private static List <Advanced.Algorithms.Geometry.Line> horizontalLines()
{
var lines = new List <Advanced.Algorithms.Geometry.Line>();
var s1 = new Advanced.Algorithms.Geometry.Line(new Advanced.Algorithms.Geometry.Point(200, 100), new Advanced.Algorithms.Geometry.Point(600, 100), tolerance);
var s2 = new Advanced.Algorithms.Geometry.Line(new Advanced.Algorithms.Geometry.Point(225, 100), new Advanced.Algorithms.Geometry.Point(625, 100), tolerance);
var s3 = new Advanced.Algorithms.Geometry.Line(new Advanced.Algorithms.Geometry.Point(250, 100), new Advanced.Algorithms.Geometry.Point(475, 100), tolerance);
var s4 = new Advanced.Algorithms.Geometry.Line(new Advanced.Algorithms.Geometry.Point(290, 100), new Advanced.Algorithms.Geometry.Point(675, 100), tolerance);
lines.AddRange(new[] { s1, s2, s3, s4 });
return(lines);
}
private static List <Advanced.Algorithms.Geometry.Line> verticalLines()
{
var lines = new List <Advanced.Algorithms.Geometry.Line>();
var s1 = new Advanced.Algorithms.Geometry.Line(new Advanced.Algorithms.Geometry.Point(100, 200), new Advanced.Algorithms.Geometry.Point(100, 600), tolerance);
var s2 = new Advanced.Algorithms.Geometry.Line(new Advanced.Algorithms.Geometry.Point(100, 225), new Advanced.Algorithms.Geometry.Point(100, 625), tolerance);
var s3 = new Advanced.Algorithms.Geometry.Line(new Advanced.Algorithms.Geometry.Point(100, 250), new Advanced.Algorithms.Geometry.Point(100, 475), tolerance);
var s4 = new Advanced.Algorithms.Geometry.Line(new Advanced.Algorithms.Geometry.Point(100, 290), new Advanced.Algorithms.Geometry.Point(100, 675), tolerance);
lines.AddRange(new[] { s1, s2, s3, s4 });
return(lines);
}
internal static Point Intersection(this Line lineA, Line lineB, double tolerance)
{
return(LineIntersection.FindIntersection(lineA, lineB, tolerance));
}
internal static bool Intersects(this Line lineA, Line lineB, double tolerance)
{
return(LineIntersection.FindIntersection(lineA, lineB, tolerance) != null);
}
public static Point Intersection(this Line lineA, Line lineB, int precision = 5)
{
return(LineIntersection.Find(lineA, lineB, precision));
}
internal static Point FindIntersection(Line lineA, Line lineB, double tolerance)
{
if (lineA == null || lineB == null)
{
return(null);
}
if (lineA == lineB)
{
throw new Exception("Both lines are the same.");
}
//make lineA as left
if (lineA.Left.X.CompareTo(lineB.Left.X) > 0)
{
var tmp = lineA;
lineA = lineB;
lineB = tmp;
}
else if (lineA.Left.X.CompareTo(lineB.Left.X) == 0)
{
if (lineA.Left.Y.CompareTo(lineB.Left.Y) > 0)
{
var tmp = lineA;
lineA = lineB;
lineB = tmp;
}
}
double x1 = lineA.Left.X, y1 = lineA.Left.Y;
double x2 = lineA.Right.X, y2 = lineA.Right.Y;
double x3 = lineB.Left.X, y3 = lineB.Left.Y;
double x4 = lineB.Right.X, y4 = lineB.Right.Y;
//equations of the form x=c (two vertical overlapping lines)
if (x1 == x2 && x3 == x4 && x1 == x3)
{
//get the first intersection in vertical sorted order of lines
var firstIntersection = new Point(x3, y3);
//x,y can intersect outside the line segment since line is infinitely long
//so finally check if x, y is within both the line segments
if (IsInsideLine(lineA, firstIntersection, tolerance) &&
IsInsideLine(lineB, firstIntersection, tolerance))
{
return(new Point(x3, y3));
}
}
//equations of the form y=c (two overlapping horizontal lines)
if (y1 == y2 && y3 == y4 && y1 == y3)
{
//get the first intersection in horizontal sorted order of lines
