  We demonstrate a method for exact determination of the quadratic curve of
minimal energy and minimal curvature variation through three non-colinear
points in the plane, including methods to determine the tangent vector and
curvature at any point along the curve and an exact expression for the arc
length of the curve between the first and last points. We then extended this to
a novel method of selecting tangent vectors for use in constructing Hermite
splines to smoothly interpolate ordered sets of control points. Our results are
spline curves of lower energy than that of many popular spline implementations
in most cases, which a series of examples demonstrate.
