EEciently identifying polygons that are visible from a changing synthetic viewpoint is an important problem in computer graphics. Even with hardware support, simple algorithms like depth-buuering cannot achieve interactive frame rates when applied to geometric models with many polygons. However, a visibility algorithm that exploits the occlu-sion properties of the scene to identify a superset o...

In this paper we survey results about affinely regular polygons. First, the definitions and classification of affinely regular polygons are given. Then the theory of Bachmann–Schmidt is outlined. There are several classical theorems about regular polygons, some of them having analogues in finite planes, such as the Napoleon–Barlotti theorem. Such analogues, variants of classical theorems are al...

A proportional contact representation of a planar graph is one where each vertex is represented by a simple polygon with area proportional to a given weight and adjacencies between polygons represent edges between the corresponding pairs of vertices. In this paper we study proportional contact representations that use only rectilinear polygons and contain no unused area or hole. There is an alg...

In this paper, we analyze the time complexity of nding regular polygons in a set of n points. We combine two di erent approaches to nd regular polygons, depending on their number of edges. Our result depends on the parameter α, which has been used to bound the maximum number of isosceles triangles that can be formed by n points. This bound has been expressed as O(n ), and the current best value...

We describe an algorithm for computing the outer common tangents of two disjoint simple polygons using linear time and only constant workspace. A tangent of a polygon is a line touching the polygon such that all of the polygon lies on the same side of the line. An outer common tangent of two polygons is a tangent of both polygons such that the polygons lie on the same side of the tangent. Each ...

We study the problem of fixturing a chain of hinged objects in a given placement with frictionless point contacts. We define the notions of immobility and robust immobility, which are comparable to second and first order immobility for a single object [8, 7, 11, 12] robust immobility differs from immobility in that it additionally requires insensitivity to small perturbations of contacts. We sh...

Several algorithms for computing the Minkowski sum of two polygons in the plane begin by decomposing each polygon into convex subpolygons. We examine different methods for decomposing polygons by their suitability for efficient construction of Minkowski sums. We study and experiment with various well-known decompositions as well as with several new decomposition schemes. We report on our experi...