Abstract: Simplicial subdivisions of the unit simplex S n that underlie simplicial algorithms have until now only been based on the K1-triangulation, the J1-triangulation, or the H1-triangulation of R n . In the previous chapter we saw that the D1-triangulation is superior to all these triangulations according to measures of efficiency such as the number of simplices, the diameter, and the average directional density. Therefore, it is interesting to develop simplicial subdivisions of the unit simplex S n that are suitable to underly simplicial algorithms on S n and being based on the D1-triangulation of R n . In this chapter, we propose such a simplicial subdivision, called the T1-triangulation of S n . It induces a suitable simplicial subdivision for the (n + l)-ray variable dimension method on the unit simplex proposed by van der Laan and Talman in [108]. Section 1 introduces the new simplicial subdivision of S n , Section 2 describes its pivot rules, and Section 3 gives a comparison on the triangulations of the unit simplex. This chapter is based on Dang and Talman’s [17].
Publication Year: 1995
Publication Date: 1995-01-01
Language: en
Type: book-chapter
Indexed In: ['crossref']
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