Geometry of inhibition and activation in kinematic waves

✍ Scribed by C.K. Au; Tony C. Woo

• Publisher: Elsevier Science
• Year: 2004
• Tongue: English
• Weight: 586 KB
• Volume: 36
• Category: Article
• ISSN: 0010-4485
• DOI: 10.1016/j.cad.2004.01.010

✦ Synopsis

Consider kinematic sources equipped with a rate of delivery and a time delay in engagement. Where the wave fronts meet, interesting geometries arise. This paper reports, for the case of two such sources, the Ovals of Descartes and, as a special case, the Limac ¸on of Pascal. In the case of a single source with a permeable interface, the Circles of Apollonius manifest.

The source -source case is the generalized Voronoi diagram from computational geometry. The source -interface case offers a physical analogy to the refraction of waves in media of different indices. There, a real source induces a virtual source with the phenomena of inhibition and activation; their conditions are detailed.