An Application of Number Theory to the Organization of Raster Graphics Memory
Name
MIT-LCS-TM-253.pdf
Size
4.78 MB
Format
Adobe PDF
Checksum (MD5)
ef975ad706f4c04de7295738f14d80ff
Author(s)
Chor, Benny
Leiserson, Charles E.
Rivest, Ronald L.
Shearer, James B.
Date Issued
April 1984
Series/Report no.
MIT-LCS-TM-253
Abstract
A high-resolution raster-graphics display is usually combined with processing power and a memory organization that facilitates basic graphics operations. For many applications, including interactive text processing, the ability to quickly move or copy small rectangles of pixels is essential. This paper proposes a novel organization of raster-graphics memory that permits all small rectangles to be moved efficiently. The memory organization is based on a doubly periodic assignment of pixels to M memory chips according to a "Fibonacci" lattice. The memory organization guarantees that if a rectilinearly oriented rectangle contains fewer than M/√5 pixels, then all pixels will reside in different memory chips, and thus can be accesses simultaneously. We also define a continuous analogue of the problem which can be posed as, "What is the maximum density of a set of points in the plane such that no two points are contained in the interior of a rectilinearly oriented rectangle of unit area." We show the existence of such a set with density 1/√5, and prove this is optimal by giving a matching upper bound.
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