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Vertex correspondence between polygons in different applications

Dharmaratne A., Harada K.

Machine Graphics and Vision

2003

Vol. 12, No. 3

311-333

This paper describes some applications in computer graphics and computational geometry where establishing a vertex correspondence between a pair of objects is necessary. We present an algorithm for establishing a correspondence between the vertices of a pair of polygons by inserting new vertices, regardless of the polygons' locations, orientations, sizes, shapes, or numbers of vertices. The new vertices can be inserted either at the existing vertices or along the corresponding edges of the polygons. After establishing a successful correspondence between the vertices, its role in compatible convex decompositions, skeleton construction and polygon morphing is discussed.

Compatible convex decompositions of simple polygons

Dharmaratne A., Harada K.

Machine Graphics and Vision

2000

Vol. 9, No. 4

851-866

In this paper, we presnt an algorithm for constructing compatible convex decompositions of two simple polygons. Given two simple polygons with an equal number of vertices, convex decompositions of these polygons are to be compatible if there exist a one-to-one mapping between them such that the two polygons are decoposed into an equal number of convex sub-polygons and the coresponding sub-polygons are defined by the corresponding sequence of vertices. In general, it may not be possible to decompose two polygons compatibly if additional vertices inside the polygon (commonly called Steiner points) are not allowed. Our algorithm calculates a compatible convex decomposition of two polugons with/without introducing Steiner points.