rigidtform2d: why not accept double type homogenous matrix?

I found out by accident why the function rigidtform2d does not accept a 3 by 3 flush matrix of type double?

T = [ 1.0000    0.0004   -0.2102
-0.0004    1.0000    3.3896
0         0    1.0000]; % T is default double type

A = rigidtform2d(single(T)); % ok
B = rigidtform2d(T); 

Error using rigidtform2d>parseOneInputSyntaxes
Invalid transformation matrix.

Error in rigidtform2d (line 40)
self = parseOneInputSyntaxes(self,varargin{1});

I then test to see if it is close to the singular matrix：

rcond(T)

ans =

0.0473

However it doesn't, which means double is more sensitive than single? Or that the function is not robust enough?

Answer 1

[xingxingcui]

A rigidtform2d object stores only rotation and translation information, and the shear 0.0004 exists in the T matrix above.

source

It is actually a robustness problem, Hopefully future versions enhance the double type of issue，caused by the following functions：

the constrained matrix is not within floating-point round-off error of the original matrix, then the original matrix is not a valid transformation matrix for the subclass.

function tf = matricesNearlyEqual(A,B)
% matricesNearlyEqual
%   matricesNearlyEqual(A,B) returns true if A and B are the
%   same, within floating-point round-off error. A and B are assumed to
%   be square and of  the same class, and this is not checked.

    coder.inline('always');
    coder.internal.prefer_const(A,B);
    t = eps(class(A)) ^ (3/4);
    R = max(norm(A),norm(B));
    R0 = 100 * realmin(class(A)) / t;
    R = max(R,R0);
    tf = (norm(A - B) / R) <= t;

end