  We extend the pre-image representation of exposed points of the numerical
range of a matrix to all extreme points. With that we characterize extreme
points which are multiply generated, having at least two linearly independent
pre-images, as the extreme points which are Hausdorff limits of flat boundary
portions on numerical ranges of a sequence converging to the given matrix.
These studies address the inverse numerical range map and the maximum-entropy
inference map which are continuous functions on the numerical range except
possibly at certain multiply generated extreme points. This work also allows us
to describe closures of subsets of 3-by-3 matrices having the same shape of the
numerical range.
