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I'm reading a paper on terrain rendering LOD and there's some math notation there I'm not clear on.

When talking about how triangles are split into pairs of smaller triangles where more detail is needed on the mesh they have an equation along the lines of

large triangle = left triangle ⊕ right triangle

From the context of the rest of the paragraph, I get that they're saying that the bigger triangle contains/is made up of the two smaller triangle. But what specifically does that symbol mean in terms of triangles & trigonometry?

Should that be interpreted as the direct sum of two triangles? If so, what does that operation actually entail? Performing a direct sum of the matrices of the triangle vertices?

Paper in question is here btw, page 4, section 4.1 has the notation I'm talking about.

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I don't see that notation on page 4, or a section 4.1. Is that the right paper? –  doppelgreener May 13 '11 at 21:58
    
I guess this would be better suited for math.stackexchange.com –  bummzack May 15 '11 at 21:43

1 Answer 1

Probably referring to Minkowski Addition?:

http://www.cut-the-knot.org/do_you_know/add_shape.shtml

(Scroll down a little ways to find where they use the same symbol.)

"Every element of A added to every element of B," meaning that if A had 4 vertices and B and 3 vertices, the resulting shape would have 12 vertices.

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I believe it is called 'dilation', a description of which can be found on Wikipedia[en.wikipedia.org/wiki/Dilation_(morphology)]. Nice catch –  Grimless May 14 '11 at 8:04

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