Method Circumcircle

Common/DataModel/vtkTriangle.cxx:805–865

------------------------------------------------------------------------------ Compute the circumcenter (center[3]) and radius squared (method return value) of a triangle defined by the three points x1, x2, and x3. (Note that the coordinates are 2D. 3D points can be used but the z-component will be ignored.)

// x3. (Note that the coordinates are 2D. 3D points can be used but
// the z-component will be ignored.)
double vtkTriangle::Circumcircle(
  const double x1[2], const double x2[2], const double x3[2], double center[2])
{
  double n12[2], n13[2], x12[2], x13[2];
  double *A[2], rhs[2], diff;

  //  calculate normals and intersection points of bisecting planes.
  //
  for (int i = 0; i < 2; i++)
  {
    n12[i] = x2[i] - x1[i];
    n13[i] = x3[i] - x1[i];
    x12[i] = (x2[i] + x1[i]) / 2.0;
    x13[i] = (x3[i] + x1[i]) / 2.0;
  }

  //  Compute solutions to the intersection of two bisecting lines
  //  (2-eqns. in 2-unknowns).
  //
  //  form system matrices
  //
  A[0] = n12;
  A[1] = n13;

  rhs[0] = vtkMath::Dot2D(n12, x12);
  rhs[1] = vtkMath::Dot2D(n13, x13);

  // Solve system of equations
  //
  if (vtkMath::SolveLinearSystem(A, rhs, 2) == 0)
  {
    center[0] = center[1] = 0.0;
    return VTK_DOUBLE_MAX;
  }
  else
  {
    center[0] = rhs[0];
    center[1] = rhs[1];
  }

  // determine average value of radius squared
  double sum = 0.0;
  for (int i = 0; i < 2; i++)
  {
    diff = x1[i] - center[i];
    sum += diff * diff;
    diff = x2[i] - center[i];
    sum += diff * diff;
    diff = x3[i] - center[i];
    sum += diff * diff;
  }

  if ((sum /= 3.0) > VTK_DOUBLE_MAX)
  {
    return VTK_DOUBLE_MAX;
  }
  else
  {