Piecewise Circular Approximation of Spirals and Polar Polynomials
نویسندگان
چکیده
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.
منابع مشابه
Scan Converting Spirals
Scan-conversion of Archimedes' spiral (a straight line in polar coordinates) is investigated. It is shown that an exact algorithm requires transcendental functions and, thus, cannot have a fast and exact integer implementation. Piecewise polynomial approximations are discussed and a simple algorithm based on piecewise circular approximation is derived. Variations of the algorithms allow to scan...
متن کاملApproximating Algebraic Space Curves by Circular Arcs
We introduce a new method to approximate algebraic space curves. The algorithm combines a subdivision technique with local approximation of piecewise regular algebraic curve segments. The local technique computes pairs of polynomials with modified Taylor expansions and generates approximating circular arcs. We analyze the connection between the generated approximating arcs and the osculating ci...
متن کاملClose interval approximation of piecewise quadratic fuzzy numbers for fuzzy fractional program
The fuzzy approach has undergone a profound structural transformation in the past few decades. Numerous studies have been undertaken to explain fuzzy approach for linear and nonlinear programs. While, the findings in earlier studies have been conflicting, recent studies of competitive situations indicate that fractional programming problem has a positive impact on comparative scenario. We pro...
متن کاملA numerical study of electrohydrodynamic flow analysis in a circular cylindrical conduit using orthonormal Bernstein polynomials
In this work, the nonlinear boundary value problem in electrohydrodynamics flow of a fluid in an ion-drag configuration in a circular cylindrical conduit is studied numerically. An effective collocation method, which is based on orthonormal Bernstein polynomials is employed to simulate the solution of this model. Some properties of orthonormal Bernstein polynomials are introduced and utilized t...
متن کاملOn 3-monotone approximation by piecewise polynomials
Abstract. We consider 3-monotone approximation by piecewise polynomials with prescribed knots. A general theorem is proved, which reduces the problem of 3-monotone uniform approximation of a 3-monotone function, to convex local L1 approximation of the derivative of the function. As the corollary we obtain Jackson-type estimates on the degree of 3-monotone approximation by piecewise polynomials ...
متن کامل