Case Study: Reducing visual complexity in plots of smooth intersecting contours

In this report I describe a nonlinear optimization model for reducing visual clutter in a plot of overlapping contours that represent aggregate scatter data. The contours are represented as smooth, closed, uniform B-splines. My method begins with a preprocessing step in which contours are converted into a piecewise linear representation. Then I solve a nonlinear optimization program which eliminates small subregions between contours, created by intersection, while preserving the overall shape and smoothness of the contours. This yields a cleaner plot of contours, devoid of extraneous and distracting visual detail.