verseshapes

Verseshapes is a term used in computational geometry and computer graphics to describe a family of shapes that connects two base shapes through a continuous morph within a fixed shape space. The concept is often employed to study shape interpolation, animation, and mesh morphing, where each intermediate form is intended to be a valid, well-formed shape.

Formally, a verseshape is a parametric family S(t) defined for t in the closed interval [0, 1], such that S(0) equals a source shape A and S(1) equals a target shape B, both belonging to the same shape class. In common practice, the morph preserves certain invariants—such as the topological type, the number and order of vertices in a polygon, or the connectivity of a mesh—so that each S(t) remains within the same class as A and B. A typical realization uses linear interpolation of corresponding vertices or control points, yielding an affine verseshape, while non-linear easing can produce more complex variants.

Properties and constraints are central to the study of verseshapes. If vertex correspondence is maintained and the interpolation avoids self-intersection, each S(t) is a simple, valid shape. However, naive linear interpolation can create artifacts, so constrained or alternative interpolation schemes are sometimes used to guarantee geometric validity throughout the path.

Examples include morphing between quadrilaterals or between simple polyhedra with corresponding faces, as well as extending the idea to three-dimensional meshes. Applications occur in computer animation, design and visualization, and any domain requiring smooth, controllable transitions between shapes.

See also: shape interpolation, morphing, homotopy, polygon morphing, shape space. Note that the term verseshape is used informally in various texts, with no single canonical definition.