Tubular Splines Using A Higher Dimensional Representation

Tubular splines are like the usual spline curves, but have thickness, i.e. locally look like circular cones. They are constructed with pieces of indefinitely differentiable surfaces whose profiles are circles, which are joined together with a prescribed degree of smoothness. We consider splines constructed joining together pieces of canal surfaces bounded by circles. A canal surface is determined by a moving sphere of changing radius. We explore a new way to control the geometric shape of the individual sections of the spline without affecting the neighboring pieces of the spline, using the representation of spheres as points in a 4-dimensional space.