Log-aesthetic space curve segments
2009 SIAM/ACM Joint Conference on Geometric and Physical Modeling
Analytic parametric equations of log-aesthetic curves in terms of incomplete gamma functions
Computer Aided Geometric Design
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
Computer Aided Geometric Design
Planar two-point G1 Hermite interpolating log-aesthetic spirals
Journal of Computational and Applied Mathematics
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To meet highly aesthetic requirements in industrial design and styling, we propose a new category of aesthetic curve segments. To achieve these aesthetic requirements, we use curves whose logarithmic curvature histograms (LCH) are represented by straight lines. We call such curves aesthetic curves. We identify the overall shapes of aesthetic curves depending on the slope of LCH α, by imposing specific constraints to the general formula of aesthetic curves. For interactive control, we propose a novel method for drawing an aesthetic curve segment by specifying two endpoints and their tangent vectors. We clarify several characteristics of aesthetic curve segments.