// Given three colinear MathPoints p, q, r, the function checks if
// MathPoint q lies on line segment 'pr'
private bool onSegment(MathPoint p, MathPoint q, MathPoint r)
{
if (q.x <= Math.Max(p.x, r.x) && q.x >= Math.Max(p.x, r.x) &&
q.y <= Math.Max(p.y, r.y) && q.y >= Math.Max(p.y, r.y))
{
return(true);
}
return(false);
}
private void Swap(MathPoint p1, MathPoint p2)
{
double temp_X = p1.x;
double temp_Y = p1.y;
p1.x = p2.x;
p1.y = p2.y;
p2.x = temp_X;
p2.y = temp_Y;
}
// To find orientation of ordered triplet (p, q, r).
// The function returns following values
// 0 --> p, q and r are colinear
// 1 --> Clockwise
// 2 --> Counterclockwise
private int orientation(MathPoint p, MathPoint q, MathPoint r)
{
// See 10th slides from following link for derivation of the formula
// http://www.dcs.gla.ac.uk/~pat/52233/slides/Geometry1x1.pdf
int val = Convert.ToInt32((q.y - p.y) * (r.x - q.x) - (q.x - p.x) * (r.y - q.y));
if (val == 0)
{
return(0); // colinear
}
return((val > 0) ? 1 : 2); // clock or counterclock wise
}
public Line(MathPoint startpoint, MathPoint endpoint)
{
this.StartPoint = startpoint;
this.EndPoint = endpoint;
//Infinite slope is the slope of the vertical line where there is no change in x-axis..so check for that
if (Math.Abs(startpoint.x - endpoint.x) > epsilon)
{
this.Slope = (endpoint.y - startpoint.y) / (endpoint.x - startpoint.x);
this.Intercept = endpoint.y - (Slope * endpoint.x); // y = mx + b where m is slope, b is y-intercept and (x,y) is any point in the line
}
else
{
infiniteslope = true;
Intercept = startpoint.x; //x-intercept
}
}
public bool DoLinesIntersect(MathPoint p1, MathPoint q1, MathPoint p2, MathPoint q2)
{
// Find the four orientations needed for general and special cases
int o1 = orientation(p1, q1, p2);
int o2 = orientation(p1, q1, q2);
int o3 = orientation(p2, q2, p1);
int o4 = orientation(p2, q2, q1);
// General case
if (o1 != o2 && o3 != o4)
{
return(true);
}
// Special Cases
// p1, q1 and p2 are colinear and p2 lies on segment p1q1
if (o1 == 0 && onSegment(p1, p2, q1))
{
return(true);
}
// p1, q1 and p2 are colinear and q2 lies on segment p1q1
if (o2 == 0 && onSegment(p1, q2, q1))
{
return(true);
}
// p2, q2 and p1 are colinear and p1 lies on segment p2q2
if (o3 == 0 && onSegment(p2, p1, q2))
{
return(true);
}
// p2, q2 and q1 are colinear and q1 lies on segment p2q2
if (o4 == 0 && onSegment(p2, q1, q2))
{
return(true);
}
return(false); // Doesn't fall in any of the above cases
}
private bool IsBetween(MathPoint start, MathPoint middle, MathPoint end)
{
return(IsBetweenValue(start.x, middle.x, end.x) && IsBetweenValue(start.y, middle.y, end.y));
}
//Easy and Simple Method using Slope and y-Intercept
public MathPoint GetIntersectionPointUsingSlopes(MathPoint p1, MathPoint q1, MathPoint p2, MathPoint q2)
{
//Rearrange the points based on x co-ordinate values to make the calculate easier
//start point should be lesser than endpoint that is p1 < q1
//Point 1 is lesser than point 2 .. p1.x < p2.x
//p1 and q1 makes a line
if (p1.x > q1.x)
{
Swap(p1, q1);
}
if (p2.x > q2.x)
{
Swap(p2, q2);
}
//check both lines
if (p1.x > p2.x)
{
Swap(p1, q1);
Swap(p2, q2);
}
//Now all the point are sorted x-axis value
Line line1 = new Line(p1, q1);
Line line2 = new Line(p2, q2);
//Two lines will intersect on two condition
//conditon 1: (both line are parallen and overlapping
// if the lines are parallel (slope are equal), they intersect only if they have the same y-interecept and start 2 in on line 1
//Condtion 2 : If two line intersect, then they will have same point of intersection and the point of intesection will be with both lines coordinates
if (line1.Slope == line2.Slope)
{
if (line1.Intercept == line2.Intercept && IsBetween(p1, p2, q1))
{
return(p2); //point of intersection will be p2
}
return(null);
}
/* Get co-ordinatinates of intersection based on the forumla
* If the 2 lines intersect, then the at the point of intersection both lines will share the same x-coordinate and y-coordinate
* so y = mx + b for lines will be equal to y = mx + b of line 2
* x = (b2 -b1)/ (m1- m2)
*/
double x = (line2.Intercept - line1.Intercept) / (line1.Slope - line2.Slope);
double y = x * line1.Slope + line1.Intercept; //y = mx + b where (x,y) are any co-ordinates in the line
MathPoint IntersectionPoint = new MathPoint(x, y);
//check whether the intesection point x and y is within line segement range
if (IsBetween(line1.StartPoint, IntersectionPoint, line1.EndPoint) && IsBetween(line2.StartPoint, IntersectionPoint, line2.EndPoint))
{
return(IntersectionPoint);
}
return(null);
}