Question

according to the CUDA programming guide, the value returned by the texture fetch is

tex(x) = (1-a)T[i] + aT[i+1] for a one-dimensional texture

where i = floor(Xb), a = frac(Xb), Xb=x-0.5

Suppose we have a one dimensional texture that only has two texals. For example:

T[0] = 0.2, T[1] = 1.5

Say we want to fetch the texal at 1, which I think should return T[1] which is 1.5.

However, if you follow the rule given in the programming guide, the return value will be:

Xb = 1 - 0.5 = 0.5
a = 0.5
i = 0
return value = 0.5*T[0] + 0.5*T[1] = 0.85

which does not make any sense to me. Can someone explain why the linear filtering is done in such way by CUDA? Thanks

Answer 1

The linear filtering algorithm in CUDA assumes texel values are located at the centroid of the interpolation volume (so voxel centered, if you like). In your 1D filtering example, the input data is implicitly taken as

T[0]=(0.5, 0.2) T[1]=(1.5, 1.5)

So your example is asking for Tex(1), which is the midpoint between the two texel values, ie.

0.5*0.2 + 0.5*1.5 = 0.85

To get T[1] returned you would require Tex(1.5) and that is the general rule – add 0.5 to coordinates if you want to treat the texture data as being at the voxel vertices, rather than the voxel center.