| polar3d(Zin,theta_min,theta_max,Rho_min,Rho_max,meshscale,varargin)
|
function [Xout, Yout, Zout] = polar3d(Zin,theta_min,theta_max,Rho_min,Rho_max,meshscale,varargin)
%
% POLAR3D Plots a 3D polar surface.
%
% POLAR3D(Zin,theta_min,theta_max,Rho_min,Rho_max,meshscale) plots
% the profiles as a mesh plot for Zin between radii Rho_min and
% Rho_max for polar angles equally spaced between theta_min and theta_max.
%
% POLAR3D(Zin,theta_min,theta_max,Rho_min,Rho_max,meshscale,plotspec)
% plots the profiles Zin between radii Rho_min and Rho_max for
% polar angles between theta_min and theta_max with a plot type
% specification. If plotspec = 'surf' a standard Matlab surface
% is plotted,whereas 'mesh', 'surfc' or 'meshc' will plot mesh,
% surface with countour, or mesh with contour, respectively.
% The size of the squares on the mesh or surf plots is determined
% by meshscale. The default plot is a mesh plot.
%
%
% [Xout,Yout,Zout] = POLAR3D(Zin,theta_min,theta_max,Rho_min,
% Rho_max, meshscale)returns Zout values corresponding to the
% Cartesian positions (Xout,Yout).
%
% SYNTAX polar3d(Zin,theta_min,theta_max,Rho_min,Rho_max,meshscale)
% polar3d(Zin,theta_min,theta_max,Rho_min,Rho_max,meshscale,plotspec)
% polar3d(Zin,theta_min,theta_max,Rho_min,Rho_max,meshscale,interpspec)
% polar3d(Zin,theta_min,theta_max,Rho_min,Rho_max,meshscale, plotspec,interpspec)
% [Xout,Yout,Zout] = polar3d(Zin,theta_min,theta_max,Rho_min,Rho_max,...)
%
% INPUT Zin input magnitude profiles where each column in Zin is
% assumed to represent the radial information in the
% plot i.e. each column represents the information
% along a radial line defined by theta, where theta
% varies between theta_min and theta_max.
%
% Zin is a (M x N) matrix, where M and N are not
% necessarily equal. If M is not equal to N then the
% data are interpolated to make them equal. The final
% size is determined by the larger value of (M,N).
%
% The N columns of Zin are assumed to be equally
% spaced measurements of the radial components, where
% Zin(1,1) corresponds to (theta_min,Rho_max) and
% Zin(M,1) corresponds to (theta_min,Rho_min), and so on.
% Zin(1,N) corresponds to (theta_max,Rho_max) and
% Zin(M,N) corresponds to (theta_max,Rho_min). Theta
% increases in the anticlockwise direction.
%
% theta_min the lower value in radians of the angular range
% over which the data is defined. Theta_min is a
% scalar quantity.
%
% theta_max the upper value in radians of the angular range
% over which the data is defined. Theta_max is a
% scalar quantity.
%
% Rho_min the lower value of the radial component for which
% the data is defined. Rho_min is a scalar quantity.
%
% Rho_max the upper value of the radial component for which
% the data is defined. Rho_max is a scalar quantity.
%
% meshscale a scalar that determines the size of the squares
% on the mesh or surf plots. If meshscale is 1, the
% mesh remains unchanged relative to the input grid;
% if meshscale is 2, the size of the squares is doubled,
% if 3.2, say, it is scaled accordingly. Moreover, if
% meshscale is less than 1, e.g. 0.2, the size of the
% squares is reduced into a finer mesh. The dimensions
% of Xout, Yout and Zout are reduced or enlarged by
% meshscale.
%
% plotspec = 'surf' produces a surface plot.
% = 'surfc' produces a surface plot with contour.
% = 'mesh' produces a mesh plot.
% = 'meshc' produces a mesh plot with countour.
% = 'contour' produces a 2D contour plot.
% = 'contourf' produces a 2D filled contour plot.
% = 'off' disengages plot function.
%
% interpspec = 'linear' bilinear interpolation on Zin.
% = 'spline' spline interpolation on Zin.
% = 'nearest' nearest neighbour interpolation on Zin.
% = 'cubic' bicubic interpolation on Zin.
%
% OUTPUT Zout output magnitude profiles defined by Zin at
% positions (Xout,Yout).
%
% Zout is square with dimensions determined by the
% maximum dimension of the input matrix Zin. The
% dimensions of Zout are reduced or enlarged by meshscale.
%
% Xout output X-positions corresponding to polar positions
% (rho,theta). Xout is square with dimensions
% determined by the maximum dimension of the input
% matrix Zin. The dimensions of Xout are reduced or
% enlarged by meshscale.
