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
This work aims at potential fields generated by point sources in conductive perforated fragments of spherical shells. Such fields are interpreted as profiles of Green＇s functions of relevant boundary-value problems s...This work aims at potential fields generated by point sources in conductive perforated fragments of spherical shells. Such fields are interpreted as profiles of Green＇s functions of relevant boundary-value problems stated in multiply-connected regions for Laplace equation written in geographical coordinates. Those are efficiently computed by a modification of the method of functional equations, with closed analytical forms preliminary obtained for Green＇s functions for the corresponding simply-connected regions.展开更多
Let G C C be a simply connected domain whose boundary L ：= G is a Jordan curve and 0 ∈ G. Let w = φ（z） be the conformal mapping of G onto the disk B（0, r0） ：= {w ： ｜w｜ 〈 r0）, satisfying φ0（0） = 0, φ＇...Let G C C be a simply connected domain whose boundary L ：= G is a Jordan curve and 0 ∈ G. Let w = φ（z） be the conformal mapping of G onto the disk B（0, r0） ：= {w ： ｜w｜ 〈 r0）, satisfying φ0（0） = 0, φ＇t（0） = 1. We consider the following extremal problem for p 〉 0：∫∫G｜φ＇（z）-P＇n（z）｜Pdσz→min in the class of all polynomials Pn（z） of degree not exceeding n with Pn（0） = 0, P＇n （0）=- 1. The solution to this extremal problem is called the p-Bieberbach polynomial of degree n for the pair （G, 0）. We study the uniform convergence of the p-Bieberbach polynomials Bn,p（z） to the φ（z） on G^- with interior and exterior zero angles determined depending on the properties of boundary arcs and the degree of their ＂touch＂.展开更多
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.
文摘This work aims at potential fields generated by point sources in conductive perforated fragments of spherical shells. Such fields are interpreted as profiles of Green＇s functions of relevant boundary-value problems stated in multiply-connected regions for Laplace equation written in geographical coordinates. Those are efficiently computed by a modification of the method of functional equations, with closed analytical forms preliminary obtained for Green＇s functions for the corresponding simply-connected regions.
文摘Let G C C be a simply connected domain whose boundary L ：= G is a Jordan curve and 0 ∈ G. Let w = φ（z） be the conformal mapping of G onto the disk B（0, r0） ：= {w ： ｜w｜ 〈 r0）, satisfying φ0（0） = 0, φ＇t（0） = 1. We consider the following extremal problem for p 〉 0：∫∫G｜φ＇（z）-P＇n（z）｜Pdσz→min in the class of all polynomials Pn（z） of degree not exceeding n with Pn（0） = 0, P＇n （0）=- 1. The solution to this extremal problem is called the p-Bieberbach polynomial of degree n for the pair （G, 0）. We study the uniform convergence of the p-Bieberbach polynomials Bn,p（z） to the φ（z） on G^- with interior and exterior zero angles determined depending on the properties of boundary arcs and the degree of their ＂touch＂.
