DogBoneForm

DogBoneForm is a geometric primitive used in computer-aided design and geometric modeling to describe an elongated, dog-bone shaped region. The figure consists of two congruent circular lobes connected by a narrower central neck, yielding a profile that is symmetric about its longitudinal axis. The form can be specified by three parameters: the lobe radius R, the neck width w, and the neck length n that separates the lobes. In a typical realization, each lobe is a circle of radius R, and the neck is a rectangular strip of width w and length n, producing a continuous boundary where straight sides meet the circular arcs.

Properties of DogBoneForm include planarity, bilateral symmetry, and a combination of curved and straight boundary segments. The shape is often used as a test case in mesh generation, collision detection, and shape optimization because it combines smooth curvature with a constricted middle region.

Variants of the form include a smoother version with filleted transitions at the junctions (rounded neck), a compact variant with a shorter neck, and a stretched version with a longer neck. The name DogBoneForm appears in CAD tutorials and geometry libraries as a descriptive label rather than a standardized primitive.

Applications span engineering design, where the form can model bone-like cross-sections or serve as a stylized fastener profile; additive manufacturing, for evaluating printing of curved boundaries; and computer graphics, where the recognizable silhouette provides a suitable test shape for rendering and shading demonstrations. See also capsules, stadium curves, and dumbbell shapes.