makeBowl

Create a binary map of a bowl within a 3D grid.

Syntax

bowl = makeBowl(grid_size, bowl_pos, radius, diameter, focus_pos)
bowl = makeBowl(grid_size, bowl_pos, radius, diameter, focus_pos, ...)

Description

makeBowl creates a binary map of a bowl from a symmetric spherical shell within a three-dimensional grid. The bowl position is denoted by 1's in the matrix with 0's elsewhere. The bowl surface within the Cartesian grid is found using a bi-directional line search along each row and column to find the grid point with radius closest to the desired radius.

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.

In some cases, the generated bowl will not be simply connected, and there will be a small number of overlapping grid points. To remove these points, set the optional input 'RemoveOverlap' to true.

Examples

% define parameters
grid_size = [32, 64, 64];
bowl_pos  = [1, 32, 32];
radius    = 60;
diameter  = 61;
focus_pos = [32, 32, 32];

% create bowl
makeBowl(grid_size, bowl_pos, radius, diameter, focus_pos, 'Plot', true);

% define parameters
grid_size = [128, 128, 128];
bowl_pos  = [80, 80, 80];
radius    = 60;
diameter  = 81;
focus_pos = [1, 1, 1];

% create bowl
makeBowl(grid_size, bowl_pos, radius, diameter, focus_pos, 'Plot', true);

Inputs

grid_size	size of the 3D grid given as a three element vector [Nx, Ny, Nz] [grid points]
bowl_pos	centre of the rear surface of the bowl given as a three element vector [bx, by, bz] [grid points]
radius	radius of curvature of the bowl [grid points]
diameter	aperture diameter of the bowl [grid points]
focus_pos	any point on the beam axis of the bowl given as a three element vector [fx, fy, fz] [grid points]

Optional Inputs

Optional 'string', value pairs that may be used to modify the default computational settings.

Input	Valid Settings	Default	Description
'Binary'	(Boolean scalar)	false	Boolean controlling whether the bowl map is returned as a double precision matrix (false) or a logical matrix (true).
'Plot'	(Boolean scalar)	false	Boolean controlling whether the bowl is plotted using voxelPlot.
'RemoveOverlap'	(Boolean scalar)	false	Boolean controlling whether overlapped grid points are removed.

Outputs

bowl	3D binary map of a bowl

See Also

makeArc, makeBall, makeCartBowl, makeMultiBowl, makeSphere, makeSphericalSection