We’ve looked at how we can geometrically find the linear combination using barycentric coordinates, but it is not the only way to do so. Natural neighbour interpolation works by observing what happens when an input point is inserted into a set of points represented by a Voronoi diagram. The Voronoi diagram is simply a partition of space into polygonal regions for each data point, such that any point inside a given region is proximal to its corresponding data point.
By WWII, scientists had already begun looking at alternative gelling substances for routine use in bacteriology, but concluded that agar was still better as it is both firmer and easier to handle. Today, some specialized microbiology applications use the colloid carrageenan (extracted from red seaweed Chondrus crispus, or “Irish Moss”), a more transparent and less auto-fluorescent alternative to agar (agar emits its own background fluorescence when excited by light). However, for routine bacteriological use, carrageenan is more difficult to dissolve, requires higher concentrations, can degrade at high temperatures, and forms weaker gels, which may result in puncturing its surface during the plating of cells.
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