Corpus ID: 236133957

On a Class of Polar Log-Aesthetic Curves

  title={On a Class of Polar Log-Aesthetic Curves},
  author={Victor Parque},
  • V. Parque
  • Published 2021
  • Computer Science, Mathematics
  • ArXiv
Curves are essential concepts that enable compounded aesthetic curves, e.g., to assemble complex silhouettes, match a specific curvature profile in industrial design, and construct smooth, comfortable, and safe trajectories in vehicle-robot navigation systems. New mechanisms able to encode, generate, evaluate, and deform aesthetic curves are expected to improve the throughput and the quality of industrial design. In recent years, the study of (log) aesthetic curves have attracted the community… Expand


An aesthetic curve in the field of Industrial design
Five types of curves are developed which have the self-affine property and can be used as a 'common language' between the designer, the modeler, and the operator of CAD systems for communicating the 'design intent'. Expand
A General Equation of Aesthetic Curves and its Self-Affinity
AbstractThe curve is the most basic design element to determine shapes and silhouettes of industrial products and works for shape designers and it is inevitable for them to make it aesthetic andExpand
Minimum variation log-aesthetic surfaces and their applications for smoothing free-form shapes
Based on variational principle the method can generate surfaces by minimizing the objective function newly proposed in this paper for given arbitrary boundary curves. Expand
The Polar-aesthetic Curve and Its Applications to Scissors Design
ABSTRACTThe origin of scissors is very old and a pair of scissors which was probably made in ancient Greece around B.C. 1000 is discovered. In Japan a new type of scissors was produced with newlyExpand
A new formulation of the minimum variation log-aesthetic surface for scale-invariance and parameterization-independence
ABSTRACTThe log-aesthetic curve, which includes the logarithmic (equiangular) spiral, clothoid, and circular involute, achieves control over the curvature distribution by defining its shape as anExpand
Variational formulation of the log-aesthetic curve
This work reformulate the LA curve with variational principle in order to analyze its properties and it is shown that the log-aesthetic curves, including the logarithmic spiral, clothoid, and involute curves, are suitable for practical use in graphical design. Expand
Analytic parametric equations of log-aesthetic curves in terms of incomplete gamma functions
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 adaptiveExpand
CAD tools for aesthetic engineering
  • C. Séquin
  • Engineering, Computer Science
  • Comput. Aided Des.
  • 2005
The role of computers and of computer-aided design tools for the creation of geometrical shapes that will be judged primarily by aesthetic considerations is reviewed and true interactivity of the CAD tools allows a more effective exploration of larger parts of the design space. Expand
On Path Planning using Minimal Aesthetic B-Spline Curves
Computational results in arbitrary polygonal environments show that the proposed path planning using aesthetic Bspline curves to render minimal-length and smooth paths that avoid obstacles is feasible. Expand
Log-aesthetic curves as similarity geometric analogue of Euler's elasticae
The result suggests that the log-aesthetic curves and their generalization can be regarded as the similarity geometric analogue of Euler's elasticae. Expand