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DESCRIPTION: A space-filling curve is a continuous\, surjective map from [0
\,1] to a d-dimensional unit volume (for example\, a cube or a simplex). Sp
ace-filling curves are usually constructed following a recursive tessellati
on of the unit volume that gives the curve useful structural properties. Th
e most prominent of these properties is that the curve tends to preserve lo
cality: points that are close to each other along the curve are (usually) c
lose to each other in d-dimensional space and (usually) vice versa. This ca
n be exploited to speed up algorithms\, in practice and sometimes even in t
heory\, by processing or storing data points in order along the curve. In t
his lecture I will show how space-filling curves can be described\, how the
y get their useful properties\, and I will show examples of their applicati
ons. This brings us to the question what would be the optimal space-filling
curves for these applications. We will encounter a number of open question
s on tessellations in 2D and 3D and on how to measure the quality of a spac
e-filling curve.
DTSTAMP:20220627T180000
DTSTART:20220718T141500
CLASS:PUBLIC
LOCATION:Freie Universität Berlin \n Institut für Informatik \n Takustr. 9
\n 14195 Berlin \n Room 005 (Ground Floor)
SEQUENCE:0
SUMMARY:Herman Haverkort (Universität Bonn): Space-filling curves: properti
es\, applications and challenges
UID:124942812@www.facetsofcomplexity.de
URL:http://www.facetsofcomplexity.de/monday/20220718-L-Haverkort.html
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