angleselective

Angleselective is a term used in geometry and computer science to describe a framework for selecting angle values within a geometric model or algorithm to optimize a given objective, such as angular distribution or surface distortion. It refers to the process of electing an angle parameter from a candidate set, potentially in an adaptive way, to improve performance metrics in tasks like mesh generation or orientation problems.

Origins and scope: The phrase is used in theoretical and applied discussions to characterize angle-focused decision rules. It is not a formal mathematical object but a descriptive label for methods that treat angle selection as an optimization variable.

Definition: An angleselective method defines a mapping from a configuration space to a chosen angle. It can be deterministic, using a rule-based selection, or stochastic, employing sampling and selection. Local objective functions, often involving neighboring angles or global criteria, guide the choice.

Applications: In computer graphics and geometric modeling, angleselective helps steer triangulation or polygon decomposition to minimize skinny triangles and improve angular uniformity. In finite element analysis, it can enforce angle constraints to enhance numerical conditioning. It also appears in robotics and sensor planning, where choosing angles affects coverage, visibility, or motion constraints.

Methods: Approaches include predefined candidate angle sets, explicit optimization over angles, and adaptive schemes that adjust angles according to error estimates or distortion measures.

Example: During mesh refinement, an angleselective rule might replace a vertex angle with a local choice that reduces the maximum angle deficiency.

See also: Angle optimization, mesh generation, adaptive methods, geometric optimization.