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Sort of like a strip-light effect; not actually a light source, but just a polygon with glowing edges.

Can this be done easily? Right now I'm contemplating drawing a line more than once with varying alpha/width values to achieve this, but I think that'll cause weird glowing points at the vertices, which is far from ideal.

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Chances are you will want a shader. – The Communist Duck May 7 '11 at 8:23

The basic idea is to extrude the line into a polygon, but do it like you'd billboard a point sprite (but for a line segment).

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