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Piecewise circular approximation of spirals and polar polynomials

: Taponecco, F.; Alexa, M.

Skala, V. ; European Association for Computer Graphics -EUROGRAPHICS-:
WSCG 2003. Posters
Plzen: University of West Bohemia, 2003
ISBN: 80-903100-2-8
International Conference in Central Europe on Computer Graphics, Visualization and Computer Vision (WSCG) <11, 2003, Plzen, Czech Republic>
Conference Paper
Fraunhofer IGD ()
scan conversion; spiral; approximation

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.