Ball-Based Shape Processing

Constant radius offsetting and blending operations are important for digital shape and image processing. They may be formulated using Minkowski sums with a ball of fixed radius. We review their extensions to variable distance offsetting. Specifically, we compare three different formulations of variable distance offsetting for planar shapes: orthogonal, radial, and ball. We discuss compatibility conditions that specify when a shape is the offset of another. We also discuss the applications of these formulations for computing the average and morph of two shapes and the centerline of an elongated shape. Finally, we discuss a set theoretic formulation of a variable radius blending of a shape.

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