Knot removal for parametric B-spline curves and surfaces
Computer Aided Geometric Design
Automatic fairing algorithm for B-spline curves
Computer-Aided Design
Progress in computer graphics (vol. 1)
Geometric concepts for geometric design
Geometric concepts for geometric design
Fundamentals of computer aided geometric design
Fundamentals of computer aided geometric design
The NURBS book
Interpolating curve with B-spline curvature function
Proceedings of the international conference on Mathematical methods for curves and surfaces II Lillehammer, 1997
A method for determining knots in parametric curve interpolation
Computer Aided Geometric Design
A New Method of Interpolation and Smooth Curve Fitting Based on Local Procedures
Journal of the ACM (JACM)
Geometric modeling with splines: an introduction
Geometric modeling with splines: an introduction
Applied Geometry for Computer Graphics
Applied Geometry for Computer Graphics
The Essentials of CAGD
Curvature and the Fairness of Curves and Surfaces
IEEE Computer Graphics and Applications
Target curvature driven fairing algorithm for planar cubic B-spline curves
Computer Aided Geometric Design
Practical Linear Algebra: A Geometry Toolbox
Practical Linear Algebra: A Geometry Toolbox
Fair NURBS curve generation using a hand-drawn sketch for computer aided aesthetic design
ISCGAV'07 Proceedings of the 7th WSEAS International Conference on Signal Processing, Computational Geometry & Artificial Vision
NURBS curve shape modification and fairness evaluation for computer aided aesthetic design
ISCGAV'07 Proceedings of the 7th WSEAS International Conference on Signal Processing, Computational Geometry & Artificial Vision
A fair curve generation algorithm based on a hand-drawn sketch
ISCGAV'06 Proceedings of the 6th WSEAS International Conference on Signal Processing, Computational Geometry & Artificial Vision
NURBS curve shape modification and fairness evaluation
WSEAS Transactions on Computers
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A method to generate a quintic B-spline curve which passes through the given points is described. In this case, there are four more unknown control point positions than there are equations. To overcome this problem three methods are described. First, solve the underdetermined system as it stands. Secondly, decrease the number of unknown control point positions in an underdetermined system in order to convert it to a determined system. Third, a method to increase the number of equations is employed to change an underdetermined system to a determined system. In addition to this, another method to generate a quintic B-spline curve using given points with gradients in sequence is described. In this case, a linear system will be either overdetermined, determined or underdetermined. This depends on the number of given points with gradients in sequence. Additionally, a method to modify a quintic B-spline curve is described. The objective is to change an aesthetically unpleasing curve to an aesthetically pleasing curve. Algebraic functions are used to determine an aesthetically pleasing radius of curvature distribution. This is accomplished by minimizing the difference between the quintic B-spline curves radius of curvature and the specified radius of curvature using the least-squares method. Examples of curve generation are given.