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Tagged: intersection, line, unit vector, direction vector
This topic contains 5 replies, has 2 voices, and was last updated by Péter Baksa 6 months ago.

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March 8, 2019 at 12:32 #4588
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

March 11, 2019 at 09:31 #4593
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
Software Engineer, Library Team
GRAPHISOFT SE 
March 11, 2019 at 11:49 #4600
Do you have any sort of examples for this by any chance?
Thanks

March 12, 2019 at 17:16 #4603
Yes, have a look at “basicStairTread_m” 3D script.
Péter Baksa
Software Engineer, Library Team
GRAPHISOFT SE 
March 13, 2019 at 11:41 #4611
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.

March 21, 2019 at 09:31 #4618
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
Software Engineer, Library Team
GRAPHISOFT SE 
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