Generation of spline approximations to parametric tessellations

被引:0
|
作者
Dannenhoffer, John F., III [1 ]
Haimes, Robert [2 ]
机构
[1] Syracuse Univ, Syracuse, NY 13244 USA
[2] MIT, Cambridge, MA 02139 USA
关键词
Cubic spline; Parametric tessellation; Least-square fit; Reparameterization; Topological editing; Behavioral morphing; FREE KNOTS;
D O I
10.1007/s00366-010-0182-x
中图分类号
TP39 [计算机的应用];
学科分类号
081203 ; 0835 ;
摘要
In geometrical modeling, one is often provided a description of a surface that is defined in terms of a triangulation, which is supported by a discrete number of nodes in space. These faceted surface representations are defined to be C-0 continuous, and therefore in general have slope and curvature discontinuities at the triangle sides, unless the tessellation is planar. Unfortunately, analytical and computational methods often require a surface description that has well-defined and smoothly varying gradients and curvatures; in general spline surfaces possess such properties. Described herein is a process for generating a cubic spline surface that approximates, to within a user-specified tolerance, a given tessellated surface that may be non-convex or multiply connected. The method combines a local least-squares technique for specifying knot properties as well as an adaptation technique for selecting the necessary knot spacings. This new technique is first described along a curve for illustrative purposes. It is then expanded to the case of the general surface. A reparameterization technique that is required for surfaces with non-smooth parameterizations is described next. Computed results for two configurations are then shown.
引用
收藏
页码:31 / 40
页数:10
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