1. A method for determining level of detail while rendering an object, the method comprises the steps of: a) updating first and second linear components of a set of derivatives when rendering a pixel of the object in a given scan line, wherein the first and second linear components are updated in a linear manner based on first and second increment values, respectively, and wherein the set of derivatives relates changes in physical coordinates of the object with changes in texture coordinates of the object; b) updating third and fourth linear components of the set of derivatives when rendering the pixel of the object corresponds to another scan line, wherein the third and fourth linear components are updated in a linear manner based on third and fourth increment values, respectively; c) comparing magnitudes of the first, second, third, and fourth linear components to obtain a selected magnitude; d) converting the selected magnitude to a logarithmic scale to produce a logarithmic magnitude; and e) combining the logarithmic magnitude with a logarithmic representation of a non-linear component of the set of derivatives to obtain the level of detail for the pixel.