import bpy


tree = bpy.data.materials['Material'].node_tree

def create_nodegroup():
    
    # create node group
    my_new_Group = bpy.data.node_groups.new('My_New_Group', 'ShaderNodeTree')

    # input
    mngInputs = my_new_Group.nodes.new('NodeGroupInput')
    mngInputs.location = (0,0)
    my_new_Group.inputs.new('NodeSocketFloat','my scale input')

    # output
    mngOutputs = my_new_Group.nodes.new('NodeGroupOutput')
    mngOutputs.location = (500,0)
    my_new_Group.outputs.new('NodeSocketFloat','my float output')
    my_new_Group.outputs.new('NodeSocketColor','my color output')



    # node in nodegroup
    texnode = my_new_Group.nodes.new('ShaderNodeTexWave')
    texnode.location = (200,0)
    
    # connect nodes
    my_new_Group.links.new(mngInputs.outputs[0],texnode.inputs[0])
    my_new_Group.links.new(texnode.outputs['Color'],mngOutputs.inputs['my color output'])
    
    return my_new_Group

################################################################
###################### Add New Node Group ######################
################################################################
groupnode = tree.nodes.new(type='ShaderNodeGroup')
groupnode.node_tree = create_nodegroup()

template<typename real_t>
inline bool isInTheTriangle(
  real_t px,  real_t py,
  real_t p0x, real_t p0y,
  real_t p1x, real_t p1y,
  real_t p2x, real_t p2y
) {
  real_t Area = 0.5 * (-p1y * p2x + p0y * (-p1x + p2x) + p0x * (p1y - p2y) + p1x * p2y);

  real_t s = 1.0 / (2.0 * Area) * (p0y * p2x - p0x * p2y + (p2y - p0y) * px + (p0x - p2x) * py);
  real_t t = 1.0 / (2.0 * Area) * (p0x * p1y - p0y * p1x + (p0y - p1y) * px + (p1x - p0x) * py);

  if (

    (0 < s) && (s < 1) &&
    (0 < t) && (t < 1) &&
    (0 < (1 - s - t)) &&
    ((1 - s - t) < 1)

    ) {
    return true;
  }
  else {
    return false;
  }
}

//! @brief 外接円を求める
//! @param [out] x 外接円の中心のx座標
//! @param [out] y 外接円の中心のy座標
//! @param [out] r 外接円の半径
//! @param [in] x1 三角形の第一頂点のx座標
//! @param [in] y1 三角形の第一頂点のy座標
//! @param [in] x2 三角形の第二頂点のx座標
//! @param [in] y2 三角形の第二頂点のy座標
//! @param [in] x3 三角形の第三頂点のx座標
//! @param [in] y3 三角形の第三頂点のy座標
//! @return なし
inline void Circumscribed_Circle(
  double* x,
  double* y,
  double* r,
  const double x1,
  const double y1,
  const double x2,
  const double y2,
  const double x3,
  const double y3
) {

  double xT =
    (y3 - y1) * (x2 * x2 - x1 * x1 + y2 * y2 - y1 * y1) +
    (y1 - y2) * (x3 * x3 - x1 * x1 + y3 * y3 - y1 * y1);
  double yT =
    (x1 - x3) * (x2 * x2 - x1 * x1 + y2 * y2 - y1 * y1) +
    (x2 - x1) * (x3 * x3 - x1 * x1 + y3 * y3 - y1 * y1);

  double c = 2 * ((x2 - x1) * (y3 - y1) - (y2 - y1) * (x3 - x1));

  *x = xT / c;
  *y = yT / c;

  *r = sqrt( (*x - x1) * (*x - x1) + (*y - y1) * (*y - y1) );
}