Options
2000
Conference Paper
Titel
Cubic Triangular Surface Reconstruction Based on a Monotone Triangulation of Scattered Data and Parameterization
Abstract
In CAD/CAM systems, surfaces are usually of lower degree and are required to have less number of patches so that operations applied on them can run efficiently and robustly. For a surface triangulation delta with n irregular sample points in 3D spaces, a monotone sequence of triangulations delta contains delta (exp 1) contains delta (exp 2) contains...delta exp (exp n-3) is constructed (Ma et al, 1999). In this paper, a smooth cubic surface is then constructed step by step over the reversed sequence of triangulations delta (exp n-3) contains ... contains delta (exp 2) contains delta (exp 1) contains delta. At each step, if there are no more than three triangles to be added, no subdivision is applied on the triangulation. Otherwise, the extra triangles are subdivided. In each step, cubic B-B surface patches are constructed inductively according to the respective continuity conditions and the parameterization. The proposed algorithm is of 0(n) complexity and the cubic surface is constructed explicitly without any implicit equation. In most practical examples, no triangle is subdivided. Therefore, the reconstruction algorithm is optimal with the least number of patches and the lowest degree.