2 research outputs found
Piecewise circular approximation of spirals and polar polynomials
Spirals are surprisingly common in science, nature, physics, astronomy, flora and fauna, and the arts. In
Cartesian coordinates they are typically transcendental functions, which makes the evaluation on Cartesian
grids an inefficient process. We propose a construction scheme for piecewise circular approximations.
The algorithm is convergent and consists of generating center coordinates and radii for quarter circles
given an arbitrary monotone polynomial, exponential, or logarithmic function in polar coordinates.
Evaluating quarter circles as well as generating the parameters can be done incrementally with few integer
operations, thus, the algorithm is fast and stable