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makehgtformS.m
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makehgtformS.m
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function m=makehgtformS(varargin)
%MAKEHGTFORM Make a 4x4 transform matrix.
% M = MAKEHGTFORM Creates an identity transform.
%
% M = MAKEHGTFORM('translate',tx,ty,tz) Translate along X
% axis by tx, along Y axis by ty, and along Z axis by tz.
%
% M = MAKEHGTFORM('scale',s) Scale uniformly by s.
%
% M = MAKEHGTFORM('scale',[sx sy sz]) Scale along X axis by
% sx, along Y axis by sy, and along Z axis by sz.
%
% M = MAKEHGTFORM('xrotate',t) Rotate around X axis by t radians.
%
% M = MAKEHGTFORM('yrotate',t) Rotate around Y axis by t radians.
%
% M = MAKEHGTFORM('zrotate',t) Rotate around Z axis by t radians.
%
% M = MAKEHGTFORM('axisrotate',[ax ay az],t) Rotate around axis
% [ax ay az] by t radians.
%
% Multiple transforms can be concatenated.
%
% Example:
%
% m = makehgtform('xrotate',pi/2,'yrotate',pi/2);
%
% is the same as:
%
% m = makehgtform('xrotate',pi/2)*makehgtform('yrotate',pi/2);
%
% See also HGTRANSFORM.
% Copyright 1984-2005 The MathWorks, Inc.
m = eye(4);
ai = 1;
numArgs = length(varargin);
while ai <= numArgs
name = varargin{ai};
ai = ai+1;
if strcmpi(name,'translate')
error(nargchk(ai,inf,numArgs,'struct'));
symbolic=false;
if ~isnumeric(varargin{ai})
if isa(varargin{ai},'sym') %test if its symbolic
x = sym(varargin{ai});
ai = ai+1;
if isscalar(x)
y = sym(varargin{ai});
ai = ai+1;
z = sym(varargin{ai});
ai = ai+1;
elseif (~isvector(x) || length(x) ~= 3)
error(message('MATLAB:makehgtform:InvalidParamTranslate3D'));
else
y = x(2);
z = x(3);
x = x(1);
end
m = m * [1 0 0 x; ...
0 1 0 y; ...
0 0 1 z; ...
0 0 0 1];
symbolic=true;
else
error(message('MATLAB:makehgtform:InvalidParamTranslateNumeric'));
end
end
if ~symbolic
x = double(varargin{ai});
ai = ai+1;
if isscalar(x)
error(nargchk(ai+1,inf,numArgs,'struct'));
if ~isnumeric(varargin{ai})
error(message('MATLAB:makehgtform:InvalidParamTranslateNumeric'));
end
y = double(varargin{ai});
ai = ai+1;
if ~isnumeric(varargin{ai})
error(message('MATLAB:makehgtform:InvalidParamTranslateNumeric'));
end
z = double(varargin{ai});
ai = ai+1;
if (~isscalar(y) || ~isscalar(z))
%todo
end
elseif (~isvector(x) || length(x) ~= 3)
error(message('MATLAB:makehgtform:InvalidParamTranslate3D'));
else
y = x(2);
z = x(3);
x = x(1);
end
if (~isfinite(x) || ~isfinite(y) || ~isfinite(z))
error(message('MATLAB:makehgtform:InvalidParamTranslateFinite'));
end
m = m * [1 0 0 x; ...
0 1 0 y; ...
0 0 1 z; ...
0 0 0 1];
end
elseif strcmpi(name,'scale')
error(nargchk(ai,inf,numArgs,'struct'));
if ~isnumeric(varargin{ai})
error(message('MATLAB:makehgtform:InvalidParamScaleNumeric'));
end
s = double(varargin{ai});
ai = ai+1;
if isscalar(s)
s = repmat(s,1,3);
elseif (~isvector(s) || length(s) ~= 3)
error(message('MATLAB:makehgtform:InvalidParamScaleFactor1D3D'));
end
if (~isfinite(s(1)) || ~isfinite(s(2)) || ~isfinite(s(3)))
error(message('MATLAB:makehgtform:InvalidParamScaleFactorFinite'));
end
if (s(1) <= 0 || s(2) <= 0 || s(3) <= 0)
error(message('MATLAB:makehgtform:InvalidParamScaleFactorPositive'));
end
m = m * [s(1) 0 0 0; ...
0 s(2) 0 0; ...
0 0 s(3) 0; ...
