[Insight-users] itk::CenteredRigid2DTransform is Linear?

[Constantine Zakkaroff]

Hello ALL.

The definition of IsLinear method of itk::CenteredRigid2DTransform is 
inherited from itk::MatrixOffsetTransformBase class, where it is defined 
very simply as this:

/** Indicates that this transform is linear. That is, given two
  * points P and Q, and scalar coefficients a and b, then
  *
  *           T(a*P + b*Q) = a * T(P) + b * T(Q)
  */
virtual bool IsLinear() const { return true; }

However, the equality

T( a*P + b*Q ) = a * T(P) + b * T(Q)

does not appear valid from what I can see with maths involved into the 
transform computations.

Also, the following code example below confirms the equality does not 
stand for itk::CenteredRigid2DTransform, producing the following output:

[56.173, -382.694] =?= [137.372, -306.153]

typedef itk::Point<double, 2> PtT;
typedef itk::Vector<double, 2> VT;
typedef itk::CenteredRigid2DTransform<double> TTrfT;
TTrfT::Pointer trf = TTrfT::New();
PtT pt;
pt[0] = 50;
pt[1] = 60;
trf->SetCenter(pt);
VT trns;
trns[0] = 10;
trns[1] = 20;
trf->SetTranslation(trns);
trf->SetAngle(0.1);

PtT P;
P[0] = 100;
P[1] = 200;
double a = 2;
PtT Q;
Q[0] = -50;
Q[1] = -200;
double b = 4;

std::cout << std::setprecision(3) << std::fixed;

std::cout << trf->TransformPoint(PtT((a * P.GetVectorFromOrigin() + b * 
Q.GetVectorFromOrigin()).GetDataPointer())) << " =?= ";

std::cout << PtT((a * trf->TransformPoint(P).GetVectorFromOrigin() + b * 
trf->TransformPoint(Q).GetVectorFromOrigin()).GetDataPointer()) << 
std::endl;

Is it a bug?

Regards,
Constantine