Convexity-preserving interpolatory parametric splines of non-uniform polynomial degree
Computer Aided Geometric Design
Shape preserving interpolation by space curves
Computer Aided Geometric Design
Constructing fair curves and surfaces with a Sobolev gradient method
Computer Aided Geometric Design
Numerical Methods for Unconstrained Optimization and Nonlinear Equations (Classics in Applied Mathematics, 16)
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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.