一种基于正则参数化的降维细分算法(英文)

In our previous work, we have given an algorithm for segmenting a simplex in the n-dimensional space into rt n＋ 1 polyhedrons and provided map F which maps the n-dimensional unit cube to these polyhedrons. In this paper, we prove that the map F is a one to one correspondence at least in lower dimensional spaces （n _〈 3）. Moreover, we propose the approximating subdivision and the interpolatory subdivision schemes and the estimation of computational complexity for triangular Bézier patches on a 2-dimensional space. Finally, we compare our schemes with Goldman＇s in computational complexity and speed.

A Dimension Reduction Subdivision Scheme Based on Proper Parameterization

In our previous work,we have given an algorithm for segmenting a simplex in the n-dimensional space into n 1 polyhedrons and provided map F which maps the n-dimensional unit cube to these polyhedrons.In this paper,we prove that the map F is a one to one correspondence at least in lower dimensional spaces(n≤3).Moreover,we propose the approximating subdivision and the interpolatory subdivision schemes and the estimation of computational complexity for triangular man's in computational complexity and speed.