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Diffstat (limited to 'transverse/polarmesh.m')
| -rw-r--r-- | transverse/polarmesh.m | 92 |
1 files changed, 92 insertions, 0 deletions
diff --git a/transverse/polarmesh.m b/transverse/polarmesh.m new file mode 100644 index 0000000..914c3e0 --- /dev/null +++ b/transverse/polarmesh.m @@ -0,0 +1,92 @@ +%----------------------------------------------------------------------------------------------
+% 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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