retarded 3D Green's function uniformly moving point source

SFS_general/direction_vector.m

@@ -1,7 +1,7 @@
 function directions = direction_vector(x1,x2)
 %DIRECTION_VECTOR return unit vector(s) pointing from x1 to x2
 %
-% Usage: n = direction_vector(x1,x2)
+% Usage: n = direction_vector(x1,[x2])
 %
 % Input parameters:
 % x1 - starting point(s) [1xn] or [mxn]
@@ -11,7 +11,8 @@
 % n - unit vector(s) pointing in the direction(s) from x1 to x2
 %
 % DIRECTION_VECTOR(x1,x2) calculates the unit vectors pointing from
-% n-dimensional points x1 to the n-dimensional points x2.
+% n-dimensional points x1 to the n-dimensional points x2. If only x1 is
+% provided the direction vectors from zero to x1 are calculated.
 %
 % See also: secondary_source_positions
 
@@ -46,15 +47,20 @@
 
 
 %% ===== Checking of input parameters ===================================
-nargmin = 2;
+nargmin = 1;
 nargmax = 2;
 narginchk(nargmin,nargmax);
-if size(x1,2)~=size(x2,2)
- error('%s: x1 and x2 need to have the same dimension.',upper(mfilename));
-end
-if size(x1,1)~=size(x2,1) && ~(size(x1,1)==1 | size(x2,1)==1)
- error(['%s: x1 and x2 need to have the same size, or one needs to ', ...
- 'be a vector.'],upper(mfilename));
+if nargin==1
+ x2 = x1;
+ x1 = zeros(1,size(x2,2));
+else
+ if size(x1,2)~=size(x2,2)
+ error('%s: x1 and x2 need to have the same dimension.',upper(mfilename));
+ end
+ if size(x1,1)~=size(x2,1) && ~(size(x1,1)==1 | size(x2,1)==1)
+ error(['%s: x1 and x2 need to have the same size, or one needs to ', ...
+ 'be a vector.'],upper(mfilename));
+ end
 end
 
 

SFS_general/retarded_time.m

@@ -0,0 +1,90 @@
+function [tau, R, Delta] = retarded_time(x, y, z, t, vs, conf)
+% RETARDED_TIME computes the retarded time for a uniformly moving point source
+%
+% Usage: [tau, R, Delta] = retarded_time(x, y, z, t, vs, conf)
+%
+% Input parameters:
+% x - x coordinate position of observer / m [nx1] or [1x1]
+% y - y coordinate position of observer / m [nx1] or [1x1]
+% z - z coordinate position of observer / m [nx1] or [1x1]
+% t - absolute time / s [nxm] or [1xm]
+% vs - velocity vector of sound source / (m/s) [1x3] or [nx3]
+% conf - configuration struct (see SFS_config)
+%
+% Output parameters:
+% tau - retarded time between sound source and observer / s [nxm]
+% R - retarded distance (R = tau*c) / m [nxm]
+% Delta - auxilary distance / m [nxm]
+%
+% RETARDED_TIMES(x, y, z, t, vs, conf) the retarded time for a point source
+% uniformly moving along a line. Hereby, vs defines its direction
+% and its velocity. The position of the sound source at t=0 is the coordinate
+% origin.
+%
+% See also:
+
+%*****************************************************************************
+% The MIT License (MIT) *
+% *
+% Copyright (c) 2010-2016 SFS Toolbox Team *
+% *
+% Permission is hereby granted, free of charge, to any person obtaining a *
+% copy of this software and associated documentation files (the "Software"), *
+% to deal in the Software without restriction, including without limitation *
+% the rights to use, copy, modify, merge, publish, distribute, sublicense, *
+% and/or sell copies of the Software, and to permit persons to whom the *
+% Software is furnished to do so, subject to the following conditions: *
+% *
+% The above copyright notice and this permission notice shall be included in *
+% all copies or substantial portions of the Software. *
+% *
+% THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR *
+% IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, *
+% FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL *
+% THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER *
+% LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING *
+% FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER *
+% DEALINGS IN THE SOFTWARE. *
+% *
+% The SFS Toolbox allows to simulate and investigate sound field synthesis *
+% methods like wave field synthesis or higher order ambisonics. *
+% *
+% http://sfstoolbox.org [email protected] *
+%*****************************************************************************
+
+%% ===== Checking of input parameters ==================================
+% nargmin = 6;
+% nargmax = 6;
+% narginchk(nargmin,nargmax);
+% isargmatrix(x,y,z,t,vs);
+% isargstruct(conf);
+
+
+%% ===== Configuration ==================================================
+c = conf.c;
+
+
+%% ===== Computation ====================================================
+
+v = vector_norm(vs,2); % velocity of sound source [n x 1] or [1 x 1]
+nvs = bsxfun(@rdivide,vs,v); % direction of movement [n x 3] or [1 x 3]
+M = v/c; % Mach number [n x 1] or [1 x 1]
+
+% vector between observer and point source d(t) = x - vs*t
+% [n x m] or [1 x m]
+dx = bsxfun(@minus, x, bsxfun(@times,t, vs(:,1)));
+dy = bsxfun(@minus, y, bsxfun(@times,t, vs(:,2)));
+dz = bsxfun(@minus, z, bsxfun(@times,t, vs(:,3)));
+% instant distance between sound source and observer position
+r = sqrt( dx.^2 + dy.^2 + dz.^2 ); % [n x m]
+% component of d(t) parallel to the direction of movement: d(t)^T * nvs
+% [n x m]
+xpara = nvs(:,1).*dx + nvs(:,2).*dy + nvs(:,3).*dz;
+% auxiliary distance 
+Delta = sqrt( M.^2.*xpara.^2 + (1-M.^2).*r.^2 ); % [n x 1]
+% retarded distance
+R = (M.*xpara + Delta)./(1-M.^2);
+% retarded time
+tau = R./c;
+
+end

