74. Asymptotes in 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...

GENERAL SOLUTION OF ELASTICITY PROBLEMS IN TWO DIMENSIONAL POLAR COORDINATES USING MELLIN TRANSFORM

Abstract In this work, the Mellin transform method was used to obtain solutions for the stress field components in two dimensional (2D) elasticity problems in terms of plane polar coordinates. the Mellin transformation was applied to the biharmonic stress compatibility equation expressed in terms of the Airy stress potential function, and the boundary value problem transformed to an algebraic  ...

The Laplacian in Spherical Polar Coordinates

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...

Height from Gradients in Polar Coordinates

This paper presents a new approach to integrate the gradient field to the relative depth or height map from multiple view directions in polar coordinates. Traditional integration techniques are based on cartesian coordinates. In this approach, the surface normals are calculated by photometric stereo method. The object is illuminated by three light sources and rotated on a controlled turntable. ...