> Date: Thu, 19 Sep 2002 10:20:05 -0400
> From: Josh Richmond <[EMAIL PROTECTED]>
>
> Run the attached program to see, but it looks like (at least using my initial
> values), the 3x3 matrix returned is not the 3x3 rotation matrix of the 4x4
> matrix, even with no affine transformation.
>
> E:\temp>java -cp . MatrixTest
> 4x4:
> 0.996823, 0.036243, 0.070927, -0.245034
> -0.036412, 0.997481, 0.001096, 0.034035
> -0.07084, -0.003675, 0.999336, 0.036529
> 0.0, 0.0, 0.0, 1.0
>
> 3x3:
> 0.03627668530489642, 0.9968262981253496, 0.07086136795886099
> 0.9993350269113018, -0.03644589019989963, 0.0010959360038394175
> -0.0036750634657327997, -0.0707744901306144, 0.997485571552428
As Mark Whitehorn <[EMAIL PROTECTED]> demonstrated, there appears to be
a problem with the general SVD implementation in vecmath.
For your particular case, the SVD *is* returning a correct result, but
the version of the SVD algorithm Java 3D uses sorts the columns in
descending order of scales. This is useful for several types of
problems but is inappropriate for the purpose of normalizing rotations.
I've submitted bug 4751283
"Transform3D.normalize() and Matrix4d.get(Matrix3d) permute matrix columns."
Note that this only a problem when the matrix contains non-uniform scales.
Possible workarounds:
1) If you just want the upper 3x3 matrix components, use
Transform3D.getRotationScale(Matrix3d) or
Matrix4d.getRotationScale(Matrix3d)
2) If you only need to make the matrix orthogonal, use
Transform3D.normalizeCP() to get a cross-product normalization.
3) If you need to make the matrix congruent (uniform scale), you can
normalize the columns yourself with something like this:
void conditionScale(double[] m) {
double[] s = new double[3] ;
s[0] = m[0]*m[0] + m[4]*m[4] + m[8]*m[8] ;
s[1] = m[1]*m[1] + m[5]*m[5] + m[9]*m[9] ;
s[2] = m[2]*m[2] + m[6]*m[6] + m[10]*m[10] ;
if (s[0] == s[1] && s[0] == s[2])
return ;
s[0] = Math.sqrt(s[0]) ;
s[1] = Math.sqrt(s[1]) ;
s[2] = Math.sqrt(s[2]) ;
int closestToOne = 0 ;
if (Math.abs(s[1] - 1.0) < Math.abs(s[0] - 1.0))
closestToOne = 1 ;
if (Math.abs(s[2] - 1.0) < Math.abs(s[closestToOne] - 1.0))
closestToOne = 2 ;
double scale ;
for (int i = 0 ; i < 3 ; i++) {
if (i == closestToOne) continue ;
scale = s[closestToOne] / s[i] ;
m[i+0] *= scale ;
m[i+4] *= scale ;
m[i+8] *= scale ;
}
}
-- Mark Hood
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