A note on determining the measure of coincidence of segments of a given conic

✍ Scribed by J.H. Graham; R.N. Horton

• Publisher: Elsevier Science
• Year: 1971
• Tongue: English
• Weight: 158 KB
• Volume: 3
• Category: Article
• ISSN: 0010-4485
• DOI: 10.1016/0010-4485(71)90004-2

✦ Synopsis

A note on determining the measure of coincidence of segments of a given conic

This note describes the mathematics of a parametrisation of segments of a conic which provide a convenient technique for determining coincidence. The technique had been applied in two different areas: the elimination of overstriking in graphical displays, and the calculation of the lengths of common boundaries of planar regions bounded by conics.

A useful technique is presented in this note for determining the portions of a segment, S, on a given conic, F, that are coincident with other segments, Sl, of the conic/'. At Sandia Laboratories, this technique has been applied to the problem of overstriking in a computer-generated graphical display, and is also being used to determine lengths of common boundaries between planar regions that are bounded by conics.

The technique consists of three parts: first, parametrisation of the conic with respect to the given segment S; second, determination of the parametric values for the endpoints of the other segments, $4; third, ordering of the parameter values.