You wont believe this ??

[K_F]

From Msofts Direct2d

If I'm not mistaken... this is a big stuffup.

The function from D2D1Helper.h

Multiplies two matrices and returns the result.

D2D1_MATRIX_3X2_F operator*(
  const D2D1_MATRIX_3X2_F &matrix1,
  const D2D1_MATRIX_3X2_F &matrix2
)

Well, first of all, multiplying two MxN (M != N) matrices is undefined ??
Anyway they proceed to...

void SetProduct(
            const Matrix3x2F &a,
            const Matrix3x2F &b
            )
        {
            _11 = a._11 * b._11 + a._12 * b._21;
            _12 = a._11 * b._12 + a._12 * b._22;
            _21 = a._21 * b._11 + a._22 * b._21;
            _22 = a._21 * b._12 + a._22 * b._22;
            _31 = a._31 * b._11 + a._32 * b._21 + b._31;
            _32 = a._31 * b._12 + a._32 * b._22 + b._32;

Doing it this way they should end up with a 3x3 matrix !!

Are they twiddling something or have they lost the plot completely?

[Gunther]

Hi K_F,

Well, first of all, multiplying two MxN (M != N) matrices is undefined ??

that's not necessary. The matrix multiplication isn't commutative, that's clear. Two matrices must be concatenated for multiplication. They are concatenated, if the number of columns of the first factor is equal to the number of rows of the second factor.

Gunther

[K_F]

My Bad, Sorry.. I meant in this case of a 3x2 (Rows x Columns).

The only way I can see this working if they extend the matrices to 3x3 placing Zero's in the newly invented vectors.
The last two calculations makes it look like the A[3,3] = 1 and the B[3,3] = 0 ..
They fudging the factors... I'll dig into this

[Gunther]

Hi K_F,

My Bad, Sorry.. I meant in this case of a 3x2 (Rows x Columns).

yes, these matrices are not concatenated. The multiplication isn't possible.

The only way I can see this working if they extend the matrices to 3x3 placing Zero's in the newly invented vectors.
The last two calculations makes it look like the A[3,3] = 1 and the B[3,3] = 0 ..
They fudging the factors... I'll dig into this

It would be interesting to figure out that point.

Gunther

[FORTRANS]

Hi,

   Multiplying two matrices is possible when the number of columns
of the first is equal to the number of rows of the second.  You can
not multiply a 3 x 2 matrix by a 3 x 2 matrix.  You can do a
3 x 2 by a 2 x 3 matrix.  And when you consider a vector as a
1 x N matrix, you can find many examples of vectors multiplied
by a N x N matrix.  Or an N x N matrix with an N x 1 vector.

   From the "CRC HANDBOOK of tables for MATHEMATICS", 4th
edition:

   c_ij = [ sum of k from 1 to n ] a_ik * b_kj

They have an example of a 2 x 3 multiplied by a 3 x 3 giving a
2 x 3 if wanted.

   Think of vector multiplication giving either a scalar, a 1 x 1 matrix,
or a cross product, an N x 1 matrix, depending on the order of
multiplication.

Regards,

Steve N.

[Gunther]

Hi Steve,

Hi,

   Multiplying two matrices is possible when the number of columns
of the first is equal to the number of rows of the second. ... 

yes, see my reply #1.

Gunther

[qWord]

When working in the XY plane, the third column of the 3x3 matrix is always {0,0,1} thus it can be omitted (see also XFORM struct)

[K_F]

Yeah.. I know, but they seem to be missing the 1 in the second Matrix

If they multiplying as it is in the code, they should end up with _13 = 0, _23 = 0 and _33 = 1 - this seems to be conveniently left out ?

[qWord]

If they multiplying as it is in the code, they should end up with _13 = 0, _23 = 0 and _33 = 1 - this seems to be conveniently left out ?

yes, it is redundant information.

[K_F]

OK.. maybe they concatenated it with an end 3x2 matrix to get it back into 2D.
I was worried they'd gone off the edge, no explanation in the header files.. 


Thanks