Drawable Region of the Generalized Log Aesthetic Curves

Abstract

The main characteristic of visually pleasing curves used for product design is a monotonic curvature profile. Recently, a planar curve called Generalized Log Aesthetic Curve (GLAC) has been extended from the Log Aesthetic Curve (LAC), and it has an additional shape parameter,ν. This curve preserves the monotonicity of curvature and is said to produce visually pleasing curves. This paper delves on the drawable region of the GLAC segment which indicates the probable solutions of shape parameters from given interpolating points and the direction of travel at those points. The first section reviews the formulation of GLAC and its related bounds. The section describes the algorithm for identifying the drawable region. It is followed by the section describing how small changes ofνwiden the drawable boundaries. The final section discusses the superiority of GLAC compared to LAC for use in industrial product design.

G2Continuous Generalized Log-Aesthetic Curves

“…3. To note, the constraints are easily satisfied during the parameter searching and the existence of solutions is proven to be far wider than the LA curves [7]. Although the final end curvatures change due to scaling, the G 2 continuity is achieved successfully.…”

“…The interactive design of GLAC satisfying G 1 Hermite data has been proposed by Gobithaasan et al [7] where its drawable region has been proven to be much wider than the leading LA curves.…”

“…GLAC produces LA curves, Generalized Cornu Spiral (GCS), logarithmic spiral, clothoid, Nielsen's spiral & circle involute a [6]. The vitality of GLAC is further elucidated in [7] where they proved that the drawable region of GLAC is wider as compared to LAC in which GLAC provides wider solution in which the LA curves could not. Recent research on GLAC includes the extension of spatial GLAC [3].…”

Aesthetic Curve Design with Linear Gradients of Logarithmic Curvature/Torsion Graphs

“…In order to indicate its robustness in Computer Aided Design applications, Gobithaasan et al (2013) showed that the Generalized Log Aesthetic Curve has wider drawable region compared to Log Aesthetic Curve. However, the Logarithmic Curvature Graph gradient of GLAC is in the form of a nonlinear function as follows: Λ 1 1 whereas LAC has LCG gradient as .…”

Rendering log aesthetic curves via Runge-Kutta method

“…In 2012, Ziatdinov et al [17] presented an analytic solution of LAC in terms of Incomplete Gamma Function which reduced the computation time up to 13 times. Recent progresses include shape analysis on GLAC [18], its drawable region which is wider than LAC [19] and the implementation of G2 LAC as plug-in for Rhino CAD system [20]. This paper proposes a numerical method which is called classical Runge-Kutta method to compute LAC.…”