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[062] Citation: Abstract
Three methods are introduced for generating complete scans of multidimensional
spaces. The traditional method is to use a raster (typically generated by
nested iteration) which generates points at the maximum resolution and fills
the space slowly. New methods are desirable, because in many applications it is
desirable for the scanned points to be distributed throughout the space and for
the resolution to increase with the number of points scanned. Three simple
methods are introduced in this paper. Two of the methods are members of a class
of methods in which the reverse-bit-order operator maps points from
"R(esolution)-space" to the desired space. In "R-space" the distance from the
origin determines the resolution level of the scanned point. The two scans
occupy points in such a way that a distance measure such as the L 1 norm or the
L (infinity) norm increases with the progress of the scan. The third method
uses iteration of primitive polynomials modulo 2 to generate a nonrepeating
sequence of binary numbers which eventually fills the space. This method is most
computationally efficient, but the L (infinity) norm method generates partial
scans which completely sample the space at intermediate levels of resolution.
Applications are expected in scientific visualization, graphics rendering,
multicriterion optimization, and progressive image transmission.
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Updated: Tue Jul 15 23:54:48 2008
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