no pretty surfaces are shown
`{:1/8:}(mu_{II}(M)//n)^2(1+o(1))`, as `n\rightarrow\infty`
`{:K_d:}(mu_{II}(M)//n)^{:2//d:}(1+o(1))` as `n\rightarrow\infty`
`int_M kappa_p dp = int_M {:1/r:} = (2 pi theta r){:1/r:} = 2 pi theta`
Dist | By | Dist. Measure |
`(mu_{II}(M)//n)^{2//d}` | Mesh | Hausdorff |
`(mu_{text{I}}(M)//n)^{1//d}` | Points on `M` | `max_{x in M} D_E(x, N)` (Hausdorff) |
`(mu_{text{I}}(M)//n)^{1+2//d}` | Points on `M` | `int_M D(x, N)^2//n` |
`(mu_{text{I}}(M)//n)^{1//d}` | N/A | Ave NN dist, uniform |
`(mu_{:f:}(M)//n)^{1//d}` | N/A | Ave edge, TSP, density `f`[BHH] |
`f(x) = f(0) + f'(0)x + f''(0)x^2//2 + O(x^3)`
`f(x) = f''(0)x^2//2 + O(x^3)`
`f(x) approx x^T Z x = sum_i alpha_i x_i^2`,
`prod_i sqrt{:|alpha_i|:} = sqrt{:|det Z|:} = sqrt kappa`