Potential Bug in vtkMath::Cross Template Function

Description

There appears to be a potential bug in the vtkMath::Cross template function within the VTK library. The issue arises from the direct assignment of values to the output vector c without using temporary variables to store intermediate results. This can cause problems, especially when the input vectors a and b overlap with the output vector c.

Current Implementation

The current implementation of the template function vtkMath::Cross is as follows:

template <class VectorT1, class VectorT2, class VectorT3> void vtkMath::Cross(VectorT1&& a, VectorT2&& b, VectorT3& c)

{

c[0] = a[1] * b[2] - a[2] * b[1];

c[1] = a[2] * b[0] - a[0] * b[2];

c[2] = a[0] * b[1] - a[1] * b[0];

}

Problem

This implementation can lead to incorrect results when the input vectors a and b overlap with the output vector c.

Proposed Fix

To avoid this issue, I suggest using temporary variables to store intermediate results before assigning them to the output vector c. Below is the modified version of the template function:

template <class VectorT1, class VectorT2, class VectorT3> void vtkMath::Cross(VectorT1&& a, VectorT2&& b, VectorT3& c)

{

// Use temporary variables to store intermediate results

auto Cx = a[1] * b[2] - a[2] * b[1];

auto Cy = a[2] * b[0] - a[0] * b[2];

auto Cz = a[0] * b[1] - a[1] * b[0];

// Assign results to c

c[0] = Cx;

c[1] = Cy;

c[2] = Cz;

}