A Functional Equation For The Computation Of Parameter Symmetries Of Path Functions

The paper considers a particular general class of parametrised path function used in computer graphics, geometric modeling and approximation theory. General methods are developed for the identification of the conditions under which parameter transformations preserve the path geometry. The determination of these 'parameter symmetries' is shown to be equivalent to the identification of the solution space of a functional equation. Case studies, each with distinctive features, are presented to illustrate the concepts developed and the generality of the approach. Full solutions are obtained and seen to provide both known and new results.

Keywords:

• Paths
• Curves
• Parametrisation
• Symmetry
• Invariance