# Molding: The Brilliant Bessel Bowl

My original concept for the week was to case a coin - which, unlike the
sample coin from last week, would have geometric depth rather than
color depth projected into depth. In order to accomplish this I wanted
to use the laser cutter to raster, rather than being stuck with the
relatively course gradations of vector path milling.

The first problem that I encountered was that I did not have a geometry
file for a face. Even if I had had one, I didn't have any method of
converting the geometry into a grayscale image indexed by depth (a la:
Neil's new stl2png).

## Laser Cutter Rastering

In order to assess the potential of the laser cutter for making molds
using grayscale depth images, I converted an image with relatively
smooth color gradations into grayscale. First I tried rastering on
the surface of cardboard.

Next I tried some deep rastering on 3/8" acrylic

## Bessel Bowl

In order to accomplish the crazy idea I had to make some serious deep
smooth 3d structure using the laser cutter, I needed to find a way of
parceling up layers with a one-to-one projection into the x-y plane.
This let to some extensions for cad.m -
my Mathematica cad package.
The shape I decided upon is a spherical bowl with a toroidal stand, and
a Bessel-function-like inner surface. In fact, it is not a Bessel
function, but a Gauss curve multiplied with the Hermite polynomial of
order 4, and summed with x to the power of 12.