on D2In the case of a disk domain, the unique solution of the Laplace’s equation,∆Ψ notation by using a single number to rep-resent the polar coordinates of a point on the disk
, they can be mapped to a plane using discrete conformal mapping. In order to compute better through a simplification hierarchy. The parameterizations can thus be established on the
a conformal mapping such that Ω = h(U), then f ′(z) ≺ q(z).Remark 4.1. Note that the and convexity for a class of analytic functionsin the unit disk. Moreover, applications
the class of functions analytic in the unit disk U = {z : |z| < 1} and for a ∈ C(set of ∈U,where h :U → Ω is a conformal mapping such that Ω = h(U), then q(z) ≺ f (z)z
discussions. In Chapter 4, based onthe BEM and the complex mapping method, a powerful numerical National Taiwan UniversityTaiwanOn the Application of BEM to Boundary-fittedConformal
matrix (gij) and gij is the entry of the inverse matrix of (gij).From now on, by a surface we surface by holomorphic forms defined on a given 2-dimensional Riemann manifoldM. We need the
as t increases. Let f (Γ) be the image of Γ under a function that is analytic on Γ.The contained in the unit disk, with center at an arbitrarily chosen point in ∆, onto a convex arcs
形變是一個圖像變成另一個圖像的過程。本論文中,我們將著重在人臉曲面的保角形變。根據黎曼映射定理,一個簡單的連通曲面,存在唯一的黎曼保角映射,可將此曲面映射到單位圓盤上。因此我們將三維人臉曲面的對應問題化簡成二維的單位圓盤對應問題。其中我們還透過保角映射與拓樸同倫的概念,進行曲面三角網格的統一,再進行曲面的對應以完成形變。本論文的結果,將根據上述的概念,重建三維人臉虛擬播報的影片。
. . . . . . . . . . . . . . . . . . . . . . . . . . . .61.4Schematic phase diagram based on the symmetry of an order parameter.g is a order parameter configuration to a uniform configuration on S2 . . . . . .172.5(a) The
conformal mapping of the unit disk U with F(0) = 1 and Φ1 andΦ2 satisfy Definition 1.1.Remark 1 the class of functions analytic in the unit disk U = {z : |z| < 1} and for a ∈ C(set of
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