Second-derivatives for sin(x) from 0 to PI
                  spline          actual
     angle      2nd deriv       2nd deriv
     0.16       -0.156832       -0.156434
     0.31       -0.309631       -0.309017
     0.47       -0.454933       -0.453991
     0.63       -0.588991       -0.587785
     0.79       -0.708561       -0.707107
     0.94       -0.810685       -0.809017
     1.10       -0.892837       -0.891007
     1.26       -0.953020       -0.951057
     1.41       -0.989715       -0.987688
     1.57       -1.002063       -1.000000
     1.73       -0.989715       -0.987688
     1.88       -0.953020       -0.951056
     2.04       -0.892835       -0.891006
     2.20       -0.810685       -0.809017
     2.36       -0.708558       -0.707107
     2.51       -0.588999       -0.587785
     2.67       -0.454920       -0.453990
     2.83       -0.309660       -0.309017
     2.98       -0.156736       -0.156434
     3.14       -0.000075        0.000000