Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)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.10410431058Brazilian Capes scholarshipPlumeri Award for Faculty Excellence from the College of William and MaryDivision of Science and Mathematics, New York University Abu Dhabi (NYUAD)Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)