Is this a valid interpolation strategy for implementing a texture or is it just a helpful thought exercise? If this is valid, how does it compare to bilinear interpolation?

Can we take points that aren't even 0, 0.5, or 1 values? For example, can we sample a texture at (0.65, 0.12)? If so, where does interpolation come in? The methodology here confuses me.

@dan I think this is somewhat separate from the bilinear interpolation step. There's an interpolation (e.g. using barycentric coordinates) to figure out where in (u, v) space a particular point (x, y) in the triangle corresponds to. Since the texture is made up of texels, it is not guaranteed that the point (x, y) will be exactly at a texel center, so then there's the (e.g. bilinear) interpolation between the texels that make up the texture to determine what the particular color at that point should be.