Matsys: Chrysalis III Angle Sum

Grasshopper
11

It is quite easy to calculate but most of the time there is 2 solutions. So I choose to use curve intersection of RhinoCommon to make the calculations.

image
image.jpg695×739 102 KB

360deg_angle_polygon.gh (1.7 MB)

 /// <summary>
  /// Return points which have a 360° sum angle with the polygon points
  /// </summary>
  /// <param name="polyline">A closed polyline</param>
  /// <returns>The line</returns>
  public List<Point3d> GetFlatCenterOfPolyline(Polyline polyline)
  {
    //Center of polygon
    Point3d center = polyline.CenterPoint();
    //Plane used to have a normal
    Plane plane = Plane.Unset;
    PlaneFitResult plfit = Plane.FitPlaneToPoints(polyline, out plane);

    //Calculation of a typical length
    BoundingBox bb = polyline.BoundingBox;
    double length = bb.Diagonal.Length / 4;
    Line line = new Line(center + plane.ZAxis * length, center - plane.ZAxis * length);

    //For many points on a line calculate the angles sum
    List<Point3d> points = new List<Point3d> ();
    for (double d = 0; d < 1.0; d += 0.01)
    {
      points.Add(new Point3d(d, GetAngle(polyline, line.PointAt(d)), 0));
    }
    //The angle sum is a curve with the line parameter in abcisse (Y) and the angle sum in ordinate (Y)
    Curve curve = Curve.CreateInterpolatedCurve(points, 3);
    //A line at ordinate = 2 * PI
    Line line2 = new Line(new Point3d(0, Math.PI * 2, 0.0), new Point3d(1, Math.PI * 2, 0.0));
    //The intersection calculation
    CurveIntersections ci = Rhino.Geometry.Intersect.Intersection.CurveLine(curve, line2, 0.0001, 0.0001);

    List<Point3d> output = new List<Point3d> ();
    for (int i = 0; i < ci.Count; i++)
    {
      output.Add(line.PointAt(ci[i].ParameterB));
    }
    return output;
  }
  /// <summary>
  ///  Calculate the angle sum from vector from the point to the polyline point
  ///Polyline must be closed
  /// </summary>
  /// <param name="polyline"></param>
  /// <param name="point"></param>
  /// <returns></returns>
  public double GetAngle(Polyline polyline, Point3d point)
  {
    double angle = 0.0;
    for (int i = 0; i < (polyline.Count - 1);i++)
    {
      Vector3d v1 = polyline[i] - point;
      Vector3d v2 = polyline[i + 1] - point;
      angle += Vector3d.VectorAngle(v1, v2);
    }
    return angle;
  }
``
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