The structured grid generation using beta-spline curve/surface modeling (Q1975666)

Beta-splines are very useful for the modeling of curves or surfaces. Their properties are basically governed by two shape parameters: one measuring the influence of the tangent at both sides of the joint, which is here called the bias parameter at that joint, and the second parameter which controls how much the spline is drawn towards the control vertices and this is called the tension parameter. Two strategies are proposed to use these beta-splines for the generation of grids on a curve or surface. The first is to model the surface starting from given control vertices and then generating the grid points using this model. The second starts from points on the surface, constructs from these a set of control vertices (solution of a triangular system in which the bias and tension parameters appear), after which strategy 1 can be applied. Some examples are given illustrating the effect of the shape parameters on the resulting grid.