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%----------------------------------------------------------------------------------------------
% PROGRAM: polarmesh
% AUTHOR: Andri M. Gretarsson
% DATE: 7/10/04
%
% SYNTAX: [rmesh,thetamesh,xmesh,ymesh]=polarmesh(r <,theta,rspacing>);
% <...> indicates optional arguments
%
% Simplified way of generating arbitrary polar meshes.
%
% INPUT ARGUMENTS:
% ----------------
% r = specification for the r mesh. If r is a 1x3 vector the entries are assumed
% to indicate r_start, r_end and n_rpts (number of r=const curves) and a set
% of equally spaced or square spaced r=const mesh curves are generated. If r is
% nx1, each entry is assumed to be a constant for which to generate an r=const
% curve in the mesh. If r is 2D (nxn, where n>1) it is assumed to be already
% in mesh form. In this case theta must be specified in mesh form and the
% function does no more than pol2cart.
% theta = specification for the theta mesh. If it is left blank the default theta is
% used (a mesh with 1 line per theta from 0 to 360). If theta is 1x3, the
% values are assumed to be [theta_start,theta_end,n_thetapts] and are used to
% generate a set of n_thetapts equally spaced theta=const curves in the mesh.
% If theta is [nx1] the one mesh curve is generated for each entry at the
% specified angle.
% rspacing = 'lin' for linear spacing of the r mesh
% 'sqr' for r-line spacing proportional to r^2.
%
% OUTPUT ARGUMENTS:
% -----------------
% rmesh,thetamesh = r and theta meshes expressed in polar coordinates
% xmesh,ymesh = the r and theta meshes expressed in cartesian coordinates.
%
% Last updated: July 18, 2004 by AMG
%----------------------------------------------------------------------------------------------
% SYNTAX: [rmesh,thetamesh,xmesh,ymesh]=polarmesh(r <,theta,rspacing>);
%----------------------------------------------------------------------------------------------
function [rmesh,thetamesh,xmesh,ymesh]=polarmesh(r,varargin)
if nargin>=2, theta=varargin{1}; defaulttheta=0; else defaulttheta=1; end
if nargin>=3 && strcmp(varargin{2},'rsqr'), linflag=0; else linflag=1; end
if min(size(r))==1 % r is 1D
if size(r,1)==1 && size(r,2)==3 % r=[r_start,r_end,rpts]
if linflag % linear r-spacing for mesh
rseed=(r(1):(r(2)-r(1))/(r(3)-1):r(2)).';
else % r-spacing proportional to r^2
rseed=(sqrt(r(1)):(sqrt(r(2))-sqrt(r(1)))/(r(3)-1):sqrt(r(2))).'.^2;
end
if defaulttheta==1 % default theta
thetaseed=(0:1:360).'*pi/180;
[thetamesh,rmesh]=meshgrid(thetaseed,rseed); % I like r to be arranged in the first position (r,theta)
thetamesh=transpose(thetamesh); % rather than (theta,r) so for consistency with (xmesh,ymesh)
rmesh=transpose(rmesh); % rmesh must have identical rows and thetamesh identical columns
else % not default theta
if size(theta,1)==1 && size(theta,2)==3 % theta =[theta_start,theta_end,theta_pts]
thetaseed=(theta(1):(theta(2)-theta(1))/(theta(3)-1):theta(2)).';
[thetamesh,rmesh]=meshgrid(thetaseed,rseed);
thetamesh=transpose(thetamesh);
rmesh=transpose(rmesh);
else % theta lines specified
[thetamesh,rmesh]=meshgrid(theta,rseed);
thetamesh=transpose(thetamesh);
rmesh=transpose(rmesh);
end
end
else % r lines specified
if size(r,1)<size(r,2), r=r.'; end % make r columnar
if defaulttheta==1 % default theta
thetaseed=(0:1:360).'*pi/180;
[thetamesh,rmesh]=meshgrid(thetaseed,r);
thetamesh=transpose(thetamesh);
rmesh=transpose(rmesh);
else % not default theta
if size(theta,1)==1 && size(theta,2)==3 % theta =[theta_start,theta_end,theta_pts]
thetaseed=(theta(1):(theta(2)-theta(1))/(theta(3)-1):theta(2)).';
[thetamesh,rmesh]=meshgrid(thetaseed,r);
thetamesh=transpose(thetamesh);
rmesh=transpose(rmesh);
else % theta lines specified
[thetamesh,rmesh]=meshgrid(theta,r); % theta and r must be the same length
thetamesh=transpose(thetamesh);
rmesh=transpose(rmesh);
end
end
end
else
thetamesh = theta; % r and theta are already mesh grids
rmesh=r; % (and are the same size)
end
[xmesh,ymesh]=pol2cart(thetamesh,rmesh);
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