An adaptive subdivision method for surface-fitting from sampled data

Abstract

A method is developed for surface-fitting from sampled data. Surface-fitting is the process of constructing a compact representation to model the surface of an object based on a fairly large number of given data points. In our case, the data is obtained from a real object using an automatic three-dimensional digitizing system. The method is based on an adaptive subdivision approach, a technique previously used for the design and display of free-form curved surface objects. Our approach begins with a rough approximating surface and progressively refines it in successive steps in regions where the data is poorly approximated. The method has been implemented using a parametric piecewise bicubic Bernstein-Bézier surface possessing G 1 geometric continuity. An advantage of this approach is that the refinement is essentially local reducing the computational requirements which permits the processing of large databases. Furthermore, the method is simple in concept, yet realizes efficient data compression. Some experimental results are given which show that the representation constructed by this method is faithful to the original database.

Piecewise smooth surface reconstruction

“…Schudy and Ballard [22,23], Brinkley [2], and Sclaroff and Pentland [24] fit embeddings of a sphere. Schmitt et al [20,21] fit embeddings of a cylinder to data from cylindrical range scans. Goshtasby [7] works with embeddings of cylinders and tori.…”

Simplification of objects rendered by polygonal approximations

“…Edge Gaps. In [ 8] the authors use bicubic Bernstein-Bezier surface patches to model the data. The transitions across patch edges to neighboring patches are guaranteed to be smooth and continuous due to the constraints applied when solving for the patch control points.…”

“…In either case, realism of the rendering must be balanced against drawing complexity and speed. The number of polygons to be drawn is a reasonable metric to be used in determining drawing complexity; however, a similar [ 8]. The technique approximates the surface represented by the sampled data points with bicubic Bemstein-Bezier surface patches.…”

Polygonization of multi-component non-manifold implicit surfaces through a symbolic-numerical continuation algorithm

“…Unlike spatial sampling techniques, surface fitting methods are not based on partitioning space into cells. Starting from a seed mesh that roughly approximates the implicit surface, these techniques progressively adapt and deform the current mesh to the implicit surface [Schmitt et al 1986] [Zhou et al 1997] [Li et al 2004].…”