Parameterization of clouds of unorganized points using dynamic base surfaces

• Published in: Computer aided design Vol. 36; no. 7; pp. 607 - 623
• Main Author: Azariadis, Phillip N.
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.06.2004
• Subjects: Base surfaces; Parameterization; Reverse engineering; Surface fitting; Surface fitting; Base surfaces; Parameterization; Reverse engineering
• ISSN: 0010-4485; 1879-2685
• DOI: 10.1016/S0010-4485(03)00138-6

In this paper a new method for parameterizing clouds of unorganized points is presented. The proposed method introduces the notion of dynamic base surfaces (DBS) which are dynamically adapted to the three-dimensional shape implied by the clouds of points. The only assumption regarding the cloud of points is the existence of a boundary defined by a closed path of four curves. The proposed method is based on an iterative procedure where a DBS is gradually improved approximating more faithfully the fundamental geometry of the cloud of points. Parameterization is achieved by orthogonally projecting the cloud of points onto the DBS. An application of the introduced parameterization method to the well-known surface least-squares fitting is presented which illustrates the effectiveness and the efficiency of the proposed approach.