Publication at Faculty of Mathematics and Physics |
2016
Abstract
We study the behavior of the support function in the neighborhood of a curve inflection. The gauss map at the inflection point is not regular and in the neighborhood is typically not injective.
The support function is thus not regular and typically multivalued. We describe this function using an implicit algebraic equation and the Puiseux series of its branches.
We show the correspondence between the degree of the approximation of the primary curve (using Taylor series) and the degree of the approximation of the support function (using Puiseux series). Based on this results we are able to approximate curve with inflections by curves with a simple support function which consequently possess rational offsets.