Section 3.3.1.5.2. Optimization of line drawings

A line drawing consisting of n line segments may be specified by anything from to 2n position vectors depending on whether the lines are end-to-end connected or independent. Appreciable gains in both processing time and storage requirements may be made in complicated drawings by arranging for line segments to be end-to-end connected as far as possible, and an algorithm for doing this is outlined below. For further details see Diamond (1984a).

Supposing that a list of nodal points (atoms if a covalent skeleton is being drawn) exists within a computer with each node appearing only once and that the line segments to be drawn between them are already determined, then at each node there are, generally, both forward and backward connections, forward connections being those to nodes further down the list. A quantity D is calculated at each node which is the number of forward connections minus the number of backward connections. At the commencement of drawing, the first connected node in the list must have a positive D, the last must have a negative D, the sum of all D values must be zero and the sum of the positive ones is the number of strokes required to draw the drawing, a `stroke' being a sequence of end-to-end connected line segments drawn without interruption. The total number of position vectors required to specify the drawing is then the number of nodes plus the number of strokes plus the number of rings minus one.

Drawing should then be done by scanning the list of nodes from the top looking for a positive D (usually found at the first node), commencing a stroke at this node and decrementing its D value by 1. This stroke is continued from node to node using the specified connections until a negative D is encountered, at which point the stroke is terminated and the D value at the terminating node is incremented by 1. This is done even though this terminating node may also possess some forward connections, as the total number of strokes required is not minimized by keeping a stroke going as far as possible, but by terminating a stroke as soon as it reaches a node at which some stroke is bound to terminate.

The next stroke is initiated by resuming the scan for positive D values at the point in the node list where the previous stroke began. If this scan encounters a zero D value at a node which has not hitherto been drawn to, or drawn from, then the node concerned is isolated and not connected to any other, and such nodes may require to be drawn with some special symbol. The expression already given for the number of vectors required is valid in the presence of isolated nodes if drawing an isolated node is allowed one position vector, this vector not being counted as a stroke.

The number of strokes generated by this algorithm is sensitive to the order in which the nodes are listed, but if this resembles a natural order then the number of strokes generated is usually close to the minimum, which is half the number of nodes having an odd number of connections. For example, the letter E has six nodes, four of which have an odd number of connections, so it may be drawn with two strokes.