Goal Scoring in Soccer: A Polar Coordinate
Analysis of Motor Skills Used by Lionel Messi.
(2009), or a polar coordinate
system as in Wang and Rose (2005), the governing equation is recast in terms of a local curvilinear system, formed by the curvilinear coordinate s along the wall and the local wall radius of curvature [r.sub.cw].
Alternatively, a polar coordinate
system can be used for targeting, with the needle angled slightly upwards as opposed to perpendicular in the Cartesian coordinate system.
In this paper, PSSE is considered in the rectangular and polar coordinate
We choose the dependence [R.sub.r]([phi]) of the oval-shaped rim radius with the eccentricity e on the polar coordinate
These transform functions are Cartesian coordinate transformation, polar coordinate
transformation and function transformation.
where [mathematical expression not reproducible] represents the angular polar coordinate
corresponding to particular pixel (i, j) [member of] M and R(i ,j), RE) represents the distance between the pixel (i, j) [epsilon] and the RE:
, as the original data is in the polar coordinate
system, an interpolation method was utilized to transform the polar coordinate
system into the three-dimensional Cartesian coordinate system.
Prior to this, we consider a generalized polar coordinate
transformation allowing one of the specific representations derived later on.
As based on the analysis of the key reasons for the inefficiency of search and poor convergence, this research proposes a novel approach that transforms the coordinate system for design variables and constraint space to local polar coordinate
A crucial step here is transformation of the amplitude spectra into the polar coordinate
system to obtain functions [A.sup.p.sub.1]; [A.sup.p.sub.2] : [R.sup.+.sub.0] x (0; 2[pi]) [right arrow] [R.sup.+.sub.-] such that [A.sup.p.sub.1]([rho];[phi]) = [A.sup.p.sub.2]([rho]; ([phi] + [theta]).
Bear  proved that if r = [K.sub.q.sup.1/2] or r = [K.sub.j.sup.-1/2] in the polar coordinate
system, mapping can form an ellipse (under the condition of three-dimensional ellipsoid), where r represents radius vector, [K.sub.q] represents permeability coefficient in the direction of the flow line, and [K.sub.j] represents permeability coefficient in the direction of the hydraulic gradient.