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# makeCartBowl

Create evenly distributed Cartesian points covering a bowl.

## Syntax

```bowl = makeCartBowl(bowl_pos, radius, diameter, focus_pos, num_points)
bowl = makeCartBowl(bowl_pos, radius, diameter, focus_pos, num_points, plot_bowl)
```

## Description

`makeCartBowl` creates a 3 x `num_points` array of the Cartesian coordinates of points evenly distributed over the surface of a bowl. The bowl points are calculated using Fermat's spiral. The position of the bowl is set by `bowl_pos`, which corresponds to the center of the rear bowl surface. The orientation of the bowl is set by `focus_pos`, which corresponds to any point on the axis of the bowl (note, this must not be equal to `bowl_pos`). It is assumed that the solid angle of the bowl is equal to or less than 2*pi steradians. If the radius is set to inf, a disc is generated. The 3D plot that is displayed after calling `makeCartBowl([0, 0, 0], 40e-3, 60e-3, [0, 0, -1], 500, true);` is given below.

## Inputs

 `bowl_pos` Cartesian position of the centre of the rear surface of the bowl given as a three element vector `[bx, by, bz]` [m] `radius` Radius of curvature of the bowl [m] `diameter` Diameter of the opening of the bowl [m] `focus_pos` Any point on the beam axis of the bowl given as a three element vector `[fx, fy, fz]` [m] `num_points` Number of points on the bowl

## Optional Inputs

 `plot_bowl` Boolean controlling whether the Cartesian coordinates are plotted (default = false)

## Outputs

 `points` 3 x `num_points` array of Cartesian coordinates

`makeBowl`, `makeCartArc`, `makeCartSphere`, `makeCartSphericalSection`,