When performing anisotropic filtering when sampling a texture to provide an output sampled texture value for use when rendering an output in a graphics processing system, a number of positions for which to sample the texture along an anisotropy direction along which samples will be taken in the texture is determined by determining the square root of the coefficient F for an ellipse having the form Ax2+Bxy+Cy2=F corresponding to the projection of the sampling point for which the texture is being sampled onto the surface to which the texture is to be applied, and using the determined square root of the ellipse coefficient F to determine the number of positions for which samples should be taken along the anisotropy direction in the texture.