spm_matrix.m

function [A] = spm_matrix(P, order)
% Return an affine transformation matrix
% FORMAT [A] = spm_matrix(P [,order])
% P(1)  - x translation
% P(2)  - y translation
% P(3)  - z translation
% P(4)  - x rotation about - {pitch} (radians)
% P(5)  - y rotation about - {roll}  (radians)
% P(6)  - z rotation about - {yaw}   (radians)
% P(7)  - x scaling
% P(8)  - y scaling
% P(9)  - z scaling
% P(10) - x affine
% P(11) - y affine
% P(12) - z affine
%
% order - application order of transformations [Default: 'T*R*Z*S']
%
% A     - affine transformation matrix
%__________________________________________________________________________
%
% spm_matrix returns a matrix defining an orthogonal linear (translation,
% rotation, scaling or affine) transformation given a vector of
% parameters (P).  By default, the transformations are applied in the
% following order (i.e., the opposite to which they are specified):
%
% 1) shear
% 2) scale (zoom)
% 3) rotation - yaw, roll & pitch
% 4) translation
%
% This order can be changed by calling spm_matrix with a string as a
% second argument. This string may contain any valid MATLAB expression
% that returns a 4x4 matrix after evaluation. The special characters 'S',
% 'Z', 'R', 'T' can be used to reference the transformations 1)-4)
% above. The default order is 'T*R*Z*S', as described above.
%
% SPM uses a PRE-multiplication format i.e. Y = A*X where X and Y are 4 x n
% matrices of n coordinates.
%__________________________________________________________________________
%
% See also: spm_imatrix.m
%__________________________________________________________________________
% Copyright (C) 1994-2011 Wellcome Trust Centre for Neuroimaging

% Karl Friston
% $Id: spm_matrix.m 4414 2011-08-01 17:51:40Z guillaume $


%-Special case: translation only
%--------------------------------------------------------------------------
if numel(P) == 3
    A = eye(4);
    A(1:3,4) = P(:);
    return;
end
    
%-Pad P with 'null' parameters
%--------------------------------------------------------------------------
q  = [0 0 0 0 0 0 1 1 1 0 0 0];
P  = [P q((length(P) + 1):12)];

%-Translation / Rotation / Scale / Shear
%--------------------------------------------------------------------------
T  =   [1   0   0   P(1);
        0   1   0   P(2);
        0   0   1   P(3);
        0   0   0   1];

R1  =  [1   0           0           0;
        0   cos(P(4))   sin(P(4))   0;
        0  -sin(P(4))   cos(P(4))   0;
        0   0           0           1];

R2  =  [cos(P(5))   0   sin(P(5))   0;
        0           1   0           0;
       -sin(P(5))   0   cos(P(5))   0;
        0           0   0           1];

R3  =  [cos(P(6))   sin(P(6))   0   0;
       -sin(P(6))   cos(P(6))   0   0;
        0           0           1   0;
        0           0           0   1];

R   = R1*R2*R3;

Z   =  [P(7)   0       0       0;
        0      P(8)    0       0;
        0      0       P(9)    0;
        0      0       0       1];

S   =  [1      P(10)   P(11)   0;
        0      1       P(12)   0;
        0      0       1       0;
        0      0       0       1];

%-Affine transformation matrix
%--------------------------------------------------------------------------
if nargin < 2
    A = T*R*Z*S;
else
    A = eval(sprintf('%s;', order));
    if ~isnumeric(A) || ~isequal(size(A),[4 4])
        error('Invalid order expression ''%s''.', order);
    end
end