CONSTRUCTING DIFFEOMORPHISMS BETWEEN SIMPLY CONNECTED PLANE DOMAINS

被引：0

作者：

Atkinson K. ^{[1
]}

Chien D. ^{[2
]}

Hansen O. ^{[2
]}

机构：

[1] University of Iowa, United States

[2] California State University San Marcos, United States

来源：

Electronic Transactions on Numerical Analysis | 2022年 / 55卷

关键词：

constructing diffeomophisms; domain transformations; shape blending;

D O I：

10.1553/etna_vol55s671

中图分类号：

学科分类号：

摘要：

Consider a simply connected domain Ω ⊂ R2 with boundary ∂Ω that is given by a smooth function φ : [a, b] 7→ R2. Our goal is to calculate a diffeomorphism Φ: B1(0) 7→ Ω, B1(0) the open unit disk in R2. We present two different methods where both methods are able to handle boundaries ∂Ω that are not star-shaped. The first method is based on an optimization algorithm that optimizes the curvature of the boundary, and the second method is based on the physical principle of minimizing a potential energy. Both methods construct first a homotopy between the boundary ∂B1(0) and ∂Ω and then extend the boundary homotopy to the inside of the domains. Numerical examples show that the method is applicable to a wide variety of domains Ω. Copyright © 2022, Kent State University.

引用

页码：671 / 686

页数：15

共 11 条

[1]

ATKINSON K., CHIEN D., HANSEN O., Spectral Methods Using Multivariate Polynomials On The Unit Ball, (2019)

[2]

ATKINSON K., HANSEN O., Creating domain mappings, Electron. Trans. Numer. Anal, 39, pp. 202-230, (2012)

[3]

DEIMLING K., Nonlinear Functional Analysis, (1985)

[4]

DELFOUR M.C., ZOLESIO J.-P., Shapes and Geometries, (2011)

[5]

DELFOUR M.C., GARON A., Transfinite interpolations for free and moving boundary problems, Pure Appl. Funct. Anal, 4, pp. 765-801, (2019)

[6]

HAIRER E., NORSETT S.P., WANNER G., Solving Ordinary Differential Equations I, (1987)

[7]

HAIRER E., WANNER G., Solving Ordinary Differential Equations II, (1991)

[8]

HILLE E., Lecture on Ordinary Differential Equations, (1969)

[9]

SABA M., SCHNEIDER T., HORMANN K., SCATENI R., Curvature-based blending of closed planar curves, Graph. Models, 76, pp. 263-272, (2014)

[10]

SEDERBERG T. W., GAO P., WANG G., MU H., 2-D shape blending: an intrinsic solution to the vertex path problem, SIGGRAPH’93: Proceedings of the 20th Annual Conference on Computer Graphics and Interactive Technique, pp. 15-18, (1993)

← 1 2 →