in the finite element method , 1970 .

[2]  J. T. Holdeman,et al.  A triangular finite element mesh generator for fluid dynamic systems of arbitrary geometry , 1980 .

[3]  Godfried T. Toussaint,et al.  An Efficient Algorithm for Decomposing a Polygon into Star-Shaped Polygons , 1981 .

[4]  Edward A. Sadek,et al.  A scheme for the automatic generation of triangular finite elements , 1980 .

[5]  Robin Sibson,et al.  Computing Dirichlet Tessellations in the Plane , 1978, Comput. J..

[6]  Theodosios Pavlidis,et al.  Decomposition of Polygons into Simpler Components: Feature Generation for Syntactic Pattern Recognition , 1975, IEEE Transactions on Computers.

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

[8]  D. T. Lee,et al.  An Optimal Algorithm for Finding the Kernel of a Polygon , 1979, JACM.

[9]  Robin Sibson,et al.  Locally Equiangular Triangulations , 1978, Comput. J..

[10]  ARISTIDES A. G. REQUICHA,et al.  Representations for Rigid Solids: Theory, Methods, and Systems , 1980, CSUR.

[11]  Bianca Falcidieno,et al.  A Delaunay-Based Method for Surface Approximation , 1983, Eurographics.

[12]  D. H. McLain,et al.  Two Dimensional Interpolation from Random Data , 1976, Comput. J..

[13]  B. Chazelle.  Computational geometry and convexity , 1980 .

[14]  Robert E. Barnhill,et al.  Representation and Approximation of Surfaces , 1977 .

[15]  Bruce J. Schachter,et al.  Decomposition of Polygons into Convex Sets , 1978, IEEE Transactions on Computers.

[16]  I. M. Klucewicz.  A piecewise c1 interpolant to arbitrarily spaced data , 1978 .

[17]  Robert E. Tarjan,et al.  Triangulating a Simple Polygon , 1978, Inf. Process. Lett..

[18]  I. Babuska,et al.  ON THE ANGLE CONDITION IN THE FINITE ELEMENT METHOD , 1976 .

[19]  D. T. Lee,et al.  Visibility of a simple polygon , 1983, Comput. Vis. Graph. Image Process..

[20]  B. A. Lewis,et al.  Triangulation of Planar Regions with Applications , 1978, Comput. J..