Automatic reconstruction of B-spline surfaces of arbitrary topological type

Abstract

Creating freeform surfaces is a challenging task even with advanced geometric modeling systems. Laser range scanners offer a promising alternative for model acquisition-the 3D scanning of existing objects or clay maquettes. The problem of converting the dense point sets produced by laser scanners into useful geometric models is referred to as surface reconstruction.In this paper, we present a procedure for reconstructing a tensor product B-spline surface from a set of scanned 3D points. Unlike previous work which considers primarily the problem of fitting a single B-spline patch, our goal is to directly reconstruct a surface of arbitrary topological type. We must therefore define the surface as a network of B-spline patches. A key ingredient in our solution is a scheme for automatically constructing both a network of patches and a parametrization of the data points over these patches. In addition, we define the B-spline surface using a surface spline construction, and demonstrate that such an approach leads to an efficient procedure for fitting the surface while maintaining tangent plane continuity. We explore adaptive refinement of the patch network in order to satisfy user-specified error tolerances, and demonstrate our method on both synthetic and real data.

Geometric accuracy analysis for discrete surface approximation

“…From corollary 3.1, the Hausdorff distance is no greater than 4kε 2 .From the proof of theorem 2, the normal distance at some sample point is less than 5kε, also from (24) and previous paragraph, any point on X is within 4ε distance to such a sample point, thus together with Lemma 2, the normal distance at any point is no greater than 9kε.…”

Reconstructing B-patch surface from triangular mesh

“…In general, the standard surface reconstructing methods interpolate the smooth surfaces by solving linear equation systems and least square problems [1] [11]. The surfaces that are generated by these methods may very well lie close to data points, but they may not be very smooth.…”

Second-order geometric continuous processing of singular points

“…In order to make the minimize of the quadratic energy function [7] , then use Lagrange multiplier method [8] , the constraints can be transformed into the following form. coefficient of the i p is E , the rest are zero.Then the corresponding trans double seventh degree control points i p are obtained by DFT and IDFT [9] .…”