/// <summary>
/// Create a rectangle from two sides of a triangle.
/// </summary>
/// <param name="a">First point.</param>
/// <param name="b">Second point.</param>
/// <param name="c">third point.</param>
/// <returns>Rectangle.</returns>
private static Rectangle3d CreateTwoSidedRectangle(Point3d a, Point3d b, Point3d c)
{
Vector3d ba = a - b;
Vector3d bc = c - b;
Vector3d ac = c - a;
if (ba.IsZero)
{
return(CreateDegenerateRectangle(a, c));
}
if (bc.IsZero)
{
return(CreateDegenerateRectangle(a, b));
}
if (ac.IsZero)
{
return(CreateDegenerateRectangle(a, b));
}
double lba = ba.Length;
double lbc = bc.Length;
Plane plane;
if (lba > lbc)
{
plane = new Plane(b, ba, bc);
}
else
{
plane = new Plane(b, bc, ba);
plane.Flip();
}
return(new Rectangle3d(plane, new Interval(0, lba), new Interval(0, lbc)));
}
/// <summary>
/// Attempts to create a rectangle from a polyline. This method only works well for
/// polylines that already closely resemble rectangles. If the polyline contains
/// more than four vertices, the least significant ones will be ignored. If the
/// polylines is non-orthogonal, the discrepancies will be averaged away.
/// This method should not be used as a Rectangle fitter.
/// </summary>
/// <param name="polyline">Polyline to parse.</param>
/// <param name="deviation">On success, the deviation will contain the largest deviation between the polyline and the rectangle.</param>
/// <param name="angleDeviation">On success, the angleDeviation will contain the largest deviation (in radians) between the polyline edges and the rectangle edges.</param>
/// <returns>A rectangle that is shaped similarly to the polyline or Rectangle3d.Unset
/// if the polyline does not represent a rectangle.</returns>
public static Rectangle3d CreateFromPolyline(IEnumerable <Point3d> polyline, out double deviation, out double angleDeviation)
{
if (polyline == null)
{
throw new ArgumentNullException(nameof(polyline));
}
deviation = 0.0;
angleDeviation = 0.0;
// Remove consecutive identical vertices.
Point3d prev = Point3d.Unset;
List <Point3d> points = new List <Point3d>();
foreach (Point3d point in polyline)
{
if (point == prev)
{
continue;
}
if (!point.IsValid)
{
continue;
}
points.Add(point);
prev = point;
}
// Remove closing vertex.
if (points.Count > 1 && points[0] == points[points.Count - 1])
{
points.RemoveAt(points.Count - 1);
}
// Special degenerate cases.
if (points.Count == 0)
{
return(Unset);
}
if (points.Count == 1)
{
return(CreateDegenerateRectangle(points[0], points[0]));
}
if (points.Count == 2)
{
return(CreateDegenerateRectangle(points[0], points[1]));
}
if (points.Count == 3)
{
points.Add(points[0] + (points[2] - points[1]));
}
if (points.Count > 5)
{
RecursiveReduceVertices(points);
}
Point3d centre = 0.25 * (points[0] + points[1] + points[2] + points[3]);
Vector3d xaxis = (points[1] - points[0]) + (points[2] - points[3]);
Vector3d yaxis = (points[3] - points[0]) + (points[2] - points[1]);
bool flip = false;
if (xaxis.Length < yaxis.Length)
{
flip = true;
Vector3d cache = xaxis;
xaxis = yaxis;
yaxis = cache;
}
Plane plane = new Plane(centre, xaxis, yaxis);
if (flip)
{
plane.Flip();
}
double x0, x1, x2, x3;
double y0, y1, y2, y3;
plane.ClosestParameter(points[0], out x0, out y0);
plane.ClosestParameter(points[1], out x1, out y1);
plane.ClosestParameter(points[2], out x2, out y2);
plane.ClosestParameter(points[3], out x3, out y3);
Interval xdomain = new Interval(0.5 * x0 + 0.5 * x3, 0.5 * x1 + 0.5 * x2);
Interval ydomain = new Interval(0.5 * y0 + 0.5 * y1, 0.5 * y2 + 0.5 * y3);
Rectangle3d rec = new Rectangle3d(plane, xdomain, ydomain);
ComputeDeviation(rec, points, out deviation, out angleDeviation);
return(rec);
}