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