Computer Graphics Methods and Systems Using Quasi-Monte Carlo Methodology

Abstract

A computer graphics system generates a pixel value for a pixel in an image, the pixel value being representative of a point in a scene as recorded on an image plane of a simulated camera, the computer graphics system comprising a sample point generator and a function evaluator. The sample point generator is configured to generate a set of sample points, at least one sample point being generated using at least one dependent sample comprising at least one element of a low-discrepancy sequence offset by at least one element of another low-discrepancy sequence. The function evaluator is configured to generate at least one value representing an evaluation of a selection function at one of the sample points, the value generated by the function evaluator corresponding to the pixel value.

1 . A computer graphics system for generating a pixel value for a pixel in an image, the pixel value being representative of a point in a scene as recorded on an image plane of a simulated camera, the computer graphics system comprising:
 A. a sample point generator configured to generate a set of sample points, at least one sample points being generated using at least one dependent sample, the at least one dependent sample comprising at least one element of a low-discrepancy sequence offset by at least one element of another low-discrepancy sequence; and   B. a function evaluator configured to generate at least one value representing an evaluation of a selected function at one of the sample points generated by said sample point generator, the value generated by the function evaluator corresponding to the pixel value.   
     
     
         2 . A computer-implemented method of generating a pixel value for a pixel in an image, the pixel value being representative of a point in a scene as recorded on an image plane of a simulated camera, the method comprising:
 A. a sample point generation step of generating a set of sample points, at least one sample points being generated using at least one dependent sample, the at least one dependent sample comprising at least one element of a low-discrepancy sequence offset by at least one element of another low-discrepancy sequence; and   B. a function evaluation step of generating at least one value representing an evaluation of a selected function at one of the sample points generated during the sample point generation step, the value generated during the function evaluation step corresponding to the pixel value.   
     
     
         3 . A computer program product for use in connection with a computer to provide a computer graphics system for generating a pixel value for a pixel in an image, the pixel value being representative of a point in a scene as recorded on an image plane of a simulated camera, the computer program product comprising a computer-readable medium having encoded thereon:
 A. a sample point generator module configured to enable the computer to generate a set of sample points, at least one sample points being generated using at least one dependent sample, the at least one dependent sample comprising at least one element of a low-discrepancy sequence offset by at least one element of another low-discrepancy sequence; and   B. a function evaluator module configured to enable the computer to generate at least one value representing an evaluation of a selected function at one of the sample points generated by said sample point generator, the value generated by the computer corresponding to the pixel value.