Categories
OpenVoronoi

Arc predicates

I started working on arc-sites for OpenVoronoi. The first things required are an in_region(p) predicate and an apex_point(p) function. It is best to rapidly try out and visualize things in python/VTK first, before committing to slower coding and design in c++.

in_region(p) returns true if point p is inside the cone-of-influence of the arc site. Here the arc is defined by its start-point p1, end-point p2, center c, and a direction flag cw for indicating cw or ccw direction. This code will only work for arcs smaller than 180 degrees.


Here randomly chosen points are shown green if they are in-region and pink if they are not.

apex_point(p) returns the closest point to p on the arc. When p is not in the cone-of-influence either the start- or end-point of the arc is returned. This is useful in OpenVoronoi for calculating the minimum distance from p to any point on the arc-site, since this is given by (p-apex_point(p)).norm().


Here a line from a randomly chosen point p to its apex_point(p) has been drawn. Either the start- or end-point of the arc is the closest point to out-of-region points (pink), while a radially projected point on the arc-site is closest to in-region points (green).

The next thing required are working edge-parametrizations for the new type of voronoi-edges that will occur when we have arc-sites (arc/point, arc/line, and arc/arc).

Leave a Reply

Your email address will not be published. Required fields are marked *

This site uses Akismet to reduce spam. Learn how your comment data is processed.