Scalar- and planar-valued curve fitting using splines under tension
Communications of the ACM
Cross-sectional design with curvature constraints
Computer-Aided Design
Interpolating curves with gradual changes in curvature
Computer Aided Geometric Design
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G. Nielson [1974] gave a piecewise polynomial alternative to splines under tension, the so-called v-splines. The v-splines are the solution of a minimal norm problem and they have curvature continuity. In this paper the v-splines are generalized to geometric spline curves and the computational equations of quintic splines curves with curvature and torsion continuity are given. These curves will be referred to as @t-splines.