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I have a graph where each node is associated with a 2D position. I would like to use a finite line to "cut" this graph into two halves, as shown below:

2d Graph

Note that the cutting line does have a direction. All vertices in that direction remain and aren't cut away.

How can I implement this?

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  • \$\begingroup\$ This is somewhat ambiguous. If the red line were just a tiny bit lower, would you want that dangling edge that would be left? Or does it have a grid structure to maintain? \$\endgroup\$ – MickLH Jan 16 '14 at 16:09
  • \$\begingroup\$ This caes is ambiguous, it doesn't have to maintain a grid structure. If the red line were a bit lower there would be an edge to the right top corner. \$\endgroup\$ – Quonux Jan 16 '14 at 16:15
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Here's the algorithm I see happening in your question: (I use "inside" meaning specifically not ON the cut line but only inside it)

P = Plane To Cut Across.
For every edge in the graph as Line A->B {
    A_inside = Is point A inside plane P?
    if (point B is on line P && !A_inside) return nothing;

    B_inside = Is point B inside plane P?
    if (point A is on line P && !B_inside) return nothing;

    if (A_inside == B_inside) {
        return Line A->B
    }
    Q = Intersection of line P and line A->B
    if (A_inside) {
        return Line A->Q
    } else {
        return Line Q->B
    }
}
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  • \$\begingroup\$ thx, what about the connections that are cutted (notice the lines on the cut line) \$\endgroup\$ – Quonux Jan 16 '14 at 16:34
  • \$\begingroup\$ I added some logic at the top to account for deleting the lines with one (or more vertices) exactly on the plane, and the other outside it. \$\endgroup\$ – MickLH Jan 16 '14 at 16:34

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