Find an intersection of a line and a part of a plane in 3D

[yus]

Hi,

suppose I have two points in 3D space:

A = ROOT.TGLVertex3(1, 1, -20)
B = ROOT.TGLVertex3(1, 1, +20)

and I construct a line from these:

myLine = ROOT.TGLLine3(A, B)

Now I define three other points and construct a plane of these three:

C = ROOT.TGLVertex3(1, 3, 0)
D = ROOT.TGLVertex3(2, 0, 0)
E = ROOT.TGLVertex3(5, 4, 0)
myPlane = ROOT.TGLPlane(C, D, E)

And I want to know whether myLine intersects myPlane and, if so, where exactly:

intersectionOfMyLineAndMyPlane = ROOT.std.pair(bool, ROOT.TGLVertex3)(ROOT.Intersection(myPlane, myLine, False))
if intersectionOfMyLineAndMyPlane.first:
    print(f"myLine intersects myPlane at x={intersectionOfMyLineAndMyPlane.second.X()}, y={intersectionOfMyLineAndMyPlane.second.Y()}, z={intersectionOfMyLineAndMyPlane.second.Z()}")
else:
    print("No intersection!")

That all works very well. But further down the road, I would like to limit the infinite myPlane by a simple 2D shape like e.g. a square, and to check if myLine intersects this square part of myPlane. Any idea how I could go about this? Maybe with some different ROOT classes?

Full code:

import ROOT

A = ROOT.TGLVertex3(1, 1, -20)
B = ROOT.TGLVertex3(1, 1, +20)

myLine = ROOT.TGLLine3(A, B)

C = ROOT.TGLVertex3(1, 3, 0)
D = ROOT.TGLVertex3(2, 0, 0)
E = ROOT.TGLVertex3(5, 4, 0)

myPlane = ROOT.TGLPlane(C, D, E)

intersectionOfMyLineAndMyPlane = ROOT.std.pair(bool, ROOT.TGLVertex3)(ROOT.Intersection(myPlane, myLine, False))
if intersectionOfMyLineAndMyPlane.first:
    print(f"myLine intersects myPlane at x={intersectionOfMyLineAndMyPlane.second.X()}, y={intersectionOfMyLineAndMyPlane.second.Y()}, z={intersectionOfMyLineAndMyPlane.second.Z()}")
else:
    print("No intersection!")

# is there any way to limit the infinite myPlane to e.g. a simple square (given by e.g. 4 points on this plane: J, K, L, M) and to check if myLine intersects myPlane inside this square?

---

ROOT Version: 6.22/06
Platform: CentOS 7

---

[Wile_E_Coyote]

TMath::IsInside ;
TGraph::IsInside

[yus]

Thanks! Is there a member function similar to the two above but operating with 3D coordinates?

[Wile_E_Coyote]

I guess, if you are sure that the point lies on the plane, then it’s sufficient to check any 2d projection.
Otherwise, you would need to create some 2d plane coordinates from the original 3d spacial ones.