Geometric Design by Means of a G2Continuous A-Spline
A cubic A-spline, suitable for free form geometric design is presented in this paper. It is constructed in such a way, that the geometry of the arc in each individual triangle may be further controlled by two additional shape handles: an interior point of the triangle may be interpolated and the symmetry of the arc may be manipulated. In any case, the prescribed interpolation of the endpoints and their corresponding slopes as well as the G2-continuity of the A-spline is attained. Unlike similar A-splines described in the literature (Patterson, Paluszny, Tovar, Bajaj) the exact curvature values at the junction points are not required. In fact this input is replaced by a more qualitative control of the designer on the symmetry of the arcs, which is closer to the spirit of free form design. The arcs are non singular and convex, furthermore, the inflection points of the A-spline must be placed at the junction points, which allows a precise control of the points where the curvature is zero.
Keywordsalgebraic cubic splines free form geometric design
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