Texture mapping is a core technique in 3D graphics and is important for computer vision applications as well. The major challenge of texture mapping is high quality antialiasing at a reasonably high speed. Previous approaches do not address this problem adequately, since they do not precisely model the anisotropic and spatially variant nature in texture mapping. In this paper, we handle this problem using signal processing and sampling theory. We first describe an analytic framework to deduce the ideal filter and the corresponding weight distribution for texture filtering. Since the ideal filter does not have a closed-form solution, we further propose a filter that is the first order, yet of high precision, approximation of the ideal filter and makes a closed-form solution possible. This first order approximating (FOA) filter has excellent anti-aliasing capability and a reasonably high rendering speed. The comparison with some wellknown filters (box, cubic, EWA, and fast footprint MIPmapping, etc.) also testifies that our filter does have better antialiasing performance.