A convenient way to define a specific composition is to define the relative amount of each component. The set of all the possible compositions of k pure components can be modeled as an abstract (k-1)-simplex: in such a simplex, each vertex represents a pure component, and each specific composition is defined by k numbers, each specifying the amount of one of the pure components. When the simplex has a geometric realization (e.g., when it is visualized), a specific composition corresponds to a unique point of the Euclidean simplex that can be specified through a linear combination of the vertices. When a function on a multidimensional domain (e.g., a liquidus surface) is sampled at a finite set of points S, the lifted Delaunay triangulation of the samples is realized through a piecewise-linear interpolation. The convex hull ch(S) of a set of points S is the smallest convex set containing S.