1. Ambiguous Rings
Requires a Wolfram Notebook System
Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.
This Demonstration explores ambiguous rings.
[more]
Contributed by: Erik Mahieu (May 2018)
Open content licensed under CC BY-NC-SA
Snapshots
Details
The parametric equation of a circular cylinder with radius inclined at an angle from the vertical is given by:
,
with parameters and .
Define the functions:
and .
The and functions define the composite curve of the -gonal base of the polygonal cylinder [1].
The parametric equation of a polygonal cylinder with sides and radius rotated by an angle around its axis is given by:
,
with parameters and .
To find the equation of the intersection curve, set . This gives the three equations:
,
,
,
with
.
These are equations with four variables, , , and . Eliminating , and by solving the equations gives the parametric equation of the intersection curve with as the only parameter:
.
Reference
[1] E. Chicurel-Uziel, "Single Equation without Inequalities to Represent a Composite Curve," Computer Aided Geometric Design, 21(1), 2004 pp. 23–42. doi:10.1016/j.cagd.2003.07.011.
Permanent Citation