Detecting Line Intersection

[James Goode]

Hello,

I’ve recently received this bit of code regarding line intersection but I’m not quite sure how to implement it into my object.

(px1, py1, px2, py2 are coordinates of points on each segments, vx1, vy1, vx2, vy2 are the direction vectors for the segments)

"LineLineIntersection":
              Scalar = ( (vx1*vx2) + (vy1*vy2) )
 
              if abs(abs(Scalar) - 1) < EPS then
                            ! no intersection, parallel lines
                            ipx = 0
                            ipy = 0
                            state = 0
              else
                            ! Calculate A1, B1 and C1 parameter
                            ! A1, B1 are equal to normal vector
                            A1 = -vy1
                            B1 = vx1
                            C1 = -(A1*px1) - (B1*py1)
 
                            ! Calculate A2, B2 and C2 parameter
                            ! A2, B2 are equal to normal vector
                            A2 = -vy2
                            B2 = vx2
                            C2 = -(A2*px2) - (B2*py2)
 
                            ! Calculate coordinates of intersection point
                            ipy = ((A1*C2) - (C1*A2)) / ((B1*A2) - (A1*B2))
 
                            if abs(A1) < EPS then
                                          ipx = (-B2*ipy - C2) / A2
                            else
                                          ipx = (-B1*ipy - C1) / A1
                            endif
 
                            state = 1
              endif
return' 

Specific to my object my line points would be something along the lines of 

line2 x[1], y[1], x[2], y[2]
line2 x[2], y[2], x[3], y[3]`

How can I implement my parameters into the example code I’ve been given

[Péter Baksa]

Hi James,

The direction vectors are unit vectors along the lines, their length have to be exactly 1 (meter). Compute the length of the vector between the two points on the line, and to set the vector length to 1, multiply its end coordinates by 1/length.

If you use an EPS value that is common in GS libparts, this code has a small bug, the lines are treated parallel (no intersections) when their angle is smaller than 0.81°, which is still quite noticable. Using EPS = 0.00000001 will set the limit to 0.0081°

Péter Baksa
Library Platform, Software Engineer
GRAPHISOFT SE

[James Goode]

Do you have any sort of examples for this by any chance?

Thanks

[Péter Baksa]

Yes, have a look at “basicStairTread_m” 3D script.

Péter Baksa
Library Platform, Software Engineer
GRAPHISOFT SE

[James Goode]

So I’ve taken a look at the basicStairTread_m 3d script but I don’t really understand what I’m supposed to be looking at. I wish there was an object which was an example purely for line intersection like there are for a few other objects in the help centre. Without being able to detect and stop line intersections in my object, it becomes unusable.

[Péter Baksa]

Hi,

There is a call (gosub) to “LineLineIntersection” in the 3D script. The input variables are set up before the call.

vx, vy is computed from two points (_intersectEdge[1] and _intersectEdge[2]) on the line, divided by the distance of the two points:

	! line 1
	vx1 = (_intersectEdge[2][1] - _intersectEdge[1][1]) / _intersectEdgeLength
	vy1 = (_intersectEdge[2][2] - _intersectEdge[1][2]) / _intersectEdgeLength

px, py is any point on the line:

	px1 = _intersectEdge[1][1]
	py1 = _intersectEdge[1][2]

This is done again for the second line:

	! line 2
	vx2 = (_intersectEdgeLeft[2][1] - _intersectEdgeLeft[1][1]) / _intersectEdgeLeftLength
	vy2 = (_intersectEdgeLeft[2][2] - _intersectEdgeLeft[1][2]) / _intersectEdgeLeftLength
	px2 = _intersectEdgeLeft[1][1]
	py2 = _intersectEdgeLeft[1][2]

The result intersection is ipx, ipy, when state = 1 (otherwise the lines are parallel):

	gosub "LineLineIntersection"	! returns ipx, ipy, state
	if state <> 0 then
		_intersectPtLeft[1] = ipx
		_intersectPtLeft[2] = ipy
	endif

Péter Baksa
Library Platform, Software Engineer
GRAPHISOFT SE

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