/// <summary>
/// Returns the signed distance (relative to the first segment) to the closest point on the second line segment.
/// </summary>
/// <param name="segment1Start">Segment 1 start point</param>
/// <param name="segment1End">Segment 1 end point</param>
/// <param name="segment2Start">Segment 2 start point</param>
/// <param name="segment2End">Segment 2 end point</param>
internal static float SignedDistanceFromSegmentToClosestPointOnOtherSegment(Vector2 segment1Start, Vector2 segment1End, Vector2 segment2Start, Vector2 segment2End)
{
var closestPoints = ClosestPointsBetweenSegments(segment1Start, segment1End, segment2Start, segment2End);
var cross = Vector2Util.Cross2D(closestPoints.SecondPoint - segment1Start, segment1End - segment1Start);
return(-Math.Sign(cross) * closestPoints.Distance);//- sign is to match with normal direction in Normal Util
}
/// <summary>
/// If a point is on the right-hand side of a segment.
/// </summary>
/// <param name="segmentStart">The segment start point.</param>
/// <param name="segmentEnd">The segment end point.</param>
/// <param name="point">The test point.</param>
internal static bool PointIsOnRightSide(Vector2 segmentStart, Vector2 segmentEnd, Vector2 point)
{
var segmentDiff = segmentEnd - segmentStart;
var pointDiff = point - segmentStart;
var cross = Vector2Util.Cross2D(pointDiff, segmentDiff);
return(cross >= 0f);
}
/// <summary>
/// Determines whether two 2D line segments (each defined by start and end points) intersect.
/// </summary>
/// <param name="segment1Start">Segment 1 start point</param>
/// <param name="segment1End">Segment 1 end point</param>
/// <param name="segment2Start">Segment 2 start point</param>
/// <param name="segment2End">Segment 2 end point</param>
/// <param name="intersectionPoint">Intersection point, if the segments intersect</param>
/// <param name="segmentFraction1">Fraction along first segment of the intersection, if the segments intersect</param>
/// <param name="segmentFraction2">Fraction along second segment of the intersection, if the segments intersect</param>
public static bool GetLineSegmentIntersection(Vector2 segment1Start, Vector2 segment1End, Vector2 segment2Start, Vector2 segment2End, out Vector2 intersectionPoint, out float segmentFraction1, out float segmentFraction2)
{
bool ret = false;
intersectionPoint = Vector2.zero;
segmentFraction1 = 0;
segmentFraction2 = 0;
var diff1 = segment1End - segment1Start;
var diff2 = segment2End - segment2Start;
var crossDiff1Diff2 = Vector2Util.Cross2D(diff1, diff2);
var vec1to2 = segment2Start - segment1Start;
var vec1To2CrossDiff1 = Vector2Util.Cross2D(vec1to2, diff1);
if (crossDiff1Diff2 == 0f)
{
if (vec1To2CrossDiff1 == 0f)
{
//collinear
var diff1MagSq = diff1.sqrMagnitude;
var diff2MagSq = diff2.sqrMagnitude;
var t0 = Vector2.Dot(vec1to2, diff1) / diff1MagSq;
var t1 = t0 + Vector2.Dot(diff1, diff2) / diff1MagSq;
var min = Mathf.Min(t0, t1);
var max = Mathf.Max(t0, t1);
if (min <= 1f && max >= 0f && diff1MagSq > 0f && diff2MagSq > 0f)
{
ret = true;
segmentFraction1 = 0.5f * (Mathf.Clamp01(min) + Mathf.Clamp01(max));
intersectionPoint = segment1Start + diff1 * segmentFraction1;
segmentFraction2 = Vector2.Dot(intersectionPoint - segment2Start, diff2);
}
else
{
//range does not intsersect [0:1]
}
}
else
{
//parallel, not collinear
ret = false;
}
}
else
{
var vec1To2CrossDiff2 = Vector2Util.Cross2D(vec1to2, diff2);
segmentFraction1 = vec1To2CrossDiff2 / crossDiff1Diff2;
segmentFraction2 = vec1To2CrossDiff1 / crossDiff1Diff2;
if (segmentFraction1 >= 0 && segmentFraction2 >= 0 && segmentFraction1 <= 1f && segmentFraction2 <= 1f)
{
ret = true;
intersectionPoint = segment1Start + diff1 * segmentFraction1;
}
}
return(ret);
}
/// <summary>
/// Determines if two segment tangent directions emanating from a common point intersect.
/// This does not take into account actual segment length or extrusion distance; only fractional distances are returned.
/// They will intersect if the segments are 'concave' with respect to the extrusion sign.
/// Note that the extrusion fraction for second tangent is negative that of the first.
/// </summary>
/// <param name="previousTangent">Tangent vector of previous segment.</param>
/// <param name="nextTangent">Tangent vector of next segment</param>
/// <param name="extrusionSign">Sign of the extrusion direction</param>
/// <param name="extrusionMagnitudeFractionFirstTangent">Fraction of extrusion magnitude along the first tangent direction that the intersection will occur.</param>
internal static bool DoNeighbouringSegmentTangentsFromCommonPointIntersect(Vector2 previousTangent, Vector2 nextTangent, float extrusionSign, out double extrusionMagnitudeFractionFirstTangent)
{
bool ret = false;
var cross = Vector2Util.Cross2D(nextTangent, previousTangent);
var dot = Vector2.Dot(previousTangent, nextTangent);
var sign = Mathf.Sign(extrusionSign);
if (cross == 0f)
{
extrusionMagnitudeFractionFirstTangent = 0f;
ret = false;
}
else
{
extrusionMagnitudeFractionFirstTangent = sign * (1f - dot) / cross;
ret = extrusionMagnitudeFractionFirstTangent <= 0f;
}
return(ret);
}
/// <summary> Returns closest point, distances, and handedness information about the closest point on a 2D segment to a test point. </summary>
/// <param name="segmentStart">Segment start point</param>
/// <param name="segmentEnd">Segment end point</param>
/// <param name="point">Test point</param>
/// <param name="closestPoint"> The closest point on the segment to the test point </param>
/// <param name="onRightSide">Whether the test point is on the right-hand side of the segment </param>
/// <param name="segmentFraction">Fraction along the segment of the closest point to the test point</param>
/// <param name="distance">Distance from the closest point to the test point</param>
/// <param name="perpendicularDistance">Perpendicular distance from the closest point to the test point</param>
/// <param name="tangentialDistance">Tangential distance from the closest point to the test point</param>
internal static void GetClosestPointToSegmentInformation(Vector2 segmentStart, Vector2 segmentEnd, Vector2 point, out Vector2 closestPoint, out bool onRightSide, out float segmentFraction, out float distance, out float perpendicularDistance, out float tangentialDistance)
{
var segmentDiff = segmentEnd - segmentStart;
Vector2 pointDiff = point - segmentStart;
var dot = Vector2.Dot(pointDiff, segmentDiff);
var segmentDiffMagSq = segmentDiff.sqrMagnitude;
if (segmentDiffMagSq == 0f)
{
onRightSide = true;
segmentFraction = 0f;
closestPoint = segmentStart;
distance = pointDiff.magnitude;
perpendicularDistance = distance;
tangentialDistance = distance;
}
else
{
var segmentMagnitude = segmentDiff.magnitude;
var segmentDirection = segmentDiff / segmentMagnitude;
segmentFraction = Mathf.Clamp01(dot / (segmentMagnitude * segmentMagnitude));
closestPoint = (segmentStart + segmentFraction * segmentDiff);
var closestPointDiff = point - closestPoint;
distance = closestPointDiff.magnitude;
var tangentialSignedDistance = Vector2.Dot(segmentDirection, closestPointDiff);
var perpendicularVector = closestPointDiff - tangentialSignedDistance * segmentDirection;
tangentialDistance = Mathf.Abs(tangentialSignedDistance);
perpendicularDistance = perpendicularVector.magnitude;
var cross = Vector2Util.Cross2D(pointDiff, segmentDiff);
onRightSide = cross >= 0f;
}
}