vtkPyramid / vtkQuadraticPyramid Inconsistencies

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Hi Folks,

I’ve got some questions regarding the pyramidal elements in vtk:

  1. First of all: Why is the GetParametricCenter() different in both cells, although they span the same domain:

    linear Pyra:
    pcoords[0] = pcoords[1] = 0.4;
    pcoords[2] = 0.2;

    quadr. Pyra:
    pcoords[0] = pcoords[1] = 6.0/13.0; // approx 0.46
    pcoords[2] = 3.0/13.0; // approx 0.23

Wouldn’t I expect that both cells have the same parametric center?

  1. Regarding the EvaluatePosition() method:
    If I look at how the initial position is chosen

    linear Pyra:
    // set initial position for Newton’s method
    double params[3] = {0.3333333, 0.3333333, 0.3333333};
    pcoords[0] = pcoords[1] = pcoords[2] = params[0];

    quadr. Pyra:
    // set initial position for Newton’s method
    pcoords[0] = pcoords[1] = pcoords[2] = 0.5;
    double params[3] = {0.5, 0.5, 0.5};

I wonder even more:

  • Why is the linear initial position set to 1./3. instead of the parametric center?
  • Why is the quadratic initial position set to 0.5 instead of the parametric center? Here I wonder even more because it looks like this point is located on the surface instead of the interior, correct?

Thanks for the help.