cylindersto

Cylindersto is a fictional geometric concept used in discussions of constructive modeling and computer-aided design. It denotes a method of approximating a complex or curved form by a chain of cylindrical segments, each with a circular cross-section and finite length, arranged along a defined spine or axis.

Definition and structure

A cylindersto consists of an ordered sequence of cylinders C1, C2, ..., Cn. Each cylinder is characterized by its radius ri, its axis direction, a central point along the spine, and a length li. The cylinders are connected at joints, and the overall shape is the union of these segments. Depending on the design, joints between consecutive cylinders can be made to provide different levels of geometric continuity, such as C0 (position continuity) or C1 (tangent continuity).

Construction approaches

Two common approaches are used. The first stacks cylinders along a predefined spine, aligning each cylinder's axis with the spine at selected intervals. The second uses optimization to fit radii, lengths, and orientations of the cylinders to approximate a target surface or curve, aiming to minimize deviations.

Continuity and limitations

Continuity can be adjusted by controlling joint alignment and radii transitions. While cylinderstos offer a simple, manufacturable primitive for decomposition, they are inherently approximate and may require many segments to capture tight features. Limitations include potential gaps in smoothness at joints and the challenge of accurately representing highly curved regions.

Applications and relation to other concepts

Cylinderstos appear in theoretical exercises for understanding cylindrical decompositions, educational demonstrations of primitive-based modeling, and exploratory CAD workflows. They relate to concepts such as polycylinder modeling, constructive solid geometry, and spine-based approximations.

Etymology and reception

The term cylindersto is a coined, not widely adopted term in established literature, used mainly in speculative discussions to illustrate how cylindrical primitives can compose complex geometries.