/// <summary>
/// Calculates the interception point of two Lines.
/// </summary>
/// <param name="other"></param>
/// <param name="tolerance"></param>
/// <returns>Returns a Point if func succeeds. If there is no interception, empty point is returned.</returns>
public Vector2? IntersectLine(LineSegment2 other, double tolerance = GeometrySettings.DEFAULT_TOLERANCE)
{
double interPntX = 0;
double interPntY = 0;
if (other == null || this.IsParallelTo(other, tolerance))
{
return null; // Lines are parralell
}
//intercept of two endless lines
if (!this.IsVertical && !other.IsVertical) { // both NOT vertical
interPntX = ((-1 * (this.YMovement - other.YMovement)) / (this.Slope - other.Slope));
interPntY = (this.Slope * interPntX + this.YMovement);
} else if (this.IsVertical) { // this vertical (so it must lie on this.X)
interPntX = this.Start.X;
interPntY = (other.Slope * interPntX + other.YMovement);
} else if (other.IsVertical) { // Line2 vertical (so it must lie on Line2.X)
interPntX = other.Start.X;
interPntY = (this.Slope * interPntX + this.YMovement);
}
var interPnt = new Vector2(interPntX, interPntY);
//check if computed intercept lies on our line.
if (this.Contains(interPnt, tolerance) && other.Contains(interPnt, tolerance))
{
return interPnt;
}else
return null;
}
/// <summary>
/// Calculates the interception point of two Lines.
/// </summary>
/// <param name="other"></param>
/// <param name="tolerance"></param>
/// <returns>Returns a Point if func succeeds. If there is no interception, empty point is returned.</returns>
public Vector2?IntersectLine(LineSegment2 other, double tolerance = GeometrySettings.DEFAULT_TOLERANCE)
{
double interPntX = 0;
double interPntY = 0;
if (other == null || this.IsParallelTo(other, tolerance))
{
return(null); // Lines are parralell
}
//intercept of two endless lines
if (!this.IsVertical && !other.IsVertical) // both NOT vertical
{
interPntX = ((-1 * (this.YMovement - other.YMovement)) / (this.Slope - other.Slope));
interPntY = (this.Slope * interPntX + this.YMovement);
}
else if (this.IsVertical) // this vertical (so it must lie on this.X)
{
interPntX = this.Start.X;
interPntY = (other.Slope * interPntX + other.YMovement);
}
else if (other.IsVertical) // Line2 vertical (so it must lie on Line2.X)
{
interPntX = other.Start.X;
interPntY = (this.Slope * interPntX + this.YMovement);
}
var interPnt = new Vector2(interPntX, interPntY);
//check if computed intercept lies on our line.
if (this.Contains(interPnt, tolerance) && other.Contains(interPnt, tolerance))
{
return(interPnt);
}
else
{
return(null);
}
}
/// <summary>
/// Circle-Line Interception
/// </summary>
/// <param name="uLine"></param>
/// <returns>Returns all intersection points</returns>
private List<Vector2> InterceptLine(LineSegment2 uLine, double tolerance = GeometrySettings.DEFAULT_TOLERANCE)
{
var intersections = new List<Vector2>();
Vector2 p1, p2;
var location = this.Location;
// we assume that the circle Middlepoint is NULL/NULL
// So we move the Line with the delta to NULL
var helperLine = new LineSegment2(uLine.Start - location, uLine.End - location);
// line
var q = helperLine.YMovement;
var m = helperLine.Slope;
if (!helperLine.IsVertical)
{
// The slope is defined as the Line isn't vertical
var discriminant = (Math.Pow(m, 2) + 1) * Math.Pow(this.Radius, 2) - Math.Pow(q, 2);
if (discriminant > 0)
{
// only positive discriminants for f() -> sqrt(discriminant) results are defined in |R
var p1X = (Math.Sqrt(discriminant) - m * (q)) / (Math.Pow(m, 2) + 1);
var p1Y = m * p1X + q;
var p2X = (-1 * (Math.Sqrt(discriminant) + m * q)) / (Math.Pow(m, 2) + 1);
var p2Y = m * p2X + q;
p1 = new Vector2(p1X, p1Y);
p2 = new Vector2(p2X, p2Y);
if (helperLine.Contains(p1, tolerance))
{
intersections.Add(p1 + location);
}
if ((p1.X != p2.X) || (p1.Y != p2.Y))
{
if (helperLine.Contains(p2, tolerance))
{
intersections.Add(p2 + location);
}
}
}
}
else
{
// undefined slope, so we have to deal with it directly
var p1X = this.Location.X + helperLine.Start.X;
var p1Y = Math.Sqrt(Math.Pow(this.Radius, 2) - Math.Pow(p1X, 2));
p1 = new Vector2(p1X, p1Y);
p2 = new Vector2(p1.X, -p1.Y);
if (helperLine.Contains(p1, tolerance))
{
intersections.Add(p1 + location);
}
if (helperLine.Contains(p2, tolerance))
{
intersections.Add(p2 + location);
}
}
return intersections;
}
/// <summary>
/// Circle-Line Interception
/// </summary>
/// <param name="uLine"></param>
/// <returns>Returns all intersection points</returns>
private List <Vector2> InterceptLine(LineSegment2 uLine, double tolerance = GeometrySettings.DEFAULT_TOLERANCE)
{
var intersections = new List <Vector2>();
Vector2 p1, p2;
var location = this.Location;
// we assume that the circle Middlepoint is NULL/NULL
// So we move the Line with the delta to NULL
var helperLine = new LineSegment2(uLine.Start - location, uLine.End - location);
// line
var q = helperLine.YMovement;
var m = helperLine.Slope;
if (!helperLine.IsVertical)
{
// The slope is defined as the Line isn't vertical
var discriminant = (Math.Pow(m, 2) + 1) * Math.Pow(this.Radius, 2) - Math.Pow(q, 2);
if (discriminant > 0)
{
// only positive discriminants for f() -> sqrt(discriminant) results are defined in |R
var p1X = (Math.Sqrt(discriminant) - m * (q)) / (Math.Pow(m, 2) + 1);
var p1Y = m * p1X + q;
var p2X = (-1 * (Math.Sqrt(discriminant) + m * q)) / (Math.Pow(m, 2) + 1);
var p2Y = m * p2X + q;
p1 = new Vector2(p1X, p1Y);
p2 = new Vector2(p2X, p2Y);
if (helperLine.Contains(p1, tolerance))
{
intersections.Add(p1 + location);
}
if ((p1.X != p2.X) || (p1.Y != p2.Y))
{
if (helperLine.Contains(p2, tolerance))
{
intersections.Add(p2 + location);
}
}
}
}
else
{
// undefined slope, so we have to deal with it directly
var p1X = this.Location.X + helperLine.Start.X;
var p1Y = Math.Sqrt(Math.Pow(this.Radius, 2) - Math.Pow(p1X, 2));
p1 = new Vector2(p1X, p1Y);
p2 = new Vector2(p1.X, -p1.Y);
if (helperLine.Contains(p1, tolerance))
{
intersections.Add(p1 + location);
}
if (helperLine.Contains(p2, tolerance))
{
intersections.Add(p2 + location);
}
}
return(intersections);
}
