/// <summary>
/// Determines the squared distance between a point <paramref name="p"/> and a line segment defined by <paramref name="a"/> and <paramref name="b"/>.
/// </summary>
/// <param name="a">An end point of a segment.</param>
/// <param name="b">An end point of a segment.</param>
/// <param name="p">A point.</param>
/// <returns>Squared distance from a point to a line segment.</returns>
[Pure] public static double DistanceSquared(Point2 a, Point2 b, Point2 p)
{
Contract.Ensures(
Contract.Result <double>() >= 0.0 ||
Double.IsNaN(Contract.Result <double>()) ||
Double.IsPositiveInfinity(Contract.Result <double>()));
Point2.Order(ref a, ref b);
var d = b - a;
var v = p - a;
var aDot = d.Dot(v);
if (aDot <= 0)
{
return(v.GetMagnitudeSquared());
}
var dMag = d.GetMagnitudeSquared();
return(
(aDot >= dMag)
? (p - b).GetMagnitudeSquared()
: Math.Max(0, v.GetMagnitudeSquared() - ((aDot * aDot) / dMag))
);
}
/// <summary>
/// Determines if this line intersect another <paramref name="segment"/>.
/// </summary>
/// <param name="segment">A segment.</param>
/// <returns><c>true</c> when another object intersects this object.</returns>
public bool Intersects(Segment2 segment)
{
if (segment == null)
{
return(false);
}
var a = segment.A;
var b = segment.B;
Point2.Order(ref a, ref b);
var d0 = b - a;
var d1 = Direction;
var e = P - a;
var cross = (d0.X * d1.Y) - (d1.X * d0.Y);
if (cross == 0.0)
{
return((e.X * d0.Y) - (e.Y * d0.X) == 0.0);
}
var s = ((e.X * d1.Y) - (e.Y * d1.X)) / cross;
return(!(s < 0.0 || s > 1.0));
}
/// <summary>
/// Calculates the intersection geometry between this ray and a segment.
/// </summary>
/// <param name="segment">The segment to find the intersection with.</param>
/// <returns>The intersection geometry or <c>null</c> for no intersection.</returns>
public IPlanarGeometry Intersection(Segment2 segment)
{
if (segment == null)
{
return(null);
}
var a = segment.A;
var b = segment.B;
Point2.Order(ref a, ref b);
return(IntersectionSegment(a, b));
}
/// <inheritdoc/>
public IPlanarGeometry Intersection(Segment2 segment)
{
if (segment == null)
{
return(null);
}
var a = segment.A;
var b = segment.B;
Point2.Order(ref a, ref b);
var d0 = b - a;
var d1 = Direction;
var e = P - a;
var tNumerator = (e.X * d0.Y) - (e.Y * d0.X);
var cross = (d0.X * d1.Y) - (d1.X * d0.Y);
if (cross == 0.0)
{
// parallel
return(tNumerator == 0.0 ? new Segment2(a, b) : null);
}
// not parallel
var s = ((e.X * d1.Y) - (e.Y * d1.X)) / cross;
if (s < 0.0 || s > 1.0)
{
return(null); // not intersecting on this segment
}
if (s == 0.0)
{
return(a);
}
if (tNumerator == 0.0)
{
return(P);
}
return(a + d0.GetScaled(s)); // it must intersect at a point, so find where
}
/// <summary>
/// Determines the if a point <paramref name="p"/> intersects a line segment defined by <paramref name="a"/> and <paramref name="b"/>.
/// </summary>
/// <param name="a">An end point of a segment.</param>
/// <param name="b">An end point of a segment.</param>
/// <param name="p">A point.</param>
/// <returns>True when a point intersects a line segment.</returns>
[Pure] public static bool Intersects(Point2 a, Point2 b, Point2 p)
{
if (p.Equals(a) || p.Equals(b))
{
return(true);
}
Point2.Order(ref a, ref b);
var d = b - a;
var v = p - a;
var aDot = d.Dot(v);
return(
(aDot <= 0)
? (0 == v.X && 0 == v.Y)
: (
!(aDot >= d.GetMagnitudeSquared()) &&
(d.X * v.Y) - (d.Y * v.X) == 0.0
)
);
}