Local control of interval tension using weighted splines
Computer Aided Geometric Design
Curves and surfaces for computer aided geometric design: a practical guide
Curves and surfaces for computer aided geometric design: a practical guide
Computer Aided Geometric Design
What is the natural generalization of a Be´zier curve?
Mathematical methods in computer aided geometric design
On the choice of parameters in shape-preserving quadratic spline interpolation
Journal of Computational and Applied Mathematics
Guest Editor's Introduction CAGD's Top Ten: What to Watch
IEEE Computer Graphics and Applications - Special issue on computer-aided geometric design
Fundamentals of computer aided geometric design
Fundamentals of computer aided geometric design
Harmonic rational Bézier curves, p-Be´zier curves and trigonometric polynomials
Computer Aided Geometric Design
Graphical Models and Image Processing
Advances in Applied Mathematics
IEEE Computer Graphics and Applications
q-Bernstein polynomials and Bézier curves
Journal of Computational and Applied Mathematics
p-Bézier curves, spirals, and sectrix curves
Computer Aided Geometric Design
The beta-spline: a local representation based on shape parameters and fundamental geometric measures
The beta-spline: a local representation based on shape parameters and fundamental geometric measures
Cubic trigonometric polynomial curves with a shape parameter
Computer Aided Geometric Design
Computer Aided Geometric Design
A Generalization of cubic curves and their Bézier representations
Mathematical and Computer Modelling: An International Journal
On a new approach to obtain spline Bézier curves
ICCOMP'10 Proceedings of the 14th WSEAS international conference on Computers: part of the 14th WSEAS CSCC multiconference - Volume II
Generalized Bézier curves and surfaces based on Lupaş q-analogue of Bernstein operator
Journal of Computational and Applied Mathematics
Curves and Surfaces Construction Based on New Basis with Exponential Functions
Acta Applicandae Mathematicae: an international survey journal on applying mathematics and mathematical applications
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A new formulation for the representation and designing of curves and surfaces is presented. It is a novel generalization of Bezier curves and surfaces. Firstly, a class of polynomial basis functions with n adjustable shape parameters is present. It is a natural extension to classical Bernstein basis functions. The corresponding Bezier curves and surfaces, the so-called Quasi-Bezier (i.e., Q-Bezier, for short) curves and surfaces, are also constructed and their properties studied. It has been shown that the main advantage compared to the ordinary Bezier curves and surfaces is that after inputting a set of control points and values of newly introduced n shape parameters, the desired curve or surface can be flexibly chosen from a set of curves or surfaces which differ either locally or globally by suitably modifying the values of the shape parameters, when the control polygon is maintained. The Q-Bezier curve and surface inherit the most properties of Bezier curve and surface and can be more approximated to the control polygon. It is visible that the properties of end-points on Q-Bezier curve and surface can be locally controlled by these shape parameters. Some examples are given by figures.