Rendering a scene using a reduced memory representation of a polynomial function to determine an output value approximating a mathematical function

A computer graphics system for rendering a scene using representations of a plurality of polynomial functions to determine an output value approximating one of a plurality of mathematical functions, the computer graphics system comprising:

• a plurality of lookup tables stored in one or more non-transitory memories, each of the plurality of lookup tables being configured to store a data value determined for a respective interval over which a respective one of the plurality of mathematical functions may be evaluated;
• and
• fixed function logic coupled to the plurality of lookup tables, the fixed function logic comprising:
• function selection logic configured to select a particular set of the plurality of lookup tables according to a particular mathematical function to be evaluated;
• interval selection logic configured to identify an interval containing a point at which the particular mathematical function is to be evaluated;
• polynomial derivation logic configured to:
• obtain, from the particular set of the plurality of lookup tables, the data value for the identified interval and data values for at least one interval adjacent each end of the identified interval, and
• derive a polynomial function from the data values, the polynomial function being for approximating the particular mathematical function over the identified interval, wherein the computer graphics system is configured to store spline control points as the data values used to derive the polynomial function;
• and
• evaluation logic configured to compute the output value of the polynomial function at the said point, and use that output value as an evaluation of the particular mathematical function thereby enabling the computer graphics system to render the scene.