public static bool IsPointInPolygon(Point P, ConvexPolygon polygon)
{
for (int i = 0; i < polygon.Count; i++)
{
Point A = polygon[i];
Point B = polygon[(i + 1) % polygon.Count];
if ((B - A).CrossProductWith(P - A).IsLess(0))
{
return(false);
}
}
return(true);
}
public Point GetCenterOfMass()
{
var centerOfMass = new Point(0, 0);
double mass = 0;
for (int i = 1; i < (int)points.Count - 1; i++)
{
var A = points[0];
var B = points[i];
var C = points[i + 1];
var M = (A + B + C) / 3;
var currentMass = new ConvexPolygon(A, B, C).GetArea();
centerOfMass += M * currentMass;
mass += currentMass;
}
return(centerOfMass / mass);
}
public static Segment NearestEdgeFromPointToPolygon(Point P, ConvexPolygon polygon)
{
double distance = double.PositiveInfinity;
Segment nearest = null;
for (int i = 0; i < polygon.Count; i++)
{
Point A = polygon[i];
Point B = polygon[(i + 1) % polygon.Count];
double curDistance = P.DistanceToSegment(new Segment(A, B));
if (curDistance < distance)
{
distance = curDistance;
nearest = new Segment(A, B);
}
distance = Math.Min(distance, P.DistanceToSegment(new Segment(A, B)));
}
return(nearest);
}
public static ConvexPolygon IntersectPolygons(ConvexPolygon a, ConvexPolygon b)
{
var interestingPoints = new List <Point>().Concat(a).Concat(b).ToList();
for (int i = 0; i < a.Count; i++)
{
Point A = a[i], B = a[(i + 1) % a.Count];
for (int s = 0; s < b.Count; s++)
{
Point C = b[s], D = b[(s + 1) % b.Count];
Segment intersection = IntersectSegments(new Segment(A, B), new Segment(C, D));
if (intersection != null)
{
interestingPoints.Add(intersection.A);
interestingPoints.Add(intersection.B);
}
}
}
interestingPoints = interestingPoints.Where(p => a.ContainsPoint(p) && b.ContainsPoint(p)).ToList();
return(new ConvexPolygon(interestingPoints));
}
public static double DistanceFromPointToPolygon(Point P, ConvexPolygon polygon)
{
return(NearestEdgeFromPointToPolygon(P, polygon).DistanceToPoint(P));
}
public static bool IsPointOnPolygonBorder(Point P, ConvexPolygon polygon)
{
return(polygon.Where((t, i) => new Segment(t, polygon[(i + 1) % polygon.Count]).ContainsPoint(P)).Any());
}
public double DistanceToPolygon(ConvexPolygon polygon)
{
return(GeometryOperations.DistanceFromPointToPolygon(this, polygon));
}
public ConvexPolygon IntersectWithPolygon(ConvexPolygon other)
{
return(GeometryOperations.IntersectPolygons(this, other));
}