Coresshapes

Coresshapes are a theoretical class of geometric forms used in computational geometry and design to model smoothly deformed shapes around a central core. The concept combines a core shape with a reshaping operation that produces a boundary or surface by offsetting, warping, or extruding the core under a controlled deformation. Coresshapes can be defined in two or three dimensions and are characterized by preserved topological structure and parameterizable curvature.

Construction and representation: A coresshape begins with a base core C, such as a polygon in 2D or a polyhedron in 3D. A reshaping map R, which may depend on distance from the core, angle around the core, or other local coordinates, is applied to generate a new boundary. The resulting surface or solid S = R(C) is often described by parametric or mesh-based representations. Variants include radial reshaping, angular reshaping, and anisotropic shaping, each offering distinct control over surface smoothness and curvature. A common feature is that small changes in the reshaping parameters produce continuous, predictable changes in the geometry.

Properties and applications: Coresshapes typically maintain the topology of the core and support easy morphing between forms. They are used in procedural modeling, character and vehicle design, architectural skins, and 3D printing workflows to create organic or ergonomic shapes with tunable complexity. In visualization, coresshapes serve as a way to study deformation behavior and to generate families of related surfaces.

History and terminology: The term coresshape is used in this article to describe a generalized deformation concept. It is employed by researchers and practitioners as a working model rather than a fixed mathematical definition, allowing cross-domain experimentation with core-based morphing.