Reconstruction of B-spline surfaces from scattered data points

Abstract

We present a new approach for reconstructing a smooth surface from a set of scattered points in 3D space. Our algorithm first decomposes a given point set into a quadtree-like data structure known as a strip tree. The strip tree is used to fit a set of least squares quadratic surfaces to the data points. These quadratic surfaces are then degree-elevated to bi-cubic surfaces and blended together to form a set of B-spline surfaces that approximates the given point set.