The use of Cornu spirals in drawing planar curves of controlled curvature
Journal of Computational and Applied Mathematics
Controlling the curvature of a quadratic Be´zier curve
Computer Aided Geometric Design
Calculation of Gauss-Kronrod quadrature rules
Mathematics of Computation
A shape controlled fitting method for Be´zier curves
Computer Aided Geometric Design
Designing Bézier conic segments with monotone curvature
Computer Aided Geometric Design
A New Aesthetic Dsign Workflow - Results from the European Project FIORES
CAD Tools and Algorithms for Product Design [Dagstuhl Seminar, November 1998]
An Aesthetic Curve in the Field of Industrial Design
VL '99 Proceedings of the IEEE Symposium on Visual Languages
Designing fair curves using monotone curvature pieces
Computer Aided Geometric Design
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
Logarithmic curvature and torsion graphs
MMCS'08 Proceedings of the 7th international conference on Mathematical Methods for Curves and Surfaces
Magnetic curves: curvature-controlled aesthetic curves using magnetic fields
Computational Aesthetics'09 Proceedings of the Fifth Eurographics conference on Computational Aesthetics in Graphics, Visualization and Imaging
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
Computer Aided Geometric Design
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Log-aesthetic curves (LACs) have recently been developed to meet the requirements of industrial design for visually pleasing shapes. LACs are defined in terms of definite integrals, and adaptive Gaussian quadrature can be used to obtain curve segments. To date, these integrals have only been evaluated analytically for restricted values (0,1,2) of the shape parameter @a. We present parametric equations expressed in terms of incomplete gamma functions, which allow us to find an exact analytic representation of a curve segment for any real value of @a. The computation time for generating an LAC segment using the incomplete gamma functions is up to 13 times faster than using direct numerical integration. Our equations are generalizations of the well-known Cornu, Nielsen, and logarithmic spirals, and involutes of a circle.