second-derivatives for sin(x) from 0 to pi
                 spline           actual
      angle      2nd deriv        2nd deriv
      0.16        -0.156832        -0.156434
      0.31        -0.309632        -0.309017
      0.47        -0.454933        -0.453990
      0.63        -0.588988        -0.587785
      0.79        -0.708564        -0.707107
      0.94        -0.810683        -0.809017
      1.10        -0.892840        -0.891007
      1.26        -0.953012        -0.951057
      1.41        -0.989725        -0.987688
      1.57        -1.002053        -1.000000
      1.73        -0.989725        -0.987688
      1.88        -0.953010        -0.951057
      2.04        -0.892845        -0.891007
      2.20        -0.810677        -0.809017
      2.36        -0.708565        -0.707107
      2.51        -0.588995        -0.587785
      2.67        -0.454923        -0.453991
      2.83        -0.309659        -0.309017
      2.98        -0.156737        -0.156434
      3.14        -0.000074         0.000000