var firstIntersection = new Point(x3, y3);
//get the first intersection in sorted order
//x,y can intersect outside the line segment since line is infinitely long
//so finally check if x, y is within both the line segments
if (IsInsideLine(lineA, firstIntersection, tolerance) &&
IsInsideLine(lineB, firstIntersection, tolerance))
{
return(new Point(x3, y3));
}
}
//equations of the form x=c (two vertical lines)
if (x1 == x2 && x3 == x4)
{
return(null);
}
//equations of the form y=c (two horizontal lines)
if (y1 == y2 && y3 == y4)
{
return(null);
}
//general equation of line is y = mx + c where m is the slope
//assume equation of line 1 as y1 = m1x1 + c1
//=> -m1x1 + y1 = c1 ----(1)
//assume equation of line 2 as y2 = m2x2 + c2
//=> -m2x2 + y2 = c2 -----(2)
//if line 1 and 2 intersect then x1=x2=x and y1=y2=y where (x,y) is the intersection point
//so we will get below two equations
//-m1x + y = c1 --------(3)
//-m2x + y = c2 --------(4)
double x, y;
//lineA is vertical x1 = x2
//slope will be infinity
//so lets derive another solution
if (Math.Abs(x1 - x2) < tolerance)
{
//compute slope of line 2 (m2) and c2
double m2 = (y4 - y3) / (x4 - x3);
double c2 = -m2 * x3 + y3;
//equation of vertical line is x = c
//if line 1 and 2 intersect then x1=c1=x
//subsitute x=x1 in (4) => -m2x1 + y = c2
// => y = c2 + m2x1
x = x1;
y = c2 + m2 * x1;
}
//lineB is vertical x3 = x4
//slope will be infinity
//so lets derive another solution
else if (Math.Abs(x3 - x4) < tolerance)
{
//compute slope of line 1 (m1) and c2
double m1 = (y2 - y1) / (x2 - x1);
double c1 = -m1 * x1 + y1;
//equation of vertical line is x = c
//if line 1 and 2 intersect then x3=c3=x
//subsitute x=x3 in (3) => -m1x3 + y = c1
// => y = c1 + m1x3
x = x3;
y = c1 + m1 * x3;
}
//lineA and lineB are not vertical
//(could be horizontal we can handle it with slope = 0)
else
{
//compute slope of line 1 (m1) and c2
double m1 = (y2 - y1) / (x2 - x1);
double c1 = -m1 * x1 + y1;
//compute slope of line 2 (m2) and c2
double m2 = (y4 - y3) / (x4 - x3);
double c2 = -m2 * x3 + y3;
//solving equations (3) and (4) => x = (c1-c2)/(m2-m1)
//plugging x value in equation (4) => y = c2 + m2 * x
x = (c1 - c2) / (m2 - m1);
y = c2 + m2 * x;
//verify by plugging intersection point (x, y)
//in orginal equations (1) and (2) to see if they intersect
//otherwise x,y values will not be finite and will fail this check
if (!(Math.Abs(-m1 * x + y - c1) < tolerance &&
Math.Abs(-m2 * x + y - c2) < tolerance))
{
return(null);
}
}
var result = new Point(x, y);
//x,y can intersect outside the line segment since line is infinitely long
//so finally check if x, y is within both the line segments
if (IsInsideLine(lineA, result, tolerance) &&
IsInsideLine(lineB, result, tolerance))
{
return(result);
}
//return default null (no intersection)
return(null);
}
public static bool Intersects(this Line lineA, Line lineB, int precision = 5)
{
return(LineIntersection.Find(lineA, lineB, precision) != null);
}
/// <summary>
/// Returns Point of intersection if do intersect otherwise default Point (null).
/// </summary>
/// <param name="precision">precision tolerance.</param>
/// <returns>The point of intersection.</returns>
public static Point Find(Line lineA, Line lineB, int precision = 5)
{
var tolerance = Math.Round(Math.Pow(0.1, precision), precision);
return(FindIntersection(lineA, lineB, tolerance));
}
