Intersection of a line and a plane

intersection

asked 2013-02-27 00:03:37 +0100

assadabbasi
43 ●5 ●6 ●12

updated 2013-02-27 00:04:35 +0100

Hi,

I have a line described by points (1, 0, 1), (4, -2, 2) and a plane x + y + z = 6. If solve by hand I get the point of intersection as (7, -4, 3). But in sage, I don't find any intersection point. My code in sage is as follows:

P = Polyhedron(eqns=[(-6,1,1,1)])

L = [[1, 0, 1], [4, -2, 2]]

L1 = Polyhedron(L)

intersect = L1.intersection(P)

Output is "The empty polyhedron in QQ^3". Whats wrong here? my calculation by hand or my code?

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answered 2013-02-27 03:48:16 +0100

twch
368 ●3 ●13 ●21

The Problem is that the way you define your line above, you only get the line segment between the two indicated points. The intersection points lies however on the line outside of this segment. So try this instead to see the difference:

P = Polyhedron(eqns=[(-6,1,1,1)])
L1 = Polyhedron([[1, 0, 1], [4, -2, 2]])
L2 = Polyhedron(vertices=[[1,0,1]], rays=[[3,-2,1],[-3,2,-1]])
print L1.intersection(P)
print L2.intersection(P).vertices()

By the way: Is there an easier way of defining a complete line as a Polyhedron?