Numerical Methods in the Compilation of Transformed Images

A New Technique for Constructing Continuous Cartograms

“…The principles of algorithm construction for the required transformation h can be found in Gusein-Zade and Tikunov (1990). We shall try to construct a one-parameter family of transformations h, (0~t~1) of the plane that begins with the identity transformation ho = id and ends with the required transformation hI = h. Moreover, the family h, must be the solution for the differential equation a -ath,(z) = l/I, (z) where *, (z) = (a(z) and~(z» is a vector field determined 170 by the function Pt(z) of the density of the variable after applying the transformation h,.…”

“…The use of cartograms is restricted because they lack sufficiently developed, relatively simple, and effectually realizable algorithms for their construction. A survey of a variety of approaches to the solution of this problem can be found in Gusein-Zade and Tikunov (1990) and Tikunov (1988). This paper will describe a new algorithm used to construct cartograms and some results of its use.…”

Distortion for readability of contextualized text explanations for visualizations

“…By spatially depicting an attribute within the map base, the cartograms emphasizes each regions' data instead of territorial land area. For a detailed discussion on cartogram construction algorithms see GuseynZade and Tikunov [10].…”

“…In fact, one of the major goals of cartogram algorithms is to preserve the shapes of the objects [10,11].…”

“…Maintain the topography, i.e. the positions of the objects relative to each other are maintained [4,10,11]. …”