Computer graphics processing and selective visual display system – Computer graphics processing – Three-dimension
Reexamination Certificate
2005-06-28
2005-06-28
Zimmerman, Mark (Department: 2671)
Computer graphics processing and selective visual display system
Computer graphics processing
Three-dimension
C345S611000, C345S613000
Reexamination Certificate
active
06911976
ABSTRACT:
A system and method for generating sample points that can generate the sample points in parallel. The sample points can be used in processing in parallel, with the results subsequently collected and used as necessary in subsequent rendering operations. Sample points are generated using a coarse Halton sequence, which makes use of coarse radical inverse values Φbi,M(j) as follows:in-line-formulae description="In-line Formulae" end="lead"?Φbi,M(j)=Φb(jM+i)in-line-formulae description="In-line Formulae" end="tail"?where base “b” is preferably a prime number, but not a divisor of “M,” and “i” is an integer. Using this definition, the s-dimensional coarse Halton sequence USCHal,i,M, which may be used to define sample points for use in evaluating integrals, is defined asin-line-formulae description="In-line Formulae" end="lead"?UsCHal,i,M=(Φb1i,M(j), . . . , Φbsi,M(j))in-line-formulae description="In-line Formulae" end="tail"?where b1, . . . , bsare the first “s” prime numbers that are not divisors of “M.” Each value of “i” defines a subsequence that is a low-discrepancy sequence, and so can be used in connection with processing. Similarly, the union of all subsequences for all values of “i” between “zero” and “M−1” is also a low-discrepancy sequence, so results of processing using the coarse Halton sequences for all such values of “i” can be collected together and used in the same manner as if the results had been generated using a Halton sequence to define the sample points.
REFERENCES:
patent: 6529193 (2003-03-01), Herken et al.
patent: WO 97 50060 (1997-12-01), None
patent: WO 98 59322 (1998-12-01), None
Jordan Richard A.
Mental Images G.m.b.H. & Co., KG
Santiago Enrique L.
Zimmerman Mark
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