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Implicit Curved Polygons

This paper presents an approach to the representation of polygons with straight and curved edges by real functions. A “carrier polygon” is an arbitrary simple polygon with straight edges. Application of our method results in a C k continuous function F(x,y) with zero value at polygon edges. We combine an efficient algorithm employing a monotone function of a boolean operation, with R-functions. The extension of the algorithm to the case of curved edges provides the possibility of designing a great variety of shapes. We discuss and illustrate the following applications: implicitization of parametric curves, implicit free-form design, shape transformation and reconstruction from cross-sections, depth data generation and synthetic relief carving .