Drawing a tree on parallel lines

On Drawing Lines on a Map

The paper is an exercise in descriptive ontology, with specific applications to problems in the geographical sphere. It presents a general typology of spatial boundaries, based in particular on an opposition between bona fide or physical boundaries on the one hand, and fiat or human-demarcation-induced boundaries on the other. Cross-cutting this opposition are further oppositions in the realm o...

Drawing series-parallel graphs on a box

On Drawing Anti-Aliased Straight Lines

In this paper, an efficient algorithm is presented for drawing anti-aliased straight lines for two grey-level case; experimental results show that it is faster than Liu’s algorithm [6]. Specifically, Liu’s algorithm determines the grey-level of one pixel at a time while our algorithm determines the grey-levels of many pixels at the same time. In addition, our results for the two grey-level case...

Drawing Straight Lines

lines, pseudolines, polar coordinates, trilinear coordinates, non-linear programming, geometry We present a graph-drawing algorithm which respects extended co-linearity constraints. These are expressed as a set of ‘straight’ paths in a planar graph. Constraints of this sort are translated into a set of inequalities over polar coordinates of lines. These inequalities provide necessary and suffic...

Drawing Graphs on Two and Three Lines

We give a linear-time algorithm to decide whether a graph has a planar LL-drawing, i.e. a planar drawing on two parallel lines. This has previously been known only for trees. We utilize this result to obtain planar drawings on three lines for a generalization of bipartite graphs, also in linear time.