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A classification of shapes according to their principal curvatures, kx and ky. The rightmost column shows the product of the two principal curvatures, known as the Gaussian curvature. Note that the Gaussian curvature of a plain and a ridge are the same, as those of a summit and basin. The saddle is unique in having a negative Gaussian curvature.
| Shapes | kx | ky | kx · ky |
|---|---|---|---|
| Plain | 0 | 0 | 0 |
| Ridge | 1 | 0 | 0 |
| Summit | 1 | 1 | 1 |
| Basin | −1 | −1 | 1 |
| Saddle | 1 | −1 | −1 |
