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# sphere_project

## (PublicToolbox/Sphere_Tessellation/sphere_project.m in BrainStorm 2.0 (Alpha))

### Function Synopsis

    V = sphere_project(v,r,c)

### Help Text

     sphere_project - project point X,Y,Z to the surface of sphere radius r

     V = sphere_project(v,r,c)

     Cartesian inputs:
     v is the vertex matrix, Nx3 (XYZ)
     r is the sphere radius, 1x1 (default 1)
     c is the sphere centroid, 1x3 (default 0,0,0)

     XYZ are converted to spherical coordinates and their radius is
     adjusted according to r, from c toward XYZ (defined with theta,phi)

     V is returned as Cartesian 3D coordinates

### Cross-Reference Information

This function is called by

    sphere_tri                         C:\BrainStorm_2001\PublicToolbox\Sphere_Tessellation\sphere_tri.m

### Listing of function C:\BrainStorm_2001\PublicToolbox\Sphere_Tessellation\sphere_project.m

    function V = sphere_project(v,r,c)

    % sphere_project - project point X,Y,Z to the surface of sphere radius r
    %
    % V = sphere_project(v,r,c)
    %
    % Cartesian inputs:
    % v is the vertex matrix, Nx3 (XYZ)
    % r is the sphere radius, 1x1 (default 1)
    % c is the sphere centroid, 1x3 (default 0,0,0)
    %
    % XYZ are converted to spherical coordinates and their radius is
    % adjusted according to r, from c toward XYZ (defined with theta,phi)
    %
    % V is returned as Cartesian 3D coordinates
    %

    % $Revision: 1 $ $Date: 5/20/04 3:58p $

    % Licence:  GNU GPL, no implied or express warranties
    % History:  06/2002, Darren.Weber_at_radiology.ucsf.edu, created
    %
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

    if ~exist('v','var'),
        msg = sprintf('SPHERE_PROJECT: No input vertices (X,Y,Z)\n');
        error(msg);
    end

    X = v(:,1);
    Y = v(:,2);
    Z = v(:,3);

    if ~exist('c','var'),
        xo = 0;
        yo = 0;
        zo = 0;
    else
        xo = c(1);
        yo = c(2);
        zo = c(3);
    end

    if ~exist('r','var'), r = 1; end

    % alternate method is to use unit vector of V
    % [ n = 'magnitude(V)'; unitV = V ./ n; ]
    % to change the radius, multiply the unitV
    % by the radius required.  This avoids the
    % use of arctan functions, which have branches.

    % Convert Cartesian X,Y,Z to spherical (radians)
    theta = atan2( (Y-yo), (X-xo) );
    phi   = atan2( sqrt( (X-xo).^2 + (Y-yo).^2 ), (Z-zo) );
    % do not calc: r = sqrt( (X-xo).^2 + (Y-yo).^2 + (Z-zo).^2);

    %   Recalculate X,Y,Z for constant r, given theta & phi.
    R = ones(size(phi)) * r;
    x = R .* sin(phi) .* cos(theta);
    y = R .* sin(phi) .* sin(theta);
    z = R .* cos(phi);

    V = [x y z];

    return

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