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I set out to find the equations describing a rope
that begins from the north pole and spirals its
way around a sphere neatly covering it and ending
at the south pole.
Taking uniform samples along this rope gives
a fairly uniform covering of the sphere.
The surface of a sphere is two dimensional,
but the rope gives a one dimensional covering
that is uniformly sampled in that dimension.
I wondered about the sampling in the other dimension
so I set out to plot it.
I found the ``generalized spiral set''
of Saff and Kuijlaars1997.
In spherical coordinates , for
, they set
| |
(1) |

| (2) |

My plot of these equations is shown in Figure 1.
There is no interesting pattern in the crossline direction.
Although my plot looks reasonable,
Saff and Kuijlaars1997
show a curious pattern in the crossline direction
that my plots do not show.
A few tests with various values of *N* and various rotations
failed to show any curious pattern.

**sphere
**

Figure 1
Helix on a sphere.
Top shows the embedded helix.
Bottom hides it.
An interesting pattern of points that appears
in the article in the Mathematical Intelligencer
is inexplicably absent here
(even though I tested several rotations and several values of *N*).

** Next:** Helical coordinate on a
** Up:** Claerbout: Helical meshes on
** Previous:** INTRODUCTION
Stanford Exploration Project

4/20/1999