The use of Cornu spirals in drawing planar curves of controlled curvature
Journal of Computational and Applied Mathematics
Calculation of Gauss-Kronrod quadrature rules
Mathematics of Computation
Designing Bézier conic segments with monotone curvature
Computer Aided Geometric Design
Journal of Computational and Applied Mathematics
Designing Fair Curves and Surfaces: Shape Quality in Geometric Modeling and Computer-Aided Design
Designing Fair Curves and Surfaces: Shape Quality in Geometric Modeling and Computer-Aided Design
Planar G2 transition with a fair Pythagorean hodograph quintic curve
Journal of Computational and Applied Mathematics
A New Aesthetic Dsign Workflow - Results from the European Project FIORES
CAD Tools and Algorithms for Product Design [Dagstuhl Seminar, November 1998]
A Discrete Spring Model for Generating Fair Curves and Surfaces
PG '99 Proceedings of the 7th Pacific Conference on Computer Graphics and Applications
An Aesthetic Curve in the Field of Industrial Design
VL '99 Proceedings of the IEEE Symposium on Visual Languages
Planar G2 transition curves composed of cubic Bézier spiral segments
Journal of Computational and Applied Mathematics
Designing fair curves using monotone curvature pieces
Computer Aided Geometric Design
Simplified and Flexible Spiral Transitions for Use in Computer Graphics and Geometric Modelling
ICIG '04 Proceedings of the Third International Conference on Image and Graphics
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Interactive aesthetic curve segments
The Visual Computer: International Journal of Computer Graphics
On PH quintic spirals joining two circles with one circle inside the other
Computer-Aided Design
G2 cubic transition between two circles with shape control
Journal of Computational and Applied Mathematics
Log-aesthetic space curve segments
2009 SIAM/ACM Joint Conference on Geometric and Physical Modeling
Applying inversion to construct planar, rational spirals that satisfy two-point G2 Hermite data
Computer Aided Geometric Design
Two-point G2 Hermite interpolation with spirals by inversion of hyperbola
Computer Aided Geometric Design
Analytic parametric equations of log-aesthetic curves in terms of incomplete gamma functions
Computer Aided Geometric Design
Curvature monotony condition for rational quadratic b-spline curves
ICCSA'06 Proceedings of the 6th international conference on Computational Science and Its Applications - Volume Part I
Logarithmic curvature and torsion graphs
MMCS'08 Proceedings of the 7th international conference on Mathematical Methods for Curves and Surfaces
A generalized log aesthetic space curve
Proceedings of the 2012 Joint International Conference on Human-Centered Computer Environments
Variational formulation of the log-aesthetic curve
Proceedings of the 2012 Joint International Conference on Human-Centered Computer Environments
Fitting G2 multispiral transition curve joining two straight lines
Computer-Aided Design
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We present superspirals, a new and very general family of fair curves, whose radius of curvature is given in terms of a completely monotonic Gauss hypergeometric function. The superspirals are generalizations of log-aesthetic curves, as well as other curves whose radius of curvature is a particular case of a completely monotonic Gauss hypergeometric function. High-accuracy computation of a superspiral segment is performed by the Gauss-Kronrod integration method. The proposed curves, despite their complexity, are the candidates for generating G^2, and G^3 non-linear superspiral splines.