A method of generating motifs aligned along a circular arc

Abstract

Patterns, that is, designs repeating some motif in a more or less systematic manner, have been used throughout the ages in creating works of beauty. One way in which patterns can be repeated is to align the motif along a specified geometrical path, be it a line, circular arc, spline, or a combination of them. This paper describes a method of generating patterns aligned along a circular arc with a set of parameters that interact to produce interestingly different patterns. These parameters include the pitch (distance between patterns), the number of patterns, automatic stretching or compression, and the choice of keeping the original entity type of certain geometrical elements. Sample runs with diverse motifs are used for illustration. The solution can be implemented as a supplement to a basic CAD/CAM system so as to benefit application users in cartography, architectural design, watch and clock face design, and ceramic design.