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On the relationship between parametrisation and invariance for curve functions

✍ Scribed by H.E. Bez

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
159 KB
Volume
17
Category
Article
ISSN
0167-8396

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✦ Synopsis

Many parametric curves, e.g., Splines and Lagrange, require sets of 'parameter' functions to be specified in addition to control-, or interpolation-point sets. It is shown here that simple group theoretic methods can be applied to this type of curve function to provide complete answers to fundamental questions such as:

(i) if the control point set is held fixed, under what conditions do different sets of parameter functions determine the same curve? and the related question:

(ii) what properties are required of the parameter functions to ensure invariance of curve shape with respect to a given set of geometric transformations of the control point set?

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