3D math question : barycentric interpolation

[madmarx]

Hi!

Not a ogre question, but more 3D math question. I am writing a software renderer that mimics opengl. I have a difficulty to do the interpolation of values from the vertex at the point inside a face in an efficient way. Also I had some difficulties to find information on the internet.
The mathematical problem would be : I got 1 2D triangle (ABC) and 1 point M which lies inside the triangle. How do I interpolate the values from vertex data ABC to get those at the point M ?

What I tried : I calculated the triangle areas ratios (MAB/MBC/MAC), but that is very calculation heavy. Does anyone got a suggestion for faster calculus ?

Best regards,

Pierre

[Daixiwen]

Can't you just use the distances MA / MB / MC as weight values for the linear interpolation?

[madmarx]

Thanks , but I don't think it works : Imagine that M is on the edge AB. Then distance MC is not null, so the interpolation is not null for C, while it should be, since M is completely at the opposite.
So I came to the conclusion that I can't use those distances.

But you gave me an idea. if I calculate distance "M to (AB)", "M to (AC)" and "M to (BC)", this might work.

[shadowfeign]

not sure if this would help or not? but maybe it will. there are five parts to the video, the next one should be pretty easy to find each time though, so I'll just link the first to save some space.

[youtube]E5papKQGrGU[/youtube]

[Daixiwen]

Thanks , but I don't think it works : Imagine that M is on the edge AB. Then distance MC is not null, so the interpolation is not null for C, while it should be, since M is completely at the opposite.
So I came to the conclusion that I can't use those distances.

Yes of course... duh! I think I should never try to answer a question about geometry without a pencil and a paper

But you gave me an idea. if I calculate distance "M to (AB)", "M to (AC)" and "M to (BC)", this might work.

Yes I agree, this looks more like it. And it's probably one of the only ways to make the interpolation linear. That said, as far as complexity goes, you aren't that far away from your first solution with the 3 triangle areas.

[bstone]

I think weighting components by incident face angles is what is used often, not that calculation heavy too.

[lunkhound]

If you are rasterizing a triangle, then you can speed things up a lot by reusing the information from adjacent pixels. If all you want is a single point, then barycentric is a good choice.

For barycentric, I'd use a cross product like (M - A) x (M - B) and then take the dot product of that with the surface normal. That is the fastest way I know to compute the area MAB (its 2x the area actually).