The neutral case for the min-max angle criterion: A generalized concept (Q1195747)

Choosing a triangulation of a point set often is reduced to chosing one of two diagonals in a quadrilateral. Often used criteria for the choice are to minimize either the smallest or the largest angle of a triangle in the triangulation. The neutral case is the one where both criteria yield the same result. \textit{D. Hansford} [Comput. Aided Geom. Des. 7, No. 5, 431-438 (1990; Zbl 0702.65013)] has shown that a necessary condition is that the four vertices be concircular. The author constructs a neutral set given two vertices and a preassigned angle.