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geom3d

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geom3d

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19 Jun 2009 (Updated )

Library to handle 3D geometric primitives: create, intersect, display, and make basic computations

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createRotationOz(varargin)
function trans = createRotationOz(varargin)
%CREATEROTATIONOZ Create the 4x4 matrix of a 3D rotation around z-axis
%
%   TRANS = createRotationOz(THETA);
%   Returns the transform matrix corresponding to a rotation by the angle
%   THETA (in radians) around the Oz axis. A rotation by an angle of PI/2
%   would transform the vector [1 0 0] into the vector [0 1 0].
%
%   The returned matrix has the form:
%   [cos(THETA) -sin(THETA)  0  0]
%   [sin(THETA)  cos(THETA)  0  0]
%   [    0           0       1  0]
%   [    0           0       0  1]
%
%   TRANS = createRotationOz(ORIGIN, THETA);
%   TRANS = createRotationOz(X0, Y0, Z0, THETA);
%   Also specifies origin of rotation. The result is similar as performing
%   translation(-X0, -Y0, -Z0), rotation, and translation(X0, Y0, Z0).
%
%
%   See also:
%   transforms3d, transformPoint3d, createRotationOx, createRotationOy
%
%   ---------
%
%   author : David Legland 
%   INRA - TPV URPOI - BIA IMASTE
%   created the 06/04/2004.
%

%   HISTORY
%   2008/11/24 changed convention for angle
%   22/04/2009 rename as createcreateRotationOz


% default values
dx = 0;
dy = 0;
dz = 0;
theta = 0;

% get input values
if length(varargin)==1
    % only angle
    theta = varargin{1};
elseif length(varargin)==2
    % origin point (as array) and angle
    var = varargin{1};
    dx = var(1);
    dy = var(2);
    dz = var(3);
    theta = varargin{2};
elseif length(varargin)==3
    % origin (x and y) and angle
    dx = varargin{1};
    dy = varargin{2};
    dz = varargin{3};
    theta = varargin{3};
end

% compute coefs
cot = cos(theta);
sit = sin(theta);

% create transformation
trans = [...
    cot -sit 0 0;...
    sit  cot 0 0;...
    0 0 1 0;...
    0 0 0 1];

% add the translation part
t = [1 0 0 dx;0 1 0 dy;0 0 1 dz;0 0 0 1];
trans = t*trans/t;

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