Functional optimization for fair surface design
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
Designing Bézier conic segments with monotone curvature
Computer Aided Geometric Design
Curves and surfaces for CAGD: a practical guide
Curves and surfaces for CAGD: a practical guide
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
Interactive aesthetic curve segments
The Visual Computer: International Journal of Computer Graphics
Computer Aided Geometric Design
Spiral fat arcs - Bounding regions with cubic convergence
Graphical Models
A generalized log aesthetic space curve
Proceedings of the 2012 Joint International Conference on Human-Centered Computer Environments
Computer Aided Geometric Design
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For designing aesthetic surfaces, such as the car bodies, it is very important to use aesthetic curves as characteristic lines. In such curves, the curvature should be monotonically varying, since it dominates the distortion of reflected images on curved surfaces. In this paper, we present an interactive control method of log-aesthetic space curves. We define log-aesthetic space curves to be curves whose logarithmic curvature and torsion graphs are both linear. The linearity of these graphs constrains that the curvature and torsion are monotonically varying. We clarify the characteristics of log-aesthetic space curves and identify their family. Moreover, we present a novel method for drawing a log-aesthetic space curve segment by specifying two endpoints, their tangents, the slopes, α and β, of straight lines of the logarithmic curvature and torsion graphs, and the torsion parameter Ω. Our implementation shows that log-aesthetic curve segments can be controlled fully interactively.