Selector

Selector

Choosing a GRG Method

Choose a method by its documented geometry, required output, error model, and implementation evidence.

Current Circle Measures

For regular binary sectors, the current formulation supplies arithmetic and weighted kernels, explicit area bounds, and exact-arithmetic convergence proofs. Use the stated domains and preserve the distinction between geometric approximation and rounding.

Historical Cartesian Methods

Projection and trapezoidal constructions are separate methods. Their endpoint behaviour, stopping rules, and error rates require independent validation.

General Shapes and Adaptivity

A circular chord–sagitta ratio alone is not a demonstrated universal curvature or stability selector. An adaptive rule must define the boundary, local error indicator, limits, and termination behaviour before it is recommended.

Performance

No automatic selector is claimed as validated here. Compare actual implementations under the benchmark protocol.

Methods

Methods

Methods and Their Scope

Current Binary Radial Kernels

The current formulation defines regular equal sectors, local chord–tangent lengths, triangular areas, and weighted kernels. Its proofs concern those definitions.

Earlier Methods

Algorithm Specifications

A runnable method must identify initial values, refinement or direct evaluation, arithmetic format, outputs, and stopping conditions. A geometry identity alone is not a runtime benchmark.

Extensions

Adaptive sampling, general curves, multiple seeds, and three-dimensional constructions require their own definitions and validation. No error order or performance advantage is transferred automatically from the regular-circle proof.