An Application of Number Theory to the Organization of Raster Graphics Memory
Author(s)
Chor, Benny; Leiserson, Charles E.; Rivest, Ronald L.; Shearer, James B.![Thumbnail](/bitstream/handle/1721.1/149063/MIT-LCS-TM-253.pdf.jpg?sequence=3&isAllowed=y)
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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.
Date issued
1984-04Series/Report no.
MIT-LCS-TM-253