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.

You can't do it by just adding or subtracting the areas of your 2 triangles because they could be completely overlapped, completely separate or somewhere in between, and that would affect the result.

What a cool project!

The only way I can think of is to calculate the intersection points, and then work out the area of the polygon so created. There will be different cases:

* no intersection at all
* just touching (various types: points touching, point touching line, etc)
* various intersections
* one fully inside another

Have a look at this page, there is a java applet where you can draw and intersect shapes: http://www.cs.mcgill.ca/~gstamm/P507/bool_op.html

Another idea: you can calculate the area of a shape by calculating the area of each line segment down to the x-axis. If you always proceed clockwise (or counter-clockwise) and assign plus or minus area based on whether the line has increasing or decreasing x value, you get the net area (or possibly the negative of the net area). This little trick may help somehow.

Perhaps by defining a polygon made up of the two triangles? In other words triangle ABC and DEF become polygon ABCADEFD, then use my area method above ... worth an experiment.

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.

I've given up adding and substracting areas as it's now clear this isn't the way to go...

I'm going to try and come up with a function of all of the tip coordinates of 2 triangles that returns the amount of common surface area, without requiring ANY if clauses. This was my goal in the first place.

But first, to avoid and possible needless hassle, I'm going to search for just such a function on the internet... If I fail to find one, I'm going to try and come up with one. Do you know of such a function? No ifs required? Please post if you do. 10x