Parameters and Notation
This page defines the current circle-kernel conventions. Historical methods may use other conventions; their symbols must be interpreted locally.
Geometric Scale
R is the positive radius. N is the number of complete sectors across one Turn. Binary depth b gives N = 2ᵇ; the nondegenerate chord–tangent kernels require b ≥ 2.
Angular Steps
The complete sector width is 1/N Turn, its half-width is 1/(2N), and the quarter-step parameter is 1/(4N). If M counts samples in a quarter of the full Turn, state explicitly how M relates to N; do not use the same symbol for both counts.
Local Geometry
a is the chord apothem, h the half-chord, and e the half-tangent side. The geometric ratios are c = a/R, s = h/R, and q = h/a.
Implementation Parameters
Specify arithmetic format, rounding, construction procedure, stopping rule, and any stored tables. Additional parameters for adaptive or noncircular methods require their own definitions.