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
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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.
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