Path splines with conic envelopes

We look at path splines as constructed by joining tangent continuously segments of envelopes of 1-parameter families of conics. Each envelope is an algebraic curve of degree four or less. A path spline interpolates a sequence of point/tangent pairs and for each segment there is an additional shape handle which allows for the dilation or contraction of that segment of the path spline without altering the rest of it. The mathematical construction of the spline reduces to defining a Bézier curve in higher dimensional space: the space of conics. The cubic hypersurface corresponding to the degenerate conics plays a role in the construction.