# 3. Ambiguous Rings Based on a Rose Curve

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This Demonstration further explores ambiguous rings.

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Contributed by: Erik Mahieu (May 2018)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

The parametric equation for with radius inclined at an angle from the vertical is given by:

.

The parametric equation of in the - plane with petals and an angular offset of from the axis is given by:

.

To find the intersection, set the corresponding components equal. This gives three equations in four unknowns: .

Eliminating , and by solving the equations gives the parametric curve of the intersection with as the only parameter:

,

with

.

This composite curve (ring set) can be split into two rings. Therefore, the parameter range for , from to , is divided into sections using the cutoff angles and .

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