0 0 0 1];
elseif strcmpi(name,'xrotate')
error(nargchk(ai,inf,numArgs,'struct'));
if ~isnumeric(varargin{ai})
error(message('MATLAB:makehgtform:InvalidParamXrotateNumeric'));
end
t = double(varargin{ai});
ai = ai+1;
if (~isscalar(t))
error(message('MATLAB:makehgtform:InvalidParamRotationScalar'));
end
if (~isfinite(t))
error(message('MATLAB:makehgtform:InvalidParamRotationFinite'));
end
[ct,st] = computeCosAndSin(t);
m = m * [1 0 0 0; ...
0 ct -st 0; ...
0 st ct 0; ...
0 0 0 1];
elseif strcmpi(name,'yrotate')
error(nargchk(ai,inf,numArgs,'struct'));
if ~isnumeric(varargin{ai})
error(message('MATLAB:makehgtform:InvalidParamYrotateNumeric'));
end
t = double(varargin{ai});
ai = ai+1;
if (~isscalar(t))
error(message('MATLAB:makehgtform:InvalidParamRotationScalar'));
end
if (~isfinite(t))
error(message('MATLAB:makehgtform:InvalidParamRotationFinite'));
end
[ct,st] = computeCosAndSin(t);
m = m * [ct 0 st 0; ...
0 1 0 0; ...
-st 0 ct 0; ...
0 0 0 1];
elseif strcmpi(name,'zrotate')
error(nargchk(ai,inf,numArgs,'struct'));
symbolic=false;
if ~isnumeric(varargin{ai})
if isa(varargin{ai},'sym') %test if its symbolic
t = sym(varargin{ai});
ai = ai+1;
[ct,st] = CosAndSin(t);
m = m * [ct -st 0 0; ...
st ct 0 0; ...
0 0 1 0; ...
0 0 0 1];
symbolic=true;
else
error(message('MATLAB:makehgtform:InvalidParamZrotate'));
end
end
if ~symbolic
t = double(varargin{ai});
ai = ai+1;
if (~isscalar(t))
error(message('MATLAB:makehgtform:InvalidParamRotationScalar'));
end
if (~isfinite(t))
error(message('MATLAB:makehgtform:InvalidParamRotationFinite'));
end
[ct,st] = computeCosAndSin(t);
m = m * [ct -st 0 0; ...
st ct 0 0; ...
0 0 1 0; ...
0 0 0 1];
end
elseif strcmpi(name,'axisrotate')
error(nargchk(ai+1,inf,numArgs,'struct'));
if ~isnumeric(varargin{ai})
error(message('MATLAB:makehgtform:InvalidParamAxisRotateNumeric'));
end
u = double(varargin{ai});
ai = ai+1;
if ~isnumeric(varargin{ai})
error(message('MATLAB:makehgtform:InvalidParamAxisRotateNumeric'));
end
t = double(varargin{ai});
ai = ai+1;
if ( ~isvector(u) || length(u) ~= 3)
error(message('MATLAB:makehgtform:BadAxis3D'));
end
if (~isfinite(u(1)) || ~isfinite(u(2)) || ~isfinite(u(3)))
error(message('MATLAB:makehgtform:BadAxisFinite'));
end
if (~isscalar(t))
error(message('MATLAB:makehgtform:InvalidParamRotationScalar'));
end
if (~isfinite(t))
error(message('MATLAB:makehgtform:InvalidParamRotationFinite'));
end
u = u./norm(u);
[c,s] = computeCosAndSin(t);
tmp = eye(4);
tmp(1:3,1:3) = c*eye(3) + (1-c)*kron(u,u') + s*SkewSymm(u);
m = m * tmp;
else
if ischar(name)
error(message('MATLAB:makehgtform:BadTransformType', name));
elseif isnumeric(name)
error(message('MATLAB:makehgtform:UnrecognizedArg', num2str( name )));
else
error(message('MATLAB:makehgtform:InvalidArg'));
end
end
end
function s=SkewSymm(v)
s = [ 0 -v(3) v(2); ...
v(3) 0 -v(1); ...
-v(2) v(1) 0];
function [ct,st] =CosAndSin(t)
ct = cos(t);
st = sin(t);
function [ct,st] = computeCosAndSin(t)
ct = cos(t);
st = sin(t);
function x = fixup(x)
vals = [0 1 -1];
i=find(abs(x-vals)<2*eps);
if ~isempty(i)
x = vals(i);
end