Fig_3_11a.m

% This script is based on a script by Benny Bernschütz 

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% This work is supplementary material for the book                        %
%                                                                         %
% Jens Ahrens, Analytic Methods of Sound Field Synthesis, Springer-Verlag %
% Berlin Heidelberg, 2012, https://doi.org/10.1007/978-3-642-25743-8      %
%                                                                         %
% It has been downloaded from http://soundfieldsynthesis.org and is       %
% licensed under a Creative Commons Attribution-NonCommercial-ShareAlike  % 
% 3.0 Unported License. Please cite the book appropriately if you use     % 
% these materials in your own work.                                       %
%                                                                         %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

clear all;

N = 13; 

% orientation of source
alpha_or = -pi;
beta_or  = pi/2;

% set up spatial grid 
resolution      = 50;
Alpha           = linspace( 0, 2*pi, resolution );  % azimuth
Beta            = linspace( 0,   pi, resolution );  % colatitude
[ alpha, beta ] = meshgrid( Alpha, Beta );
 
% initialize S_bar
S_bar = zeros( size( alpha ) );

% this loop evaluates Eq. (2.46) with (2.44)
for n = 0: N-1
    for m = -n : n
        S_bar = S_bar +  ...
             ( factorial(N-1) * factorial(N) ) / ( factorial(N+n) * factorial(N-n-1) ) .* ...
                 sphharm( n, -m, beta_or, alpha_or ) .* sphharm( n, m, beta, alpha );
    end
end

% normalize
S_bar = S_bar ./ max( abs( S_bar(:) ) );

% convert colatitude to elevation and then everything to Cartesian
% coordinates
[ Xm, Ym, Zm ] = sph2cart( alpha, pi/2 - beta, abs( real( S_bar ) ) );

figure;

colormap gray;
axes( 'position', [ 0.1 0.2 .8 .68 ] ); 

surf( Xm, Ym, Zm ); 

hold on;
% plot coordinate axes
line( [ -1 1 ], [ .0 .0], [  0 0 ], 'Marker', '.', 'LineStyle', '-', 'Color', [ .5 .5 .5 ], 'LineWidth', [ 1 ] );
line( [  0 0 ], [ -1  1], [  0 0 ], 'Marker', '.', 'LineStyle', '-', 'Color', [ .5 .5 .5 ], 'LineWidth', [ 1 ] );
line( [  0 0 ], [  0  0], [ -1 1 ], 'Marker', '.', 'LineStyle', '-', 'Color', [ .5 .5 .5 ], 'LineWidth', [ 1 ] );
hold off;

axis( [ -1 1 -1 1 -1 1 ] );

view( 35, 25 );

light( 'Position',[1 -5 3]  ); 
lighting phong; 
camzoom( 1.3 );

xlabel( '$x$', 'Interpreter', 'latex' );
ylabel( '$y$', 'Interpreter', 'latex' );
zlabel( '$z$', 'Interpreter', 'latex' );

graph_defaults;