private static bool SegmentSegmentCollinear(Vector2 leftA, Vector2 leftB, Vector2 rightA, Vector2 rightB,
out IntersectionSegmentSegment2 intersection)
{
Vector2 leftDirection = leftB - leftA;
float projectionRA = Vector2.Dot(leftDirection, leftB - rightA);
if (Mathf.Abs(projectionRA) < Geometry.Epsilon)
{
// LB == RA
// LA------LB
// RA------RB
intersection = IntersectionSegmentSegment2.Point(leftB);
return(true);
}
if (projectionRA > 0)
{
// LB > RA
// LA------LB
// RARB
// RA--RB
// RA------RB
Vector2 pointB;
float projectionRB = Vector2.Dot(leftDirection, rightB - leftA);
if (projectionRB > leftDirection.sqrMagnitude)
{
pointB = leftB;
}
else
{
pointB = rightB;
}
intersection = IntersectionSegmentSegment2.Segment(rightA, pointB);
return(true);
}
// LB < RA
// LA------LB
// RA------RB
intersection = IntersectionSegmentSegment2.None();
return(false);
}
private static bool SegmentSegmentCollinear(Vector2 leftA, Vector2 leftB, float sqrLeftLength, Vector2 rightA, Vector2 rightB,
out IntersectionSegmentSegment2 intersection)
{
Vector2 leftDirection = leftB - leftA;
float rightAProjection = Vector2.Dot(leftDirection, rightA - leftB);
if (Mathf.Abs(rightAProjection) < Geometry.Epsilon)
{
// LB == RA
// LA------LB
// RA------RB
intersection = IntersectionSegmentSegment2.Point(leftB);
return(true);
}
if (rightAProjection < 0)
{
// LB > RA
// LA------LB
// RARB
// RA--RB
// RA------RB
Vector2 pointB;
float rightBProjection = Vector2.Dot(leftDirection, rightB - leftA);
if (rightBProjection > sqrLeftLength)
{
pointB = leftB;
}
else
{
pointB = rightB;
}
intersection = IntersectionSegmentSegment2.Segment(rightA, pointB);
return(true);
}
// LB < RA
// LA------LB
// RA------RB
intersection = IntersectionSegmentSegment2.None();
return(false);
}
/// <summary>
/// Computes an intersection of the segments
/// </summary>
public static bool SegmentSegment(Vector2 segment1A, Vector2 segment1B, Vector2 segment2A, Vector2 segment2B,
out IntersectionSegmentSegment2 intersection)
{
Vector2 from2ATo1A = segment1A - segment2A;
Vector2 direction1 = segment1B - segment1A;
Vector2 direction2 = segment2B - segment2A;
float sqrSegment1Length = direction1.sqrMagnitude;
float sqrSegment2Length = direction2.sqrMagnitude;
bool segment1IsAPoint = sqrSegment1Length < Geometry.Epsilon;
bool segment2IsAPoint = sqrSegment2Length < Geometry.Epsilon;
if (segment1IsAPoint && segment2IsAPoint)
{
if (segment1A == segment2A)
{
intersection = IntersectionSegmentSegment2.Point(segment1A);
return(true);
}
intersection = IntersectionSegmentSegment2.None();
return(false);
}
if (segment1IsAPoint)
{
if (PointSegment(segment1A, segment2A, direction2, sqrSegment2Length))
{
intersection = IntersectionSegmentSegment2.Point(segment1A);
return(true);
}
intersection = IntersectionSegmentSegment2.None();
return(false);
}
if (segment2IsAPoint)
{
if (PointSegment(segment2A, segment1A, direction1, sqrSegment1Length))
{
intersection = IntersectionSegmentSegment2.Point(segment2A);
return(true);
}
intersection = IntersectionSegmentSegment2.None();
return(false);
}
float denominator = VectorE.PerpDot(direction1, direction2);
float perpDot1 = VectorE.PerpDot(direction1, from2ATo1A);
float perpDot2 = VectorE.PerpDot(direction2, from2ATo1A);
if (Mathf.Abs(denominator) < Geometry.Epsilon)
{
// Parallel
if (Mathf.Abs(perpDot1) > Geometry.Epsilon || Mathf.Abs(perpDot2) > Geometry.Epsilon)
{
// Not collinear
intersection = IntersectionSegmentSegment2.None();
return(false);
}
// Collinear
bool codirected = Vector2.Dot(direction1, direction2) > 0;
if (codirected)
{
// Codirected
float segment2AProjection = -Vector2.Dot(direction1, from2ATo1A);
if (segment2AProjection > -Geometry.Epsilon)
{
// 1A------1B
// 2A------2B
return(SegmentSegmentCollinear(segment1A, segment1B, sqrSegment1Length, segment2A, segment2B, out intersection));
}
else
{
// 1A------1B
// 2A------2B
return(SegmentSegmentCollinear(segment2A, segment2B, sqrSegment2Length, segment1A, segment1B, out intersection));
