# Intersection of a Generalized Cylinder over a Rose Curve with a Circular Cylinder

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This Demonstration shows the intersections of a circular cylinder with a generalized cylinder over a rose curve with a variable number of petals.

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Contributed by: Erik Mahieu (May 2018)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

The parametric equations of a circular cylinder with radius , inclined at an angle and offset by a distance from the horizontal are:

,

,

.

The parametric equations (with parameters and ) of a generalized upright cylinder over a rose curve in the - plane with petals and an angular offset of from the axis are:

,

,

.

To find the intersection, set the corresponding equations equal to get three equations with four unknown parameters: .

Eliminating all but gives the two sections of the parametric of the composite intersection curve:

and

with

.

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.