Logarithmic curvature graph as a shape interrogation tool

Gobithaasan, R. U.; Miura, Kenjiro T.

doi:10.12988/ams.2014.312709

Cited by 11 publications

(8 citation statements)

References 8 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…There are two fundamental equations representing adaptive RK methods as shown in Eqs. (8) and (9). The difference y nþ1 Àŷ nþ1 is the approximation for the truncation error employed to calculate the next appropriate step size h.…”

Section: Adaptive Runge-kutta Methodsmentioning

confidence: 99%

See 1 more Smart Citation

Generation of Log-aesthetic curves using adaptive Runge–Kutta methods

Gobithaasan

Teh

Piah

et al. 2014

Applied Mathematics and Computation

Self Cite

View full text Add to dashboard Cite

Section: Adaptive Runge-kutta Methodsmentioning

confidence: 99%

“…Logarithmic Curvature Graph (LCG) is an analytic representation of LDDC which was first introduced by Kanaya et al (2003). The details of LDDC