COMPUTER-AIDED GEOMETRIC DESIGN OF GEOLOGIC SURFACES AND BODIES

Bivariate quadratic simplicial B-splines are employed to obtain a C1-smooth surface from scattered positional or directional geological data given over a two-dimensional domain. Vertices are generated according to the areal distribution of data sites, and polylines are defined along real geological features. The vertices and the polylines provide a constrained Delaunay triangulation of the domain. Note that the vertices do not generally coincide with the data sites. Six linearly independent simplex B-splines are associated with each triangle. Their defining knots and finite supports are automatically deduced from the vertices. Specific knot configurations result in discontinuities of the surface or its directional derivatives. Coefficients of a simplex spline representation are visualized as geometric points controlling the shape of the surface. This approach calls for geologic modeling and interaction of the geologist up front to define vertices and polylines, and to move control points initially given by an algorithm. Thus, simplex splines associated with irregular triangles seem to be well-suited to approximate and allow further geometrically modeling of geologic surfaces, including discontinuities, from scattered data. Applications to mathematical test as well as to real geological data are given as examples. © 1990 International Association for Mathematical Geology.