%
% Yout output Y-positions corresponding to polar positions
% (rho,theta). Yout is square with dimensions
% determined by the maximum dimension of the input
% matrix Zin. The dimensions of Yout are reduced or
% enlarged by meshscale.
%
% Written by JM DeFreitas, QinetiQ Ltd, Winfrith Technology
% Centre, Dorchester DT2 8XJ, UK. jdefreitas@qinetiq.com.
%
% Revision 1.0 4 April 2005.
% Released 5 April 2005. (Beta Release).
%
% Revision 1.1 17 April 2005
% 1. Inroduced new check on Zin to cover case of dimensions (M x 2)
% or (2 x N) matrix. These are not allowed.
% 2. Changed L2 so that when meshscale > 1 and theta ranges over
% 360 degrees the data wraps around without spaces.
% 3. Removed Xout1, Yout1 and Zout1.
% 4. Changed 'theta(j,:) = ones([(L2/n) 1])*angl(j);' to
% 'theta(j,:) = ones([1 (L2/n)])*angl(j)'; so that it is
% compatible with Matlab6 R12.1.
% 5. Reorganised meshgrid so that interpolation now works with
% meshscale < 1.
% 6. Changed error traps from '((p ~= 1)&(q ~= 1))' to
% '((p ~= 1)|(q ~= 1))' where used.
%
% Full Release 26 May 2005. All Rights Reserved.
%
% Terms and Conditions of Use
%
% 1. This function is made available to Matlab users under the
% terms and conditions set out in the Matlab Exchange by
% The Mathworks, Inc.
% 2. Where the use of POLAR3D is to be cited, the following is recommended:
% J M De Freitas. POLAR3D: A 3-Dimensional Polar Plot Function
% in Matlab. QinetiQ Ltd, Winfrith Technology Centre, Winfrith,
% Dorchester DT2 8XJ. UK. 2 June 2005.
% 3. No offer of warranty is made or implied by the author and
% use of this work implies that the user has agreed to take full
% responsibility for its use.
%
if (nargin < 6)
disp('Polar3d Error: Too few input arguments.');
return
elseif (nargin > 8)
disp('Polar3d Error: Too many input arguments.');
return
end
[p,q] = size(theta_min);
if (((p ~= 1)|(q ~= 1))|~isreal(theta_min))|ischar(theta_min)
disp('Polar3d Error: theta_min must be scalar and real.');
return
end
[p,q] = size(theta_max);
if (((p ~= 1)|(q ~= 1))|~isreal(theta_max))|ischar(theta_max)
disp('Polar3d Error: theta_max must be scalar and real.');
return
end
if theta_max <= theta_min
disp('Polar3d Error: theta_max less than or equal theta_min.');
return
end
if abs(theta_max - theta_min) > 2*pi
disp('Polar3d Error: range of theta greater than 2pi.');
return
end
[p,q] = size(Rho_max);
if (((p ~= 1)|(q ~= 1))|~isreal(Rho_max))|(ischar(Rho_max)|Rho_max < 0)
disp('Polar3d Error: Rho_max must be scalar, positive and real.');
return
end
[p,q] = size(Rho_min);
if (((p ~= 1)|(q ~= 1))|~isreal(Rho_min))|(ischar(Rho_min)|Rho_min < 0)
disp('Polar3d Error: Rho_min must be scalar, positive and real.');
return
end
if Rho_max <= Rho_min
disp('Polar3d Error: Rho_max less than or equal Rho_min.');
return
end
[p,q] = size(meshscale);
if (((p ~= 1)|(q ~= 1))|~isreal(meshscale))|ischar(meshscale)
disp('Polar3d Warning: mesh scale must be scalar and real.');
meshscale = 1;
end
if (meshscale <= 0)
disp('Polar3d Warning: mesh scale must be scalar and positive.');
meshscale = 1;
end
% Set up default plot and interpolation specifications.
str1 = 'mesh';
str2 = 'linear';
if length(varargin) == 2
% Sort out plot and interpolation specification if both strings given.
str1 = [varargin{1}(:)]';
str2 = [varargin{2}(:)]';
g1 = (~isequal(str1,'mesh')&~isequal(str1,'surf'))&~isequal(str1,'off');
g2 = (~isequal(str1,'meshc')&~isequal(str1,'surfc'));
g5 = (~isequal(str1,'contour')&~isequal(str1,'contourf'));
g3 = (~isequal(str2,'cubic')&~isequal(str2,'linear'));
g4 = (~isequal(str2,'spline')&~isequal(str2,'nearest'));
if (g1&g2&g5)
disp('Polar3d Warning: Incorrect plot specification. Default to mesh plot.');
str1 = 'mesh';
end
if (g3&g4)
disp('Polar3d Warning: Incorrect interpolation specification.');
disp('Default to linear interpolation.');
str2 = 'linear';
end
elseif length(varargin) == 1
% Sort out plot or interpolation specification from single string input.
