We survey the computational geometry relevant to finite element mesh generation. We especially focus on optimal triangulations of geometric domains in two- and three-dimensions. An optimal triangulation is a partition of the domain into triangles or tetrahedra, that is best according to some criterion that measures the size, shape, or number of triangles. We discuss algorithms both for the optimization of triangulations on a fixed set of vertices and for the placement of new vertices (Steiner points). We briefly survey the heuristic algorithms used in some practical mesh generators. 1. Introduction Computational geometry claims the two aims of solving practical problems and producing beautiful mathematics. There is a natural tension between these goals: the most elegant formulation of a problem rarely occurs in practice. But surprisingly often the aims complement each other. This chapter discusses the interplay between an important practical problem---finite element mesh gener...
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