Discrete Representation of Straight Lines

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...

Euclid’s straight lines

We raise two questions on Euclid’s Elements: How to explain that Propositions 16 and 27 in his first book do not follow, strictly speaking, from his postulates (or are perhaps meaningless)? and: What are the mathematical consequences of the meanings of the term eutheia which we today often prefer to consider as different? The answer to the first question is that orientability is a tacit assumpt...

Haptically straight lines.

In this research, we set out to investigate haptically perceived space. Large deviations with respect to physical space have already been shown to exist. Here, research on haptic space is continued by investigating straight lines constructed by touch. In four experiments, subjects were asked to produce straight lines between two reference markers that were in the horizontal plane at a fixed dis...

Vector code probability and metrication error in the representation of straight lines of finite length

Proposing a new code by considering pieces of discrete straight lines in contour shapes

Pattern substrings analysis to find high redundancy in binary shapes is carried out to improve compression levels in binary objects. Modifications of a recent set of symbols to encode arbitrary contour shapes is proposed. The concept of Pieces of Discrete Straight Lines is introduced and the probability of appearance of symbols in contours is analyzed to propose a code of nine symbols, MDF9. Al...