Shape-preserving interpolation by fair discrete G3 space curves

We present a new method for interpolation by a shape-preserving space curve with third-order geometric continuity. The curve is represented by a discrete sequence of vertices along with first, second, and third derivative vectors at each vertex, where derivatives are with respect to arc length. A user need only specify the number of vertices and a single tension factor in addition to the control points to be interpolated. The method consists of minimizing the total variation of curvature subject to the interpolation and shape-preservation constraints. The method is global but relatively efficient, and it consistently produces curves with pleasing graphical behavior.