str1 = [varargin{1}(:)]';
g1 = (~isequal(str1,'mesh')&~isequal(str1,'surf'))&~isequal(str1,'off');
g2 = (~isequal(str1,'meshc')&~isequal(str1,'surfc'));
g5 = (~isequal(str1,'contour')&~isequal(str1,'contourf'));
g3 = (~isequal(str1,'cubic')&~isequal(str1,'linear'));
g4 = (~isequal(str1,'spline')&~isequal(str1,'nearest'));
if (g1&g2)&(g3&g4&g5)
disp('Polar3d Error: Incorrect plot or interpolation specification.');
return
elseif isequal(str1,'cubic')
str2 = str1;
str1 = 'mesh';
elseif isequal(str1,'linear')
str2 = str1;
str1 = 'mesh';
elseif isequal(str1,'spline')
str2 = str1;
str1 = 'mesh';
elseif isequal(str1,'nearest')
str2 = str1;
str1 = 'mesh';
elseif isequal(str1,'off')
str2 = 'linear';
end
end;
% Check if dimensions of input data are acceptable.
[r,c] = size(Zin');
if (r < 5)&(c < 5)
disp('Polar3d Error: Input matrix dimensions must be greater than (4 x 4).');
return
end
% Check if input data has two rows or columns or less.
if (r < 3)|(c < 3)
disp('Polar3d Error: One or more input matrix dimensions too small.');
return
end
% Transpose and setup input magnitude matrix.
temp = Zin';
for j = 1:c
P(:,j) = temp(:,c-j+1); % swap columns over
end
Zin = P;
[r,c] = size(Zin);
% Check if meshscale is compatible with dimensions of input data.
scalefactor = round(max(r,c)/meshscale);
if scalefactor < 3
disp('Polar3d Error: mesh scale incompatible with dimensions of input data.');
return
end
% Set up meshgrid corresponding to larger matrix dimension of Zin
% for interpolation if required.
n = meshscale;
if r > c
L = r;
L2 = fix(L/n)*n;
step = r/(c-1);
[X1,Y1] = meshgrid(0:step:r,1:r);
if n < 1
[X,Y] = meshgrid(0:n:(L2-n),0:n:(L2-n));
else
[X,Y] = meshgrid(1:n:L2,1:n:L2);
end
T = interp2(X1,Y1,Zin,X,Y,str2);
elseif c > r
L = c;
L2 = fix(L/n)*n;
step = c/(r-1);
[X1,Y1] = meshgrid(1:c,0:step:c);
if n < 1
[X,Y] = meshgrid(0:n:(L2-n),0:n:(L2-n));
else
[X,Y] = meshgrid(1:n:L2,1:n:L2);
end
T = interp2(X1,Y1,Zin,X,Y,str2);
else
L = r;
L2 = fix(L/n)*n;
[X1,Y1] = meshgrid(1:r,1:r);
if n < 1
[X,Y] = meshgrid(0:n:(L2-n),0:n:(L2-n));
else
[X,Y] = meshgrid(1:n:L2,1:n:L2);
end
T = interp2(X1,Y1,Zin,X,Y,str2);
end
[p,q] = size(T);
L2 = max(p,q);
% Set up angles
angl = theta_min:abs(theta_max-theta_min)/(L2-1):theta_max;
for j = 1:L2
theta(j,:) = ones([1 L2])*angl(j);
end
% Set up radial components
Rho = Rho_min:abs(Rho_max-Rho_min)/(L2-1):Rho_max;
% Convert to Cartesian coordinates
for j = 1:L2
[Xout(j,:) Yout(j,:) Zout(j,:)] = pol2cart(theta(j,:),Rho,T(j,:));
end
% Plot Cartesian surface
switch str1;
case 'mesh'
axis normal;
colormap([0 0 0]);
mesh(Xout,Yout,Zout);
axis off;
grid off;
case 'meshc'
axis normal;
colormap([0 0 0]);
meshc(Xout,Yout,Zout);
axis off;
grid off;
case 'surf'
axis normal;
surf(Xout,Yout,Zout);
grid off;
case 'surfc'
axis normal;
surfc(Xout,Yout,Zout);
grid off;
case 'contour'
axis normal;
h = polar([theta_min theta_max], [Rho_min Rho_max]);
delete(h)
hold on
contour(Xout,Yout,Zout,20);
hold off
colorbar;
case 'contourf'
axis normal;
contourf(Xout,Yout,Zout,20);
axis off;
grid off;
colorbar;
end
return
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