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# solid_angle2

## (Toolbox/solid_angle2.m in BrainStorm 2.0 (Alpha))

### Function Synopsis

    sangle = solid_angle2(r,r1,r2,r3)

### Help Text

    SOLID_ANGLE2 - Solid angle of a viewed triangle
     function sangle = solid_angle2(r,r1,r2,r3)

    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

     Inputs:
             r : observation point (Nobs x 3)
            r1 : First Vertice of Triangles (Nt x 3)
            r2 : Second Vertice of Triangles (Nt x 3)
            r3 : Third Vertice of Triangles (Nt x 3)

     Output:
             sangle : Function Result (Nt x Nobs)

     Ref: Oosterom, Strackee, IEEE Trans. BME, pp125-126, 1983

     Note: if r is on the triangle, sangle will be returned as 2*pi or -2*pi

     %%% John Ermer 04/04/00

    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

### Cross-Reference Information

This function calls

    crossprod                          C:\BrainStorm_2001\Toolbox\crossprod.m
    dotprod                            C:\BrainStorm_2001\Toolbox\dotprod.m
    rownorm                            C:\BrainStorm_2001\Toolbox\rownorm.m

This function is called by

    bem_xfer                           C:\BrainStorm_2001\Toolbox\bem_xfer.m

### Listing of function C:\BrainStorm_2001\Toolbox\solid_angle2.m

    function sangle = solid_angle2(r,r1,r2,r3)
    %SOLID_ANGLE2 - Solid angle of a viewed triangle
    % function sangle = solid_angle2(r,r1,r2,r3)
    %
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    %
    % Inputs:
    %         r : observation point (Nobs x 3)
    %        r1 : First Vertice of Triangles (Nt x 3)
    %        r2 : Second Vertice of Triangles (Nt x 3)
    %        r3 : Third Vertice of Triangles (Nt x 3)
    %
    % Output:
    %         sangle : Function Result (Nt x Nobs)
    %
    % Ref: Oosterom, Strackee, IEEE Trans. BME, pp125-126, 1983
    %
    % Note: if r is on the triangle, sangle will be returned as 2*pi or -2*pi
    %
    % %%% John Ermer 04/04/00
    %
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

    %<autobegin> ---------------------- 26-May-2004 11:34:26 -----------------------
    % --------- Automatically Generated Comments Block Using AUTO_COMMENTS ---------
    %
    % CATEGORY: Forward Modeling
    %
    % Alphabetical list of external functions (non-Matlab):
    %   toolbox\crossprod.m
    %   toolbox\dotprod.m
    %   toolbox\rownorm.m
    %
    % At Check-in: $Author: Mosher $  $Revision: 14 $  $Date: 5/26/04 10:02a $
    %
    % This software is part of BrainStorm Toolbox Version 2.0 (Alpha) 24-May-2004
    %
    % Principal Investigators and Developers:
    % ** Richard M. Leahy, PhD, Signal & Image Processing Institute,
    %    University of Southern California, Los Angeles, CA
    % ** John C. Mosher, PhD, Biophysics Group,
    %    Los Alamos National Laboratory, Los Alamos, NM
    % ** Sylvain Baillet, PhD, Cognitive Neuroscience & Brain Imaging Laboratory,
    %    CNRS, Hopital de la Salpetriere, Paris, France
    %
    % See BrainStorm website at http://neuroimage.usc.edu for further information.
    %
    % Copyright (c) 2004 BrainStorm by the University of Southern California
    % This software distributed  under the terms of the GNU General Public License
    % as published by the Free Software Foundation. Further details on the GPL
    % license can be found at http://www.gnu.org/copyleft/gpl.html .
    %
    % FOR RESEARCH PURPOSES ONLY. THE SOFTWARE IS PROVIDED "AS IS," AND THE
    % UNIVERSITY OF SOUTHERN CALIFORNIA AND ITS COLLABORATORS DO NOT MAKE ANY
    % WARRANTY, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO WARRANTIES OF
    % MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE, NOR DO THEY ASSUME ANY
    % LIABILITY OR RESPONSIBILITY FOR THE USE OF THIS SOFTWARE.
    %<autoend> ------------------------ 26-May-2004 11:34:26 -----------------------

    %
    Nt = size(r1,1);
    Nobs = size(r,1);
    %
    temp = reshape(repmat(r',Nt,1),3,Nt*Nobs)'; % (Nt*Nobs)x(3)
    r1_r = repmat(r1,Nobs,1) - temp;            % (Nt*Nobs)x(3)
    r2_r = repmat(r2,Nobs,1) - temp;            % (Nt*Nobs)x(3)
    r3_r = repmat(r3,Nobs,1) - temp;            % (Nt*Nobs)x(3)
    %
    n1 = rownorm(r1_r);
    n2 = rownorm(r2_r);
    n3 = rownorm(r3_r);
    %
    %%%% compute sangle for all vector sets
    %
    sangle = 2*atan2(dotprod(r1_r,crossprod(r2_r,r3_r)),n1.*n2.*n3+...
                     n1.*dotprod(r2_r,r3_r) + n2.*dotprod(r1_r,r3_r) +...
                     n3.*dotprod(r1_r,r2_r) );
    sangle = reshape(sangle,Nt,Nobs);
    %

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