Shape deformation in continuous map generalization

被引：24

作者：

Danciger, Jeff ^{[1
]}

Devadoss, Satyan L. ^{[2
]}

Mugno, John ^{[3
]}

Sheehy, Don ^{[4
]}

Ward, Rachel ^{[5
]}

机构：

[1] Stanford Univ, Stanford, CA 94305 USA

[2] Williams Coll, Williamstown, MA 01267 USA

[3] Univ Maryland, College Pk, MD 20742 USA

[4] Carnegie Mellon Univ, Pittsburgh, PA 15213 USA

[5] Princeton Univ, Princeton, NJ 08544 USA

来源：

GEOINFORMATICA | 2009年 / 13卷 / 02期

关键词：

Continuous generalization; Scale change; Homotopy; Cartograms;

D O I：

10.1007/s10707-008-0049-0

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

Given a collection of regions on a map, we seek a method of continuously altering the regions as the scale is varied. This is formalized and brought to rigor as well-defined problems in homotopic deformation. We ask the regions to preserve topology, area-ratios, and relative position as they change over time. A solution is presented using differential methods and computational geometric techniques. Most notably, an application of this method is used to provide an algorithm to obtain cartograms.

引用

页码：203 / 221

页数：19

共 16 条

[1]

[Anonymous], 1992, Spatial Tessellations: Concepts and Applications of Voronoi Diagrams

[2]

Boor C.D., 2001, A Practical Guide to Splines

[3] A combinatorial approach to cartograms [J].

Edelsbrunner, H ;

Waupotitsch, R .

COMPUTATIONAL GEOMETRY-THEORY AND APPLICATIONS, 1997, 7 (5-6) :343-360

[4] Diffusion-based method for producing density-equalizing maps [J].

Gastner, MT ;

Newman, MEJ .

PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA, 2004, 101 (20) :7499-7504

[5]

Goodman J., 2004, Handbook of Discrete and Computational Geometry

[6]

Hatcher A., 2002, Algebraic Topology

[7]

Hoff KE, 1999, COMP GRAPH, P277, DOI 10.1145/311535.311567

[8] Map generalization in the Web age [J].

Jones, CB ;

Ware, JM .

INTERNATIONAL JOURNAL OF GEOGRAPHICAL INFORMATION SCIENCE, 2005, 19 (8-9) :859-870

[9]

Lam N.S., 2004, A Research Agenda for Geographic Information Science, P93

[10] Constructing medial axis transform of planar domains with curved boundaries [J].

Ramanathan, M ;

Gurumoorthy, B .

COMPUTER-AIDED DESIGN, 2003, 35 (07) :619-632

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