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In this paper, we are concerned with the problem of creating flattening maps of simply connected open surfaces in ℝ3Using a natural principle of density diffusion in physics, we propose an effective algorithm for computing density-equalizing maps with any prescribed density distribution. By varying the initial density distribution, a large variety of flattening maps with different properties can be achieved. For instance, area-preserving parameterizations of simply connected open surfaces can be easily computed. Experimental results are presented to demonstrate the effectiveness of our proposed method. Applications to data visualization and surface remeshing are explored.

In this paper, we are concerned with the problem of creating flattening maps of simply connected open surfaces in ℝ3Using a natural principle of density diffusion in physics, we propose an effective algorithm for computing density-equalizing maps with any prescribed density distribution. By varying the initial density distribution, a large variety of flattening maps with different properties can be achieved. For instance, area-preserving parameterizations of simply connected open surfaces can be easily computed. Experimental results are presented to demonstrate the effectiveness of our proposed method. Applications to data visualization and surface remeshing are explored.

In 1972 Lou Skoda and J.C. Robertson published an isodemographic map (a cartogram) of Canada that represented a population-oriented rendering of the 1966 Canadian census divisions. The map was developed with a physical analog model that kept all of Canada together in a contiguous mass while preserving recognizable divisions and province outlines.