Reconstruction of Branched Surfaces: Experiments with Disjoint B-spline Surface

Abstract

Surface reconstruction is a process where a desired shape is constructed using the scanned data. Some of the applications are modeling of human airway tree, femur, human vasculature, automobile parts (like muffler and tubular frame parts) and terrain reconstruction. This reconstruction, at times, involves branching (furcation) i.e. creation of disjoint surfaces (branch) from one contour to two or more contours in adjacent plane. This branched surface may have various geometrical (like continuity and planarity) and topological (like shape and multi-furcation) complexities. Accordingly, different techniques in the past have addressed the problem to varying levels of complexities. Amongst them a lot of work has been done towards stepwise surface construction and then gluing them together to get a single surface. Some methods even required an additional hole filling step. These serial processes become complex and involve large computation time especially for applications like modeling of human airway tree. Therefore, in this paper we present a new and simpler method to reduce the steps by adopting a single equation to create disjoint B-spline surface which can have different orders in both parametric directions. At the same time our method addresses the requirements of continuity, geometric and topological complexities.