# Geodesic Order Types

The geodesic between two points a and b in the interior of a simple polygon P is the shortest polygonal path inside P that connects a to b. It is thus the natural generalization of straight line segments on unconstrained point sets to polygonal environments. In this paper we use this extension to generalize the concept of the order type of a set of points in the Euclidean plane to geodesic order types. In particular, we show that, for any set S of points and an ordered subset B⊆ S of at least four points, one can always construct a polygon P such that the points of B define the geodesic hull of S w.r.t. P, in the specified order. Moreover, we show that an abstract order type derived from the dual of the Pappus arrangement can be realized as a geodesic order type.

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07/10/2019

### Smoothed Analysis of Order Types

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### On the Number of Order Types in Integer Grids of Small Size

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### Constructing Order Type Graphs using an Axiomatic Approach

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### Subquadratic Encodings for Point Configurations

For most algorithms dealing with sets of points in the plane, the only r...