/// <returns>
/// the intersection of the two lines if it is a point, or <c>null</c> otherwise
/// </returns>
public static Point2D?PointIntersectionWithLine(this BoundaryLine2D line1, Line2D line2)
{
var dotProduct = line1.HalfPlane.DirectionTowardInterior.DotProduct(line2.Direction);
if (Math.Abs(dotProduct) <= Unit.ZeroDotProductTolerance)
{
// The lines are approximately parallel.
return(null);
}
return(line1.PointIntersectionWithLineUnstable(line2.GetPortSide().Boundary));
}
/// <returns>
/// the point intersection of the two lines, even if the lines are nearly parallel
/// </returns>
public static Point2D PointIntersectionWithLineUnstable(this BoundaryLine2D line1, BoundaryLine2D line2)
{
var dotProduct =
line1.HalfPlane.DirectionTowardInterior.DotProduct(line2.HalfPlane.DirectionHavingInteriorOnPortSide);
// If both lines pass through the origin, then the intersection is the origin. Otherwise, if a line is
// displaced from the origin, we need to adjust the intersection point. The first term below is the
// adjustment we need to apply to account for the offset from the origin of line1, and the second term is
// the adjustment we need to account for the offset from the origin of line2.
return
(new Point2D(
line2.HalfPlane.DirectionHavingInteriorOnPortSide.ToVector(
line1.HalfPlane.OffsetFromOrigin / dotProduct
) - line1.HalfPlane
.DirectionHavingInteriorOnPortSide
.ToVector(line2.HalfPlane.OffsetFromOrigin / dotProduct)));
}
public static IEnumerable <Point2D> IntersectWithLine(this Circle2D circle, BoundaryLine2D line)
{
var offsetToCenter = line.HalfPlane.GetOffsetFromBoundaryTowardInside(circle.Center);
if (!(offsetToCenter.AbsoluteValue() <= circle.Radius))
{
return(Enumerable.Empty <Point2D>());
}
var intersectionOfLineWithPerpendicularRadius =
circle.Center + line.HalfPlane.DirectionTowardInterior.ToVector(-offsetToCenter);
var distanceFromPerpendicularRadiusToIntersectionsSquared =
circle.Radius.Square() - offsetToCenter.Square();
// If it's negative, the line doesn't quite intersect the circle.
if (distanceFromPerpendicularRadiusToIntersectionsSquared > Unit.ZeroArea)
{
var distanceFromPerpendicularRadiusToIntersections =
distanceFromPerpendicularRadiusToIntersectionsSquared.SquareRoot();
var intersectionPoints =
line
.ParallelDirections
.Select(direction =>
intersectionOfLineWithPerpendicularRadius
+ direction.ToVector(distanceFromPerpendicularRadiusToIntersections))
.ToList();
if (intersectionPoints.DistinctEquatable().Count() > 1)
{
return(intersectionPoints);
}
}
return(intersectionOfLineWithPerpendicularRadius.Singleton());
}
public static Either <Null, Point2D, Segment2D> IntersectWithLine(this Segment2D segment, BoundaryLine2D line)
{
var baseOffset = line.HalfPlane.GetOffsetFromBoundaryTowardInside(segment.BasePoint);
var endOffset = line.HalfPlane.GetOffsetFromBoundaryTowardInside(segment.EndPoint);
var lineContainsBase = baseOffset == Unit.ZeroDistance;
var lineContainsEnd = endOffset == Unit.ZeroDistance;
if (lineContainsBase && lineContainsEnd)
{
return(segment);
}
if (baseOffset.Sign() != endOffset.Sign())
{
return(segment.AsLine().PointIntersectionWithLineUnstable(line));
}
if (lineContainsBase)
{
return(segment.BasePoint);
}
if (lineContainsEnd)
{
return(segment.EndPoint);
}
return(Null.Instance);
}
/// <returns> /// the point intersection of the two lines, even if the lines are nearly parallel /// </returns> public static Point2D PointIntersectionWithLineUnstable(this Line2D line1, BoundaryLine2D line2) => line1.AsBoundaryLine().PointIntersectionWithLineUnstable(line2);
public static Distance DistanceTo(this Point2D point, BoundaryLine2D line) => line.HalfPlane.GetOffsetFromBoundaryTowardInside(point).AbsoluteValue();