Curves and surfaces in computer aided geometric design
Curves and surfaces in computer aided geometric design
Choosing nodes in parametric curve interpolation
Computer-Aided Design
Parameter optimization in approximating curves and surfaces to measurement data
Computer Aided Geometric Design
Curves and surfaces for computer aided geometric design (3rd ed.): a practical guide
Curves and surfaces for computer aided geometric design (3rd ed.): a practical guide
Fundamentals of computer aided geometric design
Fundamentals of computer aided geometric design
Geometric Hermite interpolation
Computer Aided Geometric Design
Geometric Hermite interpolation with maximal order and smoothness
Computer Aided Geometric Design
Elimination and Resultants - Part 1: Elimination and Bivariate Resultants
IEEE Computer Graphics and Applications
IEEE Computer Graphics and Applications
An error-bounded approximate method for representing planar curves in B-splines
Computer Aided Geometric Design
Spline curve approximation and design by optimal control over the knots
Computing - Geometric modelling dagstuhl 2002
B-spline curve fitting based on adaptive curve refinement using dominant points
Computer-Aided Design
Point-tangent/point-normal B-spline curve interpolation by geometric algorithms
Computer-Aided Design
Cubic B-spline curve approximation by curve unclamping
Computer-Aided Design
The convergence of the geometric interpolation algorithm
Computer-Aided Design
G2 Hermite interpolation with circular precision
Computer-Aided Design
Optimization of parameters for curve interpolation by cubic splines
Journal of Computational and Applied Mathematics
Least eccentric ellipses for geometric Hermite interpolation
Computer Aided Geometric Design
Lagrange geometric interpolation by rational spatial cubic Bézier curves
Computer Aided Geometric Design
Local computation of curve interpolation knots with quadratic precision
Computer-Aided Design
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This paper discusses a cubic B-spline interpolation problem with tangent directional constraint in R^3 space. Given m points and their tangent directional vectors as well, the interpolation problem is to find a cubic B-spline curve which interpolates both the positions of the points and their tangent directional vectors. Given the knot vector of the resulting B-spline curve and parameter values to all of the data points, the corresponding control points can often be obtained by solving a system of linear equations. This paper presents a piecewise geometric interpolation method combining a unclamping technique with a knot extension technique, with which there is no need to solve a system of linear equations. It firstly uses geometric methods to construct a seed curve segment, which interpolates several data point pairs, i.e., positions and tangent directional vectors of the points. The seed segment is then extended to interpolate the remaining data point pairs one by one in a piecewise fashion. We show that a B-spline curve segment can always be extended to interpolate a new data point pair by adding two more control points. Methods for a curve segment extending to interpolate one more data point pair by adding one more control point are also provided, which are utilized to construct an interpolation B-spline curve with as small a number of control points as possible. Numerical examples show the effectiveness and the efficiency of the new method.