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

See Also

makeBowl, makeCartArc, makeCartSphere, makeCartSphericalSection,