Sticky splines: definition and manipulation of spline structures with maintained topological relations

This paper describes an augmentation to the spline concept to account for topological relations between different spline curves. These topological relations include incidence relations, constraining the extremes of spline curves to other spline curves, and also more general geometric relations, for example, involving the tangents of spline curves in their extremes. To maintain these incidence relations, some spline curves may have to be transformed (translated, rotated, scaled), or even deformed (i.e., the shape of the curve may change) as a result of modifying other spline curves. A data structure and algorithms are given to implement the propagation of these transformations and deformations. Based on the augmented spline concept, to be called sticky splines, both a script system to represent spline structures and an interactive system for editing drawings while automatically, maintaining their topological structure are presented.