Similarity3DTransform::SetScale should recompute m_Offset

[N-Dekker]

Description

When Similarity3DTransform::SetScale is called, it does not compute m_Offset, which appears to cause an incorrect result from similarity3DTransform.TransformPoint when TransformPoint is called directly after SetScale.

ITK/Modules/Core/Transform/include/itkSimilarity3DTransform.hxx

Lines 59 to 65 in 895fc71

	template <typename TParametersValueType>
	void
	Similarity3DTransform<TParametersValueType>::SetScale(ScaleType scale)
	{
	m_Scale = scale;
	this->ComputeMatrix();
	}

The 2D version behaves differently: Similarity2DTransform::SetScale does compute m_Offset:

ITK/Modules/Core/Transform/include/itkSimilarity2DTransform.hxx

Lines 112 to 119 in 895fc71

	template <typename TParametersValueType>
	void
	Similarity2DTransform<TParametersValueType>::SetScale(ScaleType scale)
	{
	m_Scale = scale;
	this->ComputeMatrix();
	this->ComputeOffset();
	}

Steps to Reproduce

The 2D transform:

const auto transform2D = itk::Similarity2DTransform<double>::New();
transform2D->SetCenter(7.0);
transform2D->SetScale(3.0);
std::cout << transform2D->TransformPoint({}) << '\n';

Prints [-14, -14], which looks fine to me. However, the 3D version:

const auto transform3D = itk::Similarity3DTransform<double>::New();
transform3D->SetCenter(7.0);
transform3D->SetScale(3.0);
std::cout << transform3D->TransformPoint({}) << '\n';

Prints [0, 0, 0], which appears wrong!

Expected behavior

In general, PointType(center + (scale * (input - center)). When the input point is entirely zero ({}), center = PointType(7.0) and scale = 3.0, I would expect PointType(7.0 + (3.0 * (0.0 - 7.0)) == PointType(-14.0).

Versions

ITK 5.2, as well as revision 895fc71 (today July 2, 2021 at the master branch)

Additional Information

It looks like this inconsistency between the 2D and the 3D version of the similarity transform has been there for a long time already! Comparing the 2D and 3D version from commit 5d9e2fc by Luis Ibanez (@luisibanez), 29 April 2005:

ITK/Code/Common/itkSimilarity2DTransform.txx

Lines 121 to 129 in 5d9e2fc

	// Set Scale Part
	template <class TScalarType>
	void
	Similarity2DTransform<TScalarType>
	::SetScale( ScaleType scale )
	{
	m_Scale = scale;
	this->ComputeMatrixAndOffset();
	}

ITK/Code/Common/itkSimilarity3DTransform.txx

Lines 56 to 64 in 5d9e2fc

	// Set the scale factor
	template <class TScalarType>
	void
	Similarity3DTransform<TScalarType>
	::SetScale( ScaleType scale )
	{
	m_Scale = scale;
	this->ComputeMatrix();
	}

[dzenanz]

Oh, I guess #2627 is testing this.