# Drawing nice projections of objects in space

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## Abstract

Our results on regular and minimum-crossing projections of line segments have immediate corollaries for polygonal chains, polygons, trees and more general geometric graphs in 3-D since these are all special cases of sets of line segments. Our results also have application to graph drawing for knot-theorists. Let *K* be a knot with *n* vertices. To study the knot's combinatorial properties, knot theorists obtain a planar graph *G* called the diagram of *K* by a regular projection of *K*. Many of their algorithms are applied to *G* and therefore their time complexity depends on the space complexity of *G*. By combining our algorithms we can obtain regular projections with the minimum number of crossings thereby minimizing the time complexity of their algorithms.

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