While there exist many possible ways to triangulate a set of points, the most common method for TINs is the Delaunay triangulation. This is because Delaunay triangulations tend to produce more regular tessellations that are better suited to interpolation. In theory, we can represent our colour palette as a TIN by computing the 3D Delaunay triangulation of the colours in colour space. The nice thing about this is that it makes finding an enclosing simplex much faster; the candidate selection process is simply a matter of determining the enclosing tetrahedron of an input point within the network using a walking algorithm, and taking the barycentric coordinates as the weights.
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The gains illustrate how fundamental design choices compound: batching amortizes async overhead, pull semantics eliminate intermediate buffering, and the freedom for implementations to use synchronous fast paths when data is available immediately all contribute.