SFS_helper/isargsecondarysource.m

@@ -54,9 +54,9 @@ function isargsecondarysource(varargin)
  'and weights.'], ...
  inputname(ii));
  end
- if ~all(abs(vector_norm(x0(:,4:6),2)-1)<1e-10)
- error(['The norm of the direction of %s is not 1. ', ...
- 'You can use the direction_vector function to get ', ...
- 'correct direction values.'],inputname(ii));
- end
+%  if ~all(abs(vector_norm(x0(:,4:6),2)-1)<1e-10)
+%  error(['The norm of the direction of %s is not 1. ', ...
+%  'You can use the direction_vector function to get ', ...
+%  'correct direction values.'],inputname(ii));
+%  end
 end

SFS_monochromatic/greens_function_mono.m

@@ -25,6 +25,7 @@
 % References:
 % H. Wierstorf, J. Ahrens, F. Winter, F. Schultz, S. Spors (2015) -
 % "Theory of Sound Field Synthesis"
+% J. Ahrens (2012) - "Analytic Methods of Sound Field Synthesis"
 %
 % See also: sound_field_mono
 
@@ -99,6 +100,32 @@
  %
  G = 1/(4*pi) .* (1i*omega/c + 1./r) .* scalar./r.^2 .* exp(-1i*omega/c.*r);
 
+elseif strcmp('mps',src)
+ % Source model for a uniformly moving point source: retarded 3D Green's 
+ % function.
+ %
+ % 1 e^(+-i w/c R)
+ % G(x-xs,vs,w) = --- --------------
+ % 4pi R_1
+ %
+ % vs = v * ns % velocity vector
+ % M = v/c % Mach number
+ % xparallel = (x-xs)*ns % component in direction of movement
+ % R_1 = sqrt( M^2*xparallel.^2 + (1-M^2)*|x-xs|.^2 )
+ % R = (M*xparallel + R1)./(1-M*2);
+ % 
+ % see: Ahrens (2012), eq.(5.60)
+ % 
+ [~,x1] = xyz_axes_selection(x,y,z); % get first non-singleton axis
+ % shift and vectorize coordinates
+ x = x(:)-xs(1);
+ y = y(:)-xs(2);
+ z = z(:)-xs(3);
+ % retarded time
+ [tau, ~, R1] = retarded_time(x,y,z,0,xs(4:6),conf);
+ %
+ G = zeros(size(x1));
+ G(:) = 1/(4*pi) * exp(-1i*omega.*tau)./R1;
 elseif strcmp('ls',src)
  % Source model for a line source: 2D Green's function.
  %