/// <summary>
/// Populate the Subdivision member with a spatial hierarchical structure that helps locate an extreme vertex in
/// log(Vertices_Number) steps
///
/// The arguments that start the recursion should be (0 ,total_vertices) and correspond to polygon edge normals
/// that define a sub-piece of the unit disc
/// </summary>
/// <param name="start"></param>
/// <param name="end"></param>
/// <returns></returns>
private Polygon_Tree_Node Subdivide(int start, int end)
{
bool is_subdivision_direction = true;
//this is what will be returned upwards the recursion
var node = new Polygon_Tree_Node(this);
//this predicate means we've reached a node that is just supposed to add 2 vertex leaf nodes and return
if (end - start == 1)
{
node.code = start;
var left_vertex_node = new Polygon_Tree_Node(this);
left_vertex_node.code = this.Vertex(end);
node.link_l = left_vertex_node;
var right_vertex_node = new Polygon_Tree_Node(this);
right_vertex_node.code = this.Vertex(start);
node.link_r = right_vertex_node;
return node;
}
//in the recursion's main case we just find the middle normal in this subpiece of the unit disc
// (the middle in the sense of the sequence defined by the polygon edges outwards normals starting
// at the vertex 0 - vertex 1 edge and going ccw)
// then recursively call the function on the 2 sub pieces defined by start,middle middle, end
var middle = Helper.Middle(start, end);
node.left_part_start_normal = start;
node.left_part_end_normal = middle;
node.right_part_end_normal = end;
node.code = middle;
node.link_l = Subdivide(start, middle);
node.link_r = Subdivide(middle, end);
node.division_direction = is_subdivision_direction;
return node;
}
/// <summary>
/// Uses the specified points to initialize the polygon's data
/// </summary>
/// <param name="points_inserted"></param>
public void Set(List<Vector3> points_inserted)
{
vertices_no = points_inserted.Count;
if (points_inserted.Count < 3) throw new Exception("not enough points to make a polygon");
var winding = Vector3.Cross(points_inserted[0], points_inserted[1]).Z;
if (winding < 0)
for (int i = 0; i < points_inserted.Count; i++) points_inserted[i] = new Vector3(-points_inserted[i].X, points_inserted[i].Y, 0);
Points.Clear();
Normals.Clear();
Angles.Clear();
for (int i = 0; i < points_inserted.Count; i++)
{
Points.Add(points_inserted[i]);
}
for (int i = 0; i < Points.Count - 1; i++)
{
var point1 = Points[i];
var point2 = Points[i + 1];
var vec = point2 - point1;
var normal = Vector3.Cross(vec, Vector3.Backward);
normal.Normalize();
Normals.Add(normal);
}
var point1_ = Points[Points.Count - 1];
var point2_ = Points[0];
var vec_ = point2_ - point1_;
var normal_ = Vector3.Cross(vec_, Vector3.Backward);
normal_.Normalize();
Normals.Add(normal_);
var TwoPi = (float)(2 * Math.PI);
var begin_angle = Helper.Get_Zero_Two_Pi_Angle(Normals[0]);
Beginning_Normal_Angle = begin_angle;
for (int i = 0; i < Normals.Count; i++)
{
var angle = Helper.Get_Zero_Two_Pi_Angle(Normals[i]);
angle = Helper.Fix_Angle(angle, begin_angle);
angle -= begin_angle;
Angles.Add(angle);
}
Angles.Add(TwoPi);
var res = Subdivide(0, vertices_no);
this.Subdivision = res;
}