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[Index for PublicToolbox/Sphere_Tessellation]
# 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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