# Automatic reconstruction of B-spline surfaces of arbitrary topological type

ACM SIGGRAPH 1996 Proceedings, 325-334.

Fully automatic creation of B-spline patch network from 3D point cloud.

**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.

**Hindsights:**
Reconstructing arbitrary B-spline surfaces is difficult, and this paper tackles the problem in a fully
automatic approach.
For some applications, it may be more practical to let the user manually specify the patch boundaries (see
the related

paper by Krishnamurthy and
Levoy in the same proceedings).
Still, the surface spline construction is useful in this context for maintaining C1 continuity without
resort to constrained optimization.
Sorry, the code is not available.
Subdivision surfaces, which have gained popularity recently, make this reconstruction problem so much
easier... (see

my SIGGRAPH 1994 paper).