}
}
else
{
// Contradirected
float segment2BProjection = Vector2.Dot(direction1, segment2B - segment1A);
if (segment2BProjection > -Geometry.Epsilon)
{
// 1A------1B
// 2B------2A
return(SegmentSegmentCollinear(segment1A, segment1B, sqrSegment1Length, segment2B, segment2A, out intersection));
}
else
{
// 1A------1B
// 2B------2A
return(SegmentSegmentCollinear(segment2B, segment2A, sqrSegment2Length, segment1A, segment1B, out intersection));
}
}
}
// Not parallel
float distance1 = perpDot2 / denominator;
if (distance1 < -Geometry.Epsilon || distance1 > 1 + Geometry.Epsilon)
{
intersection = IntersectionSegmentSegment2.None();
return(false);
}
float distance2 = perpDot1 / denominator;
if (distance2 < -Geometry.Epsilon || distance2 > 1 + Geometry.Epsilon)
{
intersection = IntersectionSegmentSegment2.None();
return(false);
}
intersection = IntersectionSegmentSegment2.Point(segment1A + direction1 * distance1);
return(true);
}
/// <summary>
/// Computes an intersection of the segments
/// </summary>
public static bool SegmentSegment(Vector2 segment1A, Vector2 segment1B, Vector2 segment2A, Vector2 segment2B,
out IntersectionSegmentSegment2 intersection)
{
Vector2 from2ATo1A = segment1A - segment2A;
Vector2 direction1 = segment1B - segment1A;
Vector2 direction2 = segment2B - segment2A;
float denominator = VectorE.PerpDot(direction1, direction2);
float perpDot1 = VectorE.PerpDot(direction1, from2ATo1A);
float perpDot2 = VectorE.PerpDot(direction2, from2ATo1A);
if (Mathf.Abs(denominator) < Geometry.Epsilon)
{
// Parallel
if (Mathf.Abs(perpDot1) > Geometry.Epsilon || Mathf.Abs(perpDot2) > Geometry.Epsilon)
{
// Not collinear
intersection = IntersectionSegmentSegment2.None();
return(false);
}
// Collinear or degenerate
bool segment1IsAPoint = direction1.sqrMagnitude < Geometry.Epsilon;
bool segment2IsAPoint = direction2.sqrMagnitude < Geometry.Epsilon;
if (segment1IsAPoint && segment2IsAPoint)
{
if (segment1A == segment2A)
{
intersection = IntersectionSegmentSegment2.Point(segment1A);
return(true);
}
intersection = IntersectionSegmentSegment2.None();
return(false);
}
if (segment1IsAPoint)
{
if (CollinearPointInSegment(segment2A, segment2B, point: segment1A))
{
intersection = IntersectionSegmentSegment2.Point(segment1A);
return(true);
}
intersection = IntersectionSegmentSegment2.None();
return(false);
}
if (segment2IsAPoint)
{
if (CollinearPointInSegment(segment1A, segment1B, point: segment2A))
{
intersection = IntersectionSegmentSegment2.Point(segment2A);
return(true);
}
intersection = IntersectionSegmentSegment2.None();
return(false);
}
bool codirected = Vector2.Dot(direction1, direction2) > 0;
if (codirected)
{
// Codirected
float projectionFrom2ATo1A = Vector2.Dot(direction1, from2ATo1A);
if (projectionFrom2ATo1A > 0)
{
// 2A------2B
// 1A------1B
return(SegmentSegmentCollinear(segment2A, segment2B, segment1A, segment1B, out intersection));
}
else
{
// 1A------1B
// 2A------2B
return(SegmentSegmentCollinear(segment1A, segment1B, segment2A, segment2B, out intersection));
}
}
else
{
// Contradirected
float projectionFrom1ATo2B = Vector2.Dot(direction1, segment2B - segment1A);
if (projectionFrom1ATo2B > 0)
{
// 1A------1B
// 2B------2A
return(SegmentSegmentCollinear(segment1A, segment1B, segment2B, segment2A, out intersection));
}
else
{
// 2B------2A
// 1A------1B
return(SegmentSegmentCollinear(segment2B, segment2A, segment1A, segment1B, out intersection));
}
}
}
// The segments are skew
float distance1 = perpDot2 / denominator;
if (distance1 < -Geometry.Epsilon || distance1 > 1 + Geometry.Epsilon)
{
intersection = IntersectionSegmentSegment2.None();
return(false);
}
float distance2 = perpDot1 / denominator;
if (distance2 < -Geometry.Epsilon || distance2 > 1 + Geometry.Epsilon)
{
intersection = IntersectionSegmentSegment2.None();
return(false);
}
intersection = IntersectionSegmentSegment2.Point(segment1A + direction1 * distance1);
return(true);
}