The whole notebook in one image. A triangle mesh has no curvature, no spectrum, no notion of distance — none of differential geometry — until you build it. The surprise is that a single sparse matrix, the cotangent Laplacian, manufactures all of it. Here is the same torus seen four ways through that one operator: its Gaussian curvature, its Laplace-Beltrami vibration modes, mean-curvature flow, and heat-method geodesic distance.
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