shapesuch

Shapesuch is a term used in geometry and digital design to describe a family of shapes produced by morphing between two base outlines. The concept emphasizes smooth, controllable deformation and boundary continuity as a parameter varies. While not tied to a single formal definition, shapesuch is commonly realized in computational workflows as a parametric interpolation between two polygonal or spline-based shapes. The name blends shape with a suffix implying synthesis or form generation.

Construction methods typically start with two compatible shapes, A and B, represented by vertex paths or distance-field descriptions. A shapesuch at time t in [0,1] is formed by interpolating corresponding boundary points, S_t = (1−t)A + tB, and then applying a smoothing operator to preserve a well-formed boundary. In distance-field form, S_t(x) = (1−t) d_A(x) + t d_B(x), with the boundary defined by the zero level set. Interpolation with compatible topology ensures a continuous family from A to B; results depend on mesh resolution and smoothing strength. The approach can also incorporate non-linear or user-controlled easing to emphasize or suppress certain features during the morph.

Properties and limitations include continuity in t and potential changes in convexity or self-intersections if constraints are not imposed. Area and perimeter typically vary smoothly under mild conditions, though they may exhibit non-monotonic behavior during the transition.

Applications span computer graphics, font design, and industrial design, where shapesuch morphs aid visualization, animation, and explorations of form space. Examples range from a circular outline evolving into a square, to silhouettes transitioning between organic and geometric motifs. The concept has appeared in contemporary computational design discussions and artistic practice as a practical tool for exploring deformable forms.