/// <summary>Returns true if this point lies between the lines or on either line.</summary>
/// <exception cref='ArgumentException'>Lines A and B must be parallel.</exception>
/// <exception cref='ArgumentException'>Lines A and B cannot be coincidental. (They must be different lines.)</exception>
public bool Between(WLine lineA, WLine lineB)
{
if (!lineA.Parallel(lineB))
{
throw new ArgumentException("Lines A and B must be parallel.");
}
if (lineA.Coincidental(lineB))
{
throw new ArgumentException("Lines A and B cannot be coincidental. (They must be different lines.)");
}
//vertical lines - just check the X value
if (lineA.IsVertical)
{
return(this.X >= Math.Min(lineA.A.X, lineB.A.X) && this.X <= Math.Max(lineA.A.X, lineB.A.X));
}
//horizontal lines - just check the Y value
if (lineA.IsHorizontal)
{
return(this.Y >= Math.Min(lineA.A.Y, lineB.A.Y) && this.Y <= Math.Max(lineA.A.Y, lineB.A.Y));
}
//otherwise
//find vertical line through "this" point
//if it intersects one line higher than "this" (or equal to it) and the other line lower than "this" (or equal to it), then "this" is between the lines
WLine verticalLine = WLine.Vertical(this);
return(false);
}
/// <returns>Null (no intercepts), or array of length 1 or 2.</returns>
public WPoint[] GetIntersectionPoints(WLine line)
{
//line does not intersect if perpendicular line from circle-center to line is longer than circle-radius
WPoint perpendicularToCenter = line.GetPerpendicularIntersect(Center);
if (perpendicularToCenter.Distance(Center) > Radius)
{
return(null);
}
//equation of circle with radius r and center (h, k)
//is (x - h)^2 + (y - k)^2 = r^2
//line: y = mx + b
//circle: (x - h)^2 + (y - k)^2 = r^2
//substitute y: (x - h)^2 + (mx + b - k)^2 = r^2
//expand: x^2 - 2hx + h^2 + m^2x^2 + 2(b - k)mx + (b - k)^2 - r^2 = 0
//group: (1 + m^2)x^2 + (-2h + 2(b - k)m)x + (h^2 + (b - k)^2 - r^2) = 0
//quadratic equation: if 0 = Ax^2 + Bx + C, then x = (-B +- sqrt(B^2 - 4AC)) / 2A
double A = 1 + Math.Pow(line.Slope, 2);
double B = (-2 * Center.X) + (2 * (line.YIntercept - Center.Y) * line.Slope);
double C = Math.Pow(Center.X, 2) + Math.Pow(line.YIntercept - Center.Y, 2) - Math.Pow(Radius, 2);
double x1 = (-1 * B + Math.Sqrt(Math.Pow(B, 2) - (4 * A * C))) / (2 * A);
double x2 = (-1 * B - Math.Sqrt(Math.Pow(B, 2) - (4 * A * C))) / (2 * A);
double y1 = line.Slope * x1 + line.YIntercept;
double y2 = line.Slope * x2 + line.YIntercept;
if (line.IsVertical)
{
x1 = line.A.X;
x2 = line.A.X;
//must use circle equation instead of line equation to find y's
y1 = Center.Y + Math.Sqrt(Math.Pow(Radius, 2) - Math.Pow(x1 - Center.X, 2));
y2 = Center.Y - Math.Sqrt(Math.Pow(Radius, 2) - Math.Pow(x1 - Center.X, 2));
}
if (line.IsHorizontal)
{
y1 = line.A.Y;
y2 = line.A.Y;
}
WPoint point1 = new WPoint(x1, y1);
WPoint point2 = new WPoint(x2, y2);
List <WPoint> result = new List <WPoint>()
{
point1
};
if (point1 != point2)
{
result.Add(point2);
}
return(result.ToArray());
}
/// <summary>Returns the intersection between the two lines.</summary>
public virtual Intersection GetIntersection(WLine b)
{
if (this.Parallel(b))
{
if (this.Coincidental(b))
{
return(new Intersection(this));
}
return(Intersection.NONE);
}
//y = mx + b AND y = m'x + b'
//mx + b = m'x + b'
//mx - m'x = b' - b
//x(m - m') = b' - b
//x = (b' - b) / (m - m')
double intersectionX = (b.YIntercept - this.YIntercept) / (this.Slope - b.Slope);
if (this.IsVertical)
{
intersectionX = this.A.X;
}
else if (b.IsVertical)
{
intersectionX = b.A.X;
}
//y = mx + b
double intersectionY = (this.Slope * intersectionX) + this.YIntercept;
if (this.IsVertical)
{
intersectionY = (b.Slope * intersectionX) + b.YIntercept;
}
else if (this.IsHorizontal)
{
intersectionY = this.A.Y;
}
if (b.IsHorizontal)
{
intersectionY = b.A.Y;
}
return(new Intersection(new WPoint(intersectionX, intersectionY)));
}
/// <summary></summary>
public Intersection GetIntersection(WLine line)
{
//if line intersects 1 corner, that's one point
//if line intersects 2 corners, that's a line segment
List <WPoint> overlapsCorners = new List <WPoint>();
foreach (WPoint corner in Corners)
{
if (corner.Overlaps(line))
{
overlapsCorners.Add(corner);
}
}
if (overlapsCorners.Count == 1)
{
return(new Intersection(overlapsCorners[0]));
}
if (overlapsCorners.Count == 2)
{
return(new Intersection(overlapsCorners.ToArray()));
}
//either line intersects two edges, or none at all
List <WPoint> intersections = new List <WPoint>();
foreach (WLineSegment edge in Edges)
{
Intersection intersection = edge.GetIntersection(line);
if (intersection == Intersection.NONE)
{
continue;
}
intersections.Add(intersection.Point);
}
if (intersections.Count == 2)
{
return(new Intersection(intersections.ToArray()));
}
return(Intersection.NONE);
}
/// <summary>Returns intersection between a line segment and a line.</summary>
public override Intersection GetIntersection(WLine b)
{
if (this.Parallel(b))
{
if (b.Overlaps(this.A))
{
return(new Intersection(this));
}
return(Intersection.NONE);
}
WLine thisLine = this.ToWLine();
Intersection potentialIntersection = thisLine.GetIntersection(b);
if (this.Overlaps(potentialIntersection.Point))
{
return(potentialIntersection);
}
return(Intersection.NONE);
}
/// <summary>Returns false. An infinite line cannot be coincidental to a finite line.</summary>
public override bool Coincidental(WLine b)
{
return(false);
}
/// <summary></summary>
public Intersection(WLine line)
{
Type = IntersectionType.Line;
this.line = line;
}
/// <summary>Returns true if lines are coincidental to each other.</summary>
/// <remarks>Coincidental means that every point on this line is also on the other, and vice versa. In short, the lines are equal.</remarks>
public virtual bool Coincidental(WLine b)
{
return(Parallel(b) && Geometry.WithinMarginOfError(this.YIntercept, b.YIntercept));
}
/// <summary>Returns true if the lines are parallel to each other.</summary>
/// <remarks>Parallel means they have the same slope.</remarks>
public bool Parallel(WLine b)
{
return(Geometry.WithinMarginOfError(this.Slope, b.Slope));
}
/// <summary>Returns true if this point overlaps any part of the <pararef name='line'/>.</summary>
public bool Overlaps(WLine line)
{
return(line.Overlaps(this));
}
