A pedestrian approach to ray shooting: shoot a ray, take a walk

TLDR: In this paper, a simple Steiner triangulation of a simple polygon with the property that a ray can intersect at most O(log n) triangles before reaching the polygon boundary is presented.

Abstract: We propose a very simple ray-shooting algorithm, whose only data structure is a triangulation. The query algorithm, after locating the triangle containing the origin of the ray, walks along the ray, advancing from one triangle to a neighboring one until the polygon boundary is reached. The key result of the paper is a Steiner triangulation of a simple polygon with the property that a ray can intersect at most O(log n) triangles before reaching the polygon boundary. We are able to compute such a triangulation in linear sequential time, or in O(log n) parallel time using O(n/log n) processors. This gives a simple, yet optimal, ray-shooting algorithm for a simple polygon. Using a well-known technique, we can extend our triangulation procedure to a multiconnected polygon with k components and n vertices, so that a ray intersects at most O(√κ log n) triangles. © 1995 Academic Press, Inc.