elec_sphere_points - Generate points on a hemisphere, radius R
Useage: [X,Y,Z] = elec_sphere_points(Epoints, Rpoints, R)
Epoints number of elevations (phi)
Rpoints number of points in rotation (theta)
for each level of elevation. Works best
when a multiple of 4 or 2, asymmetrical
when odd.
R sphere radius
[X,Y,Z] cartesian points
size = (Epoints * Rpoints) - (Rpoints - 1)
` because the vertex point has no rotation.
Example: [x,y,z] = elec_sphere_points(10,16,1); plot3(x,y,z,'o');
Note: The points are more numerous closer to the vertex. It
is tricky to create points with constant arc length
separation.
This function cannot create standard 10-20 electrode
positions. These are given in spherical coordinates
in the text files 'elec_10-20*.txt'.0001 function [x,y,z] = elec_sphere_points(Epoints,Rpoints,R) 0002 0003 % elec_sphere_points - Generate points on a hemisphere, radius R 0004 % 0005 % Useage: [X,Y,Z] = elec_sphere_points(Epoints, Rpoints, R) 0006 % 0007 % Epoints number of elevations (phi) 0008 % Rpoints number of points in rotation (theta) 0009 % for each level of elevation. Works best 0010 % when a multiple of 4 or 2, asymmetrical 0011 % when odd. 0012 % R sphere radius 0013 % 0014 % [X,Y,Z] cartesian points 0015 % size = (Epoints * Rpoints) - (Rpoints - 1) 0016 % ` because the vertex point has no rotation. 0017 % 0018 % Example: [x,y,z] = elec_sphere_points(10,16,1); plot3(x,y,z,'o'); 0019 % 0020 % Note: The points are more numerous closer to the vertex. It 0021 % is tricky to create points with constant arc length 0022 % separation. 0023 % 0024 % This function cannot create standard 10-20 electrode 0025 % positions. These are given in spherical coordinates 0026 % in the text files 'elec_10-20*.txt'. 0027 % 0028 0029 % $Revision: 1.2 $ $Date: 2005/07/12 22:56:12 $ 0030 0031 % Licence: GNU GPL, no implied or express warranties 0032 % History: 08/01 Darren.Weber_at_radiology.ucsf.edu 0033 % It would be nice to decrease number of Rotation 0034 % points for every increase in elevation, but it 0035 % is tricky to maintain symmetry. If possible, 0036 % this could maintain near constant arc length 0037 % between points. 0038 % 0039 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 0040 0041 0042 eegversion = '$Revision: 1.2 $'; 0043 fprintf('ELEC_SPHERE_POINTS [v %s]\n',eegversion(11:15)); 0044 fprintf('...generating spherical points\n'); 0045 tic; 0046 0047 phi = linspace(0,pi/2,Epoints); % elevation, vertex = 0 0048 0049 theta1 = linspace(0,2*pi,Rpoints+1); % 360 degree rotation 0050 theta1 = theta1(1:end-1); % remove 2*pi (== 0) 0051 0052 thetad = (theta1(2) - theta1(1))/2; % provide staggered rotation 0053 0054 n = 0; odd = 1; 0055 for i = 1:length(phi) 0056 0057 % every 2nd level of elevation, stagger rotation by thetad 0058 if(odd == 1), odd = 0; theta = theta1; 0059 else, odd = 1; theta = theta1 + thetad; 0060 end 0061 0062 if isequal(phi(i),0), % vertex point 0063 n = n + 1; x(n) = 0; y(n) = 0; z(n) = R; 0064 elseif(phi(i) < (pi/8)), 0065 for j = 1:length(theta) 0066 0067 A(1) = x(n); 0068 A(2) = y(n); 0069 A(3) = z(n); 0070 B(1) = R * sin(phi(i)) * cos(theta(j)); 0071 B(2) = R * sin(phi(i)) * sin(theta(j)); 0072 B(3) = R * cos(phi(i)); 0073 0074 A_len = sqrt ( sum(A.^2) ); 0075 B_len = sqrt ( sum(B.^2) ); 0076 0077 angle = acos( dot(A,B) / (A_len * B_len) ); 0078 0079 if and((phi(i) < (pi/16)),(angle>(pi/90))), 0080 n = n + 1; 0081 x(n) = B(1); y(n) = B(2); z(n) = B(3); 0082 elseif(angle>(pi/45)), 0083 n = n + 1; 0084 x(n) = B(1); y(n) = B(2); z(n) = B(3); 0085 end 0086 end 0087 else 0088 for j = 1:length(theta) 0089 n = n + 1; 0090 x(n) = R * sin(phi(i)) * cos(theta(j)); 0091 y(n) = R * sin(phi(i)) * sin(theta(j)); 0092 z(n) = R * cos(phi(i)); 0093 end 0094 end 0095 end 0096 x = x'; 0097 y = y'; 0098 z = z'; 0099 0100 t = toc; fprintf('...done (%6.2f sec).\n\n',t); 0101 0102 return