DEVELOPMENT: Polar Coordinates

Betweenness in Polar Coordinates

betweenness, geometry, lines, polar coordinates, trilinear coordinates We consider straight line drawings. From a graph theoretic point of view these are plane graphs with a set of preferred paths. This graph is expressed in geometric terms through the consideration of the betweenness of the points of intersection along each of the lines. If we fix a reference system for polar coordinates, we c...

The Laplacian in Spherical Polar Coordinates

Fast Laser Scan Matching using Polar Coordinates

In this paper a novel Polar Scan Matching (PSM) approach is described that works in the laser scanner’s polar coordinate system, therefore taking advantage of the structure of the laser measurements and eliminates the need for an expensive search for corresponding points in other scan match approaches. PSM belongs to the family of point to point scan matching approaches with its matching bearin...

Geodesic Polar Coordinates on Polygonal Meshes

Geodesic Polar Coordinates (GPCs) on a smooth surface S are local surface coordinates that relates a surface point to a planar parameter point by the length and direction of a corresponding geodesic curve on S. They are intrinsic to the surface and represent a natural local parameterization with useful properties. We present a simple and efficient algorithm to approximate GPCs on both triangle ...

Colour Image Analysis in 3D-Polar Coordinates

The use of 3D-polar coordinate representations of the RGB colour space is widespread, although many of these representations, such as HLS and HSV, have deficiencies rendering them unsuitable for quantitative image analysis. Three prerequisites for 3D-polar coordinate colour spaces which do not suffer from these deficiencies are suggested, and the results of the derivation of three colour spaces...