7. Parameters of the Shell Generator

This section gives detailed information about the parameters of the shell generator. All explanations are very theoretical. If you cannot understand them, print the "Reference Sheet" ("doc/reference.ps") and try to find the parameter in question there. Playing around with the GUI for some time might also be a good idea.

The basic idea of the algorithm is to simulate a shell shape by rotating a growing ellipse around the z-axis, and simultaneously displacing it from the z-axis. This results in a flat spiral. If we move the ellipse along the z-axis while rotating, a shell like shape will appear. The curve determined by all centers of all ellipses is a so called helico-spiral.

The parameters of this process are divided into 5 groups. Parameters that need to be given in degrees are marked with an asterisk ("*").

Angular Parameters:

These parameters change the shape of the helico-spiral ("alpha"* and "beta"*) and the tilt of the ellipse against the axes of the local coordinate system of the ellipse ("phi"*, "my"*, "omega"*). Note, that "alpha"* does determine the growth rate of the ellipse too.

Linear Parameters:

They change the size (and shape) of the ellipse ("a", "b") and the distance of the first ellipses center from the z-axis ("A").

Dimensional Parameters:

They set how many ellipses are calculated ("omin"*, "omax"*, "od"*), and how many points on each ellipse are calculated ("smin"*, "smax"*, "sd"*). Finally, a global scale-factor, independent from all file format specific scaling, might be applied using "Scale".

Nodule Parameters:

Change all aspects of nodules, position on the ellipse ("P"*), size ("W1"*, "W2"*), length ("L"), number of nodules per whorl ("N") and starting point on the spiral ("Nstart"*).

There are three independent groups of nodules. Add a "2" to each nodule parameter to set parameters of the second nodule group. Length of second nodule is therefore "L2". Do the same for the third nodule, with a "3". There are two more parameters to control an offset between the three groups of nodules, "Off2"* is the offset between nodule 1 and nodule 2 and "Off3"* is the offset between nodule 1 and nodule 3.

Nodule-Mode Parameters:

"Scano", "Scans", "Hdo", "Hds" refer to section Calculation Modi for information on this parameters.

The most important parameters are "alpha", "beta", "A", "a" and "b".

Here are some hints on how certain values change the shape of the shell.

• Alpha 90 means no growing of the ellipse and no spiral shape at all. If beta is 90, too, this will produce a torus like shape. If alpha gets smaller the spiral will form and the ellipse will grow.
• Beta 90 means no moving of the ellipse along z-axis. This is fine for shells like "Nautilus", "Planorbis", "Ammonite" or several cockles. If you want to shape a "Turritella" or "Natalina" you have to decrease beta.
• The meaning of a certain value of A depends highly on a and b. Generally, A should be higher as a and b, otherwise the shell may look like a sphere.