/// <summary> Calculates the point of intersection. Returns NaN when the specified lines are parallel. </summary>
protected static Point FindExtrapolatedIntersection(Line line1, Line line2)
{
if (line1.IsParallelTo(line2))
{
return(new Point(float.NaN, float.NaN));
}
var x = (line2.LinearAddend - line1.LinearAddend) / (line1.LinearCoefficient - line2.LinearCoefficient);
Contract.Assert(FloatingTypeEqualityComparisonHelper.EqualByTolerance(line1.GetYValueAt(x), line2.GetYValueAt(x)), "bug in line above");
return(new Point(x, line1.GetYValueAt(x)));
}
/// <summary> Gets the linear coefficient and linear addend, respectively, for a line intersecting the two specified points. </summary>
private static Tuple <double, double> GetLinearCoefficientAndAddend(Point a, Point b)
{
double linearCoefficient, linearAddend;
if (FloatingTypeEqualityComparisonHelper.EqualByTolerance(a.X, b.X))
{
linearCoefficient = a.Y < b.Y ? float.NegativeInfinity : float.PositiveInfinity;
linearAddend = float.NaN;
}
else
{
linearCoefficient = (b.Y - a.Y) / (b.X - a.X);
linearAddend = a.Y - a.X * linearCoefficient;
}
return(new Tuple <double, double>(linearCoefficient, linearAddend));
}
/// <summary> Returns whether this line contains the specified point. </summary>
public virtual bool Contains(Point point)
{
return(FloatingTypeEqualityComparisonHelper.EqualByTolerance(LinearAddend + LinearCoefficient * point.X, point.Y));
}
/// <summary> Gets whether the specified line is parallel or antiparallel to this line. </summary>
public bool IsParallelTo(Line other)
{
return(FloatingTypeEqualityComparisonHelper.EqualByTolerance(Math.Abs(other.LinearCoefficient), Math.Abs(this.LinearCoefficient)));
}
/// <summary> Determines whether the specified line is equal to the current. </summary>
public virtual bool Equals(Line other)
{
return(FloatingTypeEqualityComparisonHelper.EqualByTolerance(this.LinearCoefficient, other.LinearCoefficient) &&
FloatingTypeEqualityComparisonHelper.EqualByTolerance(this.LinearAddend, other.LinearAddend));
}
/// <summary> Returns whether this line segment contains the specified point. </summary>
public override bool Contains(Point point)
{
return(base.Contains(point) && //the base case returns whether the point lies on (the extrapolation of) this line segment
FloatingTypeEqualityComparisonHelper.InToleranceInterval(point.X, this.A.X, this.B.X) && // point.X ∈ (-ε + min(A.X, B.X), max(A.X, B.X) + ε)
FloatingTypeEqualityComparisonHelper.InToleranceInterval(point.X, this.A.X, this.B.X)); // point.Y ∈ (-ε + min(A.Y, B.Y), max(A.Y, B.Y) + ε)
}
