CULTURES OF CURVES AND STRAIGHT LINES

Segmenting curves into elliptic arcs and straight lines

A method is described for segmenting edge data into a combination of stmight lines and elliptic am. The westage process first segments the data into straight line segments. Ellipses are then fitted to the line data. ntis is much fmter than curve fitting directly topire1 data since the lines provide a great reduction in data. Segmentation is pegormed in the paradigm suwsted by Lowe [5]. A measur...

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...

Digital straight line segments and curves