Method InterpolateDerivs

Common/DataModel/vtkLagrangeTriangle.cxx:116–198

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//------------------------------------------------------------------------------
void vtkLagrangeTriangle::InterpolateDerivs(const double pcoords[3], double* derivs)
{
  // Analytic differentiation of the triangle shape functions, as defined in
  // P. Silvester, "High-Order Polynomial Triangular Finite Elements for
  // Potential Problems". Int. J. Engng Sci. Vol. 7, pp. 849-861. Pergamon
  // Press, 1969. The generic method is valid for all orders, but we unroll the
  // first two orders to reduce computational cost.

  double tau[3] = { pcoords[0], pcoords[1], 1. - pcoords[0] - pcoords[1] };

  vtkIdType n = this->GetOrder();

  if (n == 1)
  {
    derivs[0] = -1;
    derivs[1] = 1;
    derivs[2] = 0;
    derivs[3] = -1;
    derivs[4] = 0;
    derivs[5] = 1;
  }
  else if (n == 2)
  {
#ifdef SEVEN_POINT_TRIANGLE
    if (this->GetPoints()->GetNumberOfPoints() == 7)
    {
      double tmr = tau[2] - tau[0];
      double tms = tau[2] - tau[1];
      derivs[0] = -1.0 + 3.0 * tau[1] * tmr - 2.0 * tmr + 2.0 * tau[1];
      derivs[1] = 1.0 + 3.0 * tau[1] * tmr - 2.0 * tmr - 2.0 * tau[1];
      derivs[2] = 3.0 * tau[1] * tmr;
      derivs[3] = 4.0 * tmr - 12.0 * tau[1] * tmr;
      derivs[4] = 4.0 * tau[1] - 12.0 * tau[1] * tmr;
      derivs[5] = -4.0 * tau[1] - 12.0 * tau[1] * tmr;
      derivs[6] = 27.0 * tau[1] * tmr;
      derivs[7] = -1.0 + 3.0 * tau[0] * tms - 2.0 * tms + 2.0 * tau[0];
      derivs[8] = 3.0 * tau[0] * tms;
      derivs[9] = 1.0 + 3.0 * tau[0] * tms - 2.0 * tms - 2.0 * tau[0];
      derivs[10] = -4.0 * tau[0] - 12.0 * tau[0] * tms;
      derivs[11] = 4.0 * tau[0] - 12.0 * tau[0] * tms;
      derivs[12] = 4.0 * tms - 12.0 * tau[0] * tms;
      derivs[13] = 27.0 * tau[0] * tms;
      return;
    }
#endif
    derivs[0] = 1.0 - 4.0 * tau[2];
    derivs[1] = 4.0 * tau[0] - 1.0;
    derivs[2] = 0.0;
    derivs[3] = 4.0 * (tau[2] - tau[0]);
    derivs[4] = 4.0 * tau[1];
    derivs[5] = -4.0 * tau[1];
    derivs[6] = 1.0 - 4.0 * tau[2];
    derivs[7] = 0.0;
    derivs[8] = 4.0 * tau[1] - 1.0;
    derivs[9] = -4.0 * tau[0];
    derivs[10] = 4.0 * tau[0];
    derivs[11] = 4.0 * (tau[2] - tau[1]);
  }