Computing the minimum Hausdorff distance for point sets under translation
SCG '90 Proceedings of the sixth annual symposium on Computational geometry
Geometric concepts for geometric design
Geometric concepts for geometric design
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
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
Shape approximation using circular grids
WSEAS Transactions on Information Science and Applications
WSEAS Transactions on Mathematics
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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. Algebraic functions such as linear, quadratic, cubic, quartic, quintic, and six degrees are applied to the radius of curvature distribution of the designed curve as the specified radius of curvature. The radius of curvature distributions given by these six algebraic functions are considered monotone, because the independent variable of these algebraic functions is monotone to the corresponding dependent variable of these functions. Similarity is evaluated using the radius of curvature distribution according to six algebraic functions as references and the radius of curvature distribution of the designed curves as matches by using correlation matching. Curve shape similarity evaluation is tried using an example. Considering that a curve with a monotone variation of radius of curvature distribution is fair, the similarity of the designed curve to a fair curve is evaluated. This measured similarity expresses fairness to the fair curve. Using this technique, the fairness of a curve is evaluated by using the similarity of the radius of curvature distribution.