hypersphere / n-sphere

Generate n-dimensional Ellipsoid or Sphere

S = hypersphere( sz )
S = hypersphere( sz, 'fullOrVoid' )
S = hypersphere( sz, matSize )
S = hypersphere( sz, matSize, 'fullOrVoid' )

S is a logical array of size max( sz, matSize ) where "true" (or 1)
defines the points of an n-dimensional ellipsoid or sphere,
with n == length(sz).

The input "sz" defines the size of an ellipsoid:

To create a circle with diameter 101 points:
sz = [101 101 ]

For an ellipse with short axis of 39 points vertical and long axis of 101 points horizontal:
sz = [ 39 101 ]

For a 3D sphere with diameter 101 points:
sz = [101 101 101]

4D hypersphere with diameter 101 points
sz = [101 101 101 101 ]

==> sz may have any size and positive integer values


Use the flag 'void' (default) to have an empty object, e.g. only the line of a circle, or 'full' to have a filled object, e.g. a disc.

The parameter matSize:

You may want to embed the object into the centre of a larger array/matrix.
You can specify matSize the same way as the sz-input.
matSize must have equal length as sz and all( matSize >= sz ).

With sz = [30 1 30 30] and matSize = [100 100 100 100] you embed
a small 3D sphere into a larger 4D array.