Interpolation according to a function represented using unevenly spaced samples of the function

A non-transitory computer program product, encoded on a computer-readable medium, operable to cause data processing apparatus to perform operations comprising:

• receiving an input value of image data;
• identifying one of multiple first locations, corresponding to the input value, in a first Graphics Processing Unit (GPU) texture storing index values corresponding to second locations, wherein the second locations store sample outputs, y, of a function y=f(x) within a domain, the function being represented by a set of unevenly spaced sample points, x, and the corresponding sample outputs, y, and the first locations correspond to a set of evenly spaced sample points within the domain;
• finding two index values stored in the first locations using the one of the first locations as a starting point the finding comprising:
• looking up a first index value in the one of the first locations in the first GPU texture;
• and
• determining the first index value and a second index value such that corresponding x values of the unevenly spaced sample points in a second GPU texture bound the input value, the determining comprising:
• looking up an x value in the second GPU texture using the second index value, the second index value being one different than the first index value;
• and
• incrementally increasing or decreasing the first and second index values while the x values corresponding to the first and second index values fail to bound the input value;
• and
• generating an image data output value corresponding to the input value by interpolation using two sample outputs, y, obtained from the second locations using the two index values.

A system comprising:

• a memory structure comprising an array of first locations storing index values corresponding to second locations, wherein the second locations store sample outputs, y, of a function y=f(x) within a domain, the function being represented by a set of unevenly spaced sample points, x, and the corresponding sample outputs, y, and the first locations correspond to a set of evenly spaced sample points within the domain, wherein the memory structure comprises a first texture in a Graphics Processing Unit (GPU) populated with the index values corresponding to the second locations;
• and
• one or more computers operable to effect an image processing application configured to receive an input value, identify one of the first locations corresponding to the input value, find two index values stored in the first locations using the one of the first locations as a starting point including looking up a first index value in the one of the first locations in the first texture, and to determine the first index value and a second index value such that corresponding x values of the unevenly spaced sample points in a second texture bound the input value including to look up an x value in the second texture using the second index value, the second index value being one different than the first index value, and to incrementally increase or decrease the first and second index values while the x values corresponding to the first and second index values fail to bound the input value, and generate an output value corresponding to the input value by interpolation using two sample outputs, y, obtained from the second locations using the two index values.