private void ComputeCirclePoints()
{
Coordinate[] pts;
// handle degenerate or trivial cases
if (_input.IsEmpty)
{
_extremalPts = new Coordinate[0];
return;
}
if (_input.NumPoints == 1)
{
pts = _input.Coordinates;
_extremalPts = new[] { pts[0].Copy() };
return;
}
/**
* The problem is simplified by reducing to the convex hull.
* Computing the convex hull also has the useful effect of eliminating duplicate points
*/
var convexHull = _input.ConvexHull();
// check for degenerate or trivial cases
var hullPts = convexHull.Coordinates;
// strip duplicate final point, if any
pts = hullPts;
if (hullPts[0].Equals2D(hullPts[hullPts.Length - 1]))
{
pts = new Coordinate[hullPts.Length - 1];
CoordinateArrays.CopyDeep(hullPts, 0, pts, 0, hullPts.Length - 1);
}
/**
* Optimization for the trivial case where the CH has fewer than 3 points
*/
if (pts.Length <= 2)
{
_extremalPts = CoordinateArrays.CopyDeep(pts);
return;
}
// find a point P with minimum Y ordinate
var P = LowestPoint(pts);
// find a point Q such that the angle that PQ makes with the x-axis is minimal
var Q = PointWitMinAngleWithX(pts, P);
/**
* Iterate over the remaining points to find
* a pair or triplet of points which determine the minimal circle.
* By the design of the algorithm,
* at most <tt>pts.length</tt> iterations are required to terminate
* with a correct result.
*/
for (int i = 0; i < pts.Length; i++)
{
var R = PointWithMinAngleWithSegment(pts, P, Q);
// if PRQ is obtuse, then MBC is determined by P and Q
if (AngleUtility.IsObtuse(P, R, Q))
{
_extremalPts = new Coordinate[] { P.Copy(), Q.Copy() };
return;
}
// if RPQ is obtuse, update baseline and iterate
if (AngleUtility.IsObtuse(R, P, Q))
{
P = R;
continue;
}
// if RQP is obtuse, update baseline and iterate
if (AngleUtility.IsObtuse(R, Q, P))
{
Q = R;
continue;
}
// otherwise all angles are acute, and the MBC is determined by the triangle PQR
_extremalPts = new Coordinate[] { P.Copy(), Q.Copy(), R.Copy() };
return;
}
Assert.ShouldNeverReachHere("Logic failure in Minimum Bounding Circle algorithm!");
}