The authors consider the problem of developing a new description for curves that includes, in addition to the geometric definition of spline curves, explicit description of topological relations (that is, incidence relations for locations and tangents) between curves. The work focuses on interactive drawing, so it also deals with transformations and deformations, which are necessary to maintain incidence relations, and with the required hierarchical structure to correctly propagate information concerning these transformations and deformations.

Following an extensive introduction and review of related work, section 3.1 focuses on nonlinear mappings related to sophisticated incidence relations, that is, those imposing tangency relations between curves. A sketchy description of a method for performing such mappings is presented, which allegedly guarantees that “as much as possible of the original shape of the canonical curve is preserved.” (By “canonical,” the authors mean the original shape of a spline curve as defined by the user.) Section 3.2 proposes notation for defining and evaluating a canonical spline, for evaluating a spline subject to a transformation or deformation, and for describing these transformations and deformations.

Finally, section 3.4 deals with dependencies between curves and introduces the concept of spline substructure--the substructure of the spline C defines and draws all those curves that should accompany the appearance of C on the screen.

Section 4 materializes the proposals of section 3.2 and section 3.4 into the Sticky Spline Programming Language, which is partially implemented in an interactive graphical editor (section 5), allowing a user to manipulate the geometry of canonical curves and to define dependencies between curves. More specifically, the editor’s internal representation is a two-parent directed graph possessing no recursion, iteration, or substructures, where any node may have arbitrarily many children.

This paper raises an important issue in curve drawing, namely maintaining topological relations, and offers interesting ideas that solve some of the related problems. Further research, along the directions highlighted in the last section of this paper, would improve the robustness and efficiency of the sticky spline concept and, ideally, offer practitioners a useful model for developing curve-drawing systems.