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Cubic Triangular Surface Reconstruction Based on a Monotone Triangulation of Scattered Data and Parameterization

: Ma, L.; Qiang, W.; Chan Kai Yun, T.

Singh, J.; Lew, S.C.; Gay, R. ; Gintic Institute of Manufacturing Technology; Nanyang Technological University Singapore:
Computer Integrated Manufacturing. Proceedings. Technologies for New Millennium Manufacturing
Singapore: Gintic Institute of Manufacturing Technology, 2000
ISBN: 981-04-1997-X
International Conference on Computer Integrated Manufacturing (ICCIM) <5, 2000, Singapore>
Conference Paper
Fraunhofer IGD ()
Interpolation; Parameterization of surfaces; Recursive algorithm; Curve modeling; surface modeling

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) 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.