Cubic helical splines with Frenet-frame continuity Original Research Article

We present a scheme of interpolating a sequence of points image in image by a piecewise-cubic-helical spline with continuous Frenet frame. Each cubic helical segment image connecting image and image is constructed such that its end tangents are symmetric with respect to the displacement vector image. The existence condition of such a segment image is formulated in terms of the configuration involving image and the Frenet frame of image at image. A Frenet-frame-continuous spline is obtained by matching the Frenet frames of sequentially constructed segments at their juncture points.