Recall that a barycentric coordinate system is given with respect to a -dimensional simplex, where is no larger than the dimensional space. Given a set of scattered points, it’s possible to create a tessellation of the space by forming simplices from the points, such that any input point that lies within the convex hull of the scattered set can be expressed in terms of the enclosing simplex and its corresponding barycentric coordinates2. This can be understood as a kind of triangulated irregular network (TIN).
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Agar is so critical that since WWII, scientists have tried to find alternatives in the event of a supply chain breakdown, especially as recent shortages have caused similar alarm. But while other colloid jellies have emerged, agar remains integral to laboratory protocols because no alternatives can yet compete on performance, cost, and ease of use.