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Maybe if you explained what your goals are ... give us a wider picture of what you are after.
i now realise my approach was wrong. The reason i don't wan't to use edge intersection is that this would lead to a huge increase in complexity when coding. This little problem is only part of a much larger one that involves many other little problems all of which, once solved, will need to be computed as efficiently as possible by a computer... This means that the simplest/fastest formula will need to be used. Of course, a formula is always better than an algo.
Why can't you calculate the intersections? Is it too computationally intensive?
What a cool project!
The only restriction is that I may not calculate any edge intersections. Other than that, anything goes. I have tried splitting the triangles into more triangles and using their areas in additions and calculations, nothing I tried worked...
It looks tricky. You could sketch the two triangles to see which of the lines overlap, work out the points of the shape formed and use the semi-perimeter rule to work out the area of that shape (splitting the shape up into triangles if it has 4, 5 or 6 sides), but you said you didn't want it to be done that way.
How can you find the amount of common surface area between 2 triangles, knowing the coordinates of all the 6 tips (and thus being able to calculate areas), without actually calculating intersections between edges, just by adding and substracting the different areas?