/// <summary>
/// Find the distance from a point to a line segment. This is done by projecting the vector
/// from point to segment.PointA onto the line segment, then calculating the distance between
/// the projected point and original point.
/// @param segment - the line segment
/// @param point - the point
/// @out projectedPoint - vector point -> segment.PointA projected onto segment
/// @out projectedLineLength - the length of vector point -> segment.PointA
/// @returns the distance between point and projectedPoint
/// </summary>
public static float FindDistanceToPoint(
LineSegment2D segment,
Vector2 point,
out Vector2 projectedPoint,
out float projectedLineLength)
{
Vector2 segmentVector = segment.ToVector2();
Vector2 projectingVector = point - segment.PointA;
float dotProduct = Mathf.Infinity;
Vector2 projectedVector = segmentVector.Project(projectingVector, out dotProduct);
projectedPoint = segment.PointA + projectedVector;
projectedLineLength = projectedVector.magnitude;
return(Vector2.Distance(projectedPoint, point));
}
/// <summary>
/// Determine if a point is inside a segment
/// @param P - point
/// @param S - collinear segment
/// @returns - 0 = P is not inside S
/// 1 = P is inside S
/// </summary>
public static int ContainsPoint(Vector2 P, LineSegment2D S)
{
// S is not vertical
if (S.PointA.x != S.PointB.x)
{
if ((S.PointA.x <= P.x && P.x <= S.PointB.x) ||
(S.PointA.x >= P.x && P.x >= S.PointB.x))
{
return(1);
}
}
// S is vertical, so test y coordinate
else
{
if ((S.PointA.y <= P.y && P.y <= S.PointB.y) ||
(S.PointA.y >= P.y && P.y >= S.PointB.y))
{
return(1);
}
}
return(0);
}
/// <summary>
/// Check whether two finite line segments intersect.
/// NOTE: The out values may not always exist.
/// @param segmentA - Finite line segment.
/// @param segmentB - Finite line segment.
/// @out i0 - Intersection point (if it exists)
/// @out i1 - Intersection end point (if the segments overlap)
/// @returns - 0: Disjointed, no intersection.
/// 1: Intersection at unique point 'intersectPoint'.
/// 2: Overlapping segments from 'intersectPoint' to 'intersectEndpoint'.
/// </summary>
public static int CheckIntersection(
LineSegment2D segmentA,
LineSegment2D segmentB,
out Vector2 i0,
out Vector2 i1)
{
Vector2 u = segmentA.PointB - segmentA.PointA;
Vector2 v = segmentB.PointB - segmentB.PointA;
Vector2 w = segmentA.PointA - segmentB.PointA;
float D = ArePerpindicular(u, v);
i0 = Vector2.zero;
i1 = Vector2.zero;
// test if they are parallel (includes either being a point)
if (Mathf.Abs(D) < 0.01f)
{
// segmentA and segmentB are parallel
// test if they are NOT collinear
if (ArePerpindicular(u, w) != 0 || ArePerpindicular(v, w) != 0)
{
return(0);
}
// they are collinear or degenerate
// check if they are degenerate points
float du = Vector2.Dot(u, u);
float dv = Vector2.Dot(v, v);
// both segments are points
if (du == 0 && dv == 0)
{
// they are distinct points
if (segmentA.PointA != segmentB.PointA)
{
return(0);
}
// they are the same point
i0 = segmentA.PointA;
return(1);
}
// test if segmentA is a single point
if (du == 0)
{
// but is not in segmentB
if (ContainsPoint(segmentA.PointA, segmentB) == 0)
{
return(0);
}
i0 = segmentA.PointA;
return(1);
}
// test if segmentB is a single point
if (dv == 0)
{
// but is not in segmentA
if (ContainsPoint(segmentB.PointA, segmentA) == 0)
{
return(0);
}
i0 = segmentB.PointA;
return(1);
}
// they are collinear segments - test for overlap (or not)
// endpoints of segmentA in eqn for segmentB
float t0, t1;
Vector2 w2 = segmentA.PointB - segmentB.PointA;
if (v.x != 0)
{
t0 = w.x / v.x;
t1 = w2.x / v.x;
}
else
{
t0 = w.y / v.y;
t1 = w2.y / v.y;
}
// must have t0 smaller than t1
// swap if not
if (t0 > t1)
{
float t = t0;
t0 = t1;
t1 = t;
}
if (t0 > 1 || t1 < 0)
{
// NO overlap
return(0);
}
t0 = t0 < 0 ? 0 : t0; // clip to min 0
t1 = t1 > 1 ? 1 : t1; // clip to max 1
if (t0 == t1)
{
// intersect is a point
i0 = segmentB.PointA + t0 * v;
return(1);
}
// they overlap in a valid subsegment
i0 = segmentB.PointA + t0 * v;
i1 = segmentB.PointA + t1 * v;
return(2);
}
// the segments are skew and may intersect in a point
// get the intersect parameter for segmentA
float sI = ArePerpindicular(v, w) / D;
// no intersect with segmentA
if (sI < 0 || sI > 1)
{
return(0);
}
// get the intersect parameter for segmentB
float tI = ArePerpindicular(u, w) / D;
// no intersect with segmentB
if (tI < 0 || tI > 1)
{
return(0);
}
// compute segmentA intersect point
i0 = segmentA.PointA + sI * u;
return(1);
}
/// <summary>
/// Calculate the smallest difference in angles between two line segments, in degrees.
/// @param a - line segment
/// @param b - line segment
/// @returns - the smallest angle between the line segments
/// </summary>
public static float MinimumAngleDifferenceInDegrees(LineSegment2D a, LineSegment2D b)
{
float diff = Mathf.Abs(a.DirectionInDegrees - b.DirectionInDegrees) % 180f;
return(Mathf.Min(diff, Mathf.Abs(diff - 180f)));
}
