Adaptive thinning algorithm of nonsingular triangulation

This paper studies adaptive thinning strategies for the non-singular triangulation of scattered data by C1-rational spline function. Given a set of points in R2, Luo, Liu and Chen have presented a triangulation algorithm which ensures the non-singularity of S21(▵) and S31(▵) spaces. In this paper, we improve the algorithm to reduce the number of knots of the triangulation within a given tolerance, while the non-singularity of S21(▵) and S31(▵) spaces is ensured. Our strategies presented here depend on both the locations of the data points in the plane, and the data values at these points. We give the definition of discrete norm for C1-rational spline function by using its coefficients. Then a weight is assigned to each knot, which is a measure of the importance of knot in the representation of spline. When the weight of the knot is less than the given tolerance, its influence is regarded negligible, then it can be removed. It's a discrete method. In the end of this paper several numerical examples are presented to show the feasibility and validity of our algorithm.