Geometric concepts for geometric design
Geometric concepts for 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
An automated curve fairing algorithm for cubic B-spline curves
Journal of Computational and Applied Mathematics - Special issue on computational methods in computer graphics
Designing Bézier conic segments with monotone curvature
Computer Aided Geometric Design
Applied Geometry for Computer Graphics
Applied Geometry for Computer Graphics
The Essentials of CAGD
A New Aesthetic Dsign Workflow - Results from the European Project FIORES
CAD Tools and Algorithms for Product Design [Dagstuhl Seminar, November 1998]
Modifying Curvatures at Design Points for Convex B-spline Curves
CGI '97 Proceedings of the 1997 Conference on Computer Graphics International
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
Curve generation and modification based on radius of curvature smoothing
MACMESE'08 Proceedings of the 10th WSEAS international conference on Mathematical and computational methods in science and engineering
Geometry modeling for cotton leaf based on NURBS
WSEAS Transactions on Information Science and Applications
Quintic B-spline curve generation and modification based on specified radius of curvature
MATH'09 Proceedings of the 14th WSEAS International Conference on Applied mathematics
Adaptive moving least squares for scattering points fitting
WSEAS Transactions on Computers
The theory and application of an adaptive moving least squares for non-uniform samples
WSEAS Transactions on Computers
WSEAS Transactions on Mathematics
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For the purpose of evaluation, a NURBS curve is used, because it is commonly used in the areas of CAD/CAM and Computer Graphics. A curve with a monotone radius of curvature distribution is considered as a fair curve in the area of Computer Aided Aesthetic Design (CAAD). But no official standards have been established. Therefore, a criterion for a fair curve is proposed. A quintic NURBS curve, the first derivative of a quintic NURBS curve, curvature vector, curvature, and radius of curvature are expressed. The concept of radius of curvature specification to modify the shape of a NURBS curve is illustrated. The difference between the NURBS curve radius of curvature and the specified radius of curvature is minimized by introducing the least-squares method to modify the shape of the NURBS curve. As curve fairness evaluation, radius of curvature distribution is used as an alternative characteristic of a curve. Algebraic functions such as linear, quadratic, cubic, quartic, quintic, and six degrees are applied to the radius of curvature distribution of the designed curve to specify the radius of curvature. Then, the shape of the curve is modified according to the specified radius of curvature distribution. In this manner, six NURBS curves whose radius of curvature are these algebraic functions are generated, and are predefined. Using the correlation matching, the similarity is evaluated by comparing the radius of curvature distribution of the designed curve with those of six NURBS curves predefined. The highest similarity curve to the designed curve among these predefined curves is selected. The similarity evaluated of the selected curve is determined as fairness of the designed curve.