OpenGL Interpolation algorithm

Question

I've written my own 3D Game Engine in Java by using OpenGL (LWJGL). I'd like to write a Raytracer that works on the CPU, not on the GPU because the memory for my GPU is limited and the amount of data that I use might be bigger than the memory available on my graphics card.

I did some ray-triangle intersection stuff and so on but I need to know how to interpolate values in a triangle like OpenGL does.

What I know is the x,y and z coordinate of each vertex.

What algorithm is usually used in OpenGL for doing Interpolation like I described.

This wouldn't work because the left blue point in my graphics would also be influenced by value_2 — Luecx, Aug 07 '17 at 11:40
how do you get the 0.0? did you take the distance from the line(value_1, value_3) to value_2 ? — Luecx, Aug 07 '17 at 11:44
Let us [continue this discussion in chat](http://chat.stackoverflow.com/rooms/151269/discussion-between-androbin-and-luecx). — Androbin, Aug 07 '17 at 11:44
@Luecx see [Reflection and refraction impossible without recursive ray tracing?](https://stackoverflow.com/a/45140313/2521214) I know you want CPU side ... but look at the fragment where I do the ray triangle intersection. It computes barycentric `u,v` and then interpolate the color from vertex colors which is exactly what you want ... — Spektre, Aug 07 '17 at 11:55
@Luecx yes I got also CPU side SW raytracer but that code I linked was available directly ... For the SW render I would need to dig into my archives and I am lazy for that. — Spektre, Aug 07 '17 at 11:59

score 2 · Accepted Answer · answered Aug 07 '17 at 11:58

Borrowed from gamedev.stackexchange.com

You simply need to project vector AP onto vector AB, then add the resulting vector to point A.

Here is one way to compute it:

A + dot(AP,AB) / dot(AB,AB) * AB This formula will work in 2D and in 3D. In fact it works in all dimensions.

In your case, A = value_1, AB = value_3 - value_1 and AP = value - value_1

OpenGL Interpolation algorithm

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