Pseudo-random interval arithmetic sampling techniques in computer graphics
An improved branch-and-bound process of interval arithmetic subdivision in furtherance of computation of rigorous error bounds on integrated digital scene information for two dimensional display is provided. More particularly, a first aspect of the subject process includes pseudo-randomly subdividing an interval domain comprising a set of interval variables in furtherance of ascertaining a characteristic contribution of the interval variables of said set of interval variables to an image space comprising at least a sub-pixel area. A further aspect, either alone or in combination with the first aspect contemplates pseudo-randomly discarding a select partitioning of interval variables of a set of interval variables of a geometric function from a computed solution of an interval arithmetic branch-and-bound process.
1. In a method of photorealistic image synthesis characterized by a two dimensional display of integrated three dimensional digital scene information animated over a select time interval, the three dimensional digital scene information delimited by a geometric function relating a set of interval variables to an image space comprising a pixel domain, the set of interval variables including at least the select time interval, the steps comprising:
a. partitioning pixels of the pixel domain into subpixel fragments wherein each subpixel fragment of said subpixel fragments delimits a unique area of the pixel domain;
b. defining a correlation pattern for said subpixel fragments, said correlation pattern associating said unique area of the pixel domain delimited by each subpixel fragment of said subpixel fragments to a unique portion of the select time interval;
c. partitioning the set of interval variables of the geometric function in furtherance of deterministically ascertaining a characteristic contribution of the set of interval variables to the image space comprising said unique area of the pixel domain delimited by each subpixel fragment of said subpixel fragments;
d. deterministically defining and discarding, via said partitioning, a select portion of discarded interval variables of the set of interval variables of the geometric function, said select portion of discarded interval variables comprising partitioned interval subsets of the set of interval variables of the geometric function wherein said partitioned interval subsets contain, as a result of said partitioning, a deterministically partitioned interval subset of the select time interval that does not intersect said unique portion of the select time interval associated, via said correlation pattern, with said unique area of the pixel domain delimited by each subpixel fragment of said subpixel fragments; and,
e. integrating the characteristic contribution to the image space of the set of interval variables that do not belong to said select portion of discarded interval variables in order to synthesize a display result for each pixel of the pixel domain of the two dimensional display.