The present article is an account of results on univalent functions in multiply connected domains obtained by the author. It contains two rery simple proofs of Villat's formula; Schwarz's formula, Poisson'...The present article is an account of results on univalent functions in multiply connected domains obtained by the author. It contains two rery simple proofs of Villat's formula; Schwarz's formula, Poisson's formula and Poisson-Jensen formula in multiply connected domains; the differentiability theorem with respect to the parameter of analytic function family containing one parametric variable on multiply connected domains; variation theorem and parametric representation theorem of univalent functions in multiply connected domains; the solution of an extremal problem of differentiable functionals.展开更多
An improved algorithm of Delaunay triangulation is proposed by expanding the scope from a convex polygon to an arbitrary polygon area in which holes can be contained in the subdivision procedure. The data structure of...An improved algorithm of Delaunay triangulation is proposed by expanding the scope from a convex polygon to an arbitrary polygon area in which holes can be contained in the subdivision procedure. The data structure of generated triangles and the exuviationslike method play a key role, and a single connectivity domain (SCD) without holes is constructed as the initial part of the algorithm. Meanwhile, some examples show that the method can be applied to the triangulation of the trimmed NURBS surface. The result of surface tessellation can be used in many applications such as NC machining, finite element analysis, rendering and mechanism interference detection.展开更多
文摘The present article is an account of results on univalent functions in multiply connected domains obtained by the author. It contains two rery simple proofs of Villat's formula; Schwarz's formula, Poisson's formula and Poisson-Jensen formula in multiply connected domains; the differentiability theorem with respect to the parameter of analytic function family containing one parametric variable on multiply connected domains; variation theorem and parametric representation theorem of univalent functions in multiply connected domains; the solution of an extremal problem of differentiable functionals.
文摘An improved algorithm of Delaunay triangulation is proposed by expanding the scope from a convex polygon to an arbitrary polygon area in which holes can be contained in the subdivision procedure. The data structure of generated triangles and the exuviationslike method play a key role, and a single connectivity domain (SCD) without holes is constructed as the initial part of the algorithm. Meanwhile, some examples show that the method can be applied to the triangulation of the trimmed NURBS surface. The result of surface tessellation can be used in many applications such as NC machining, finite element analysis, rendering and mechanism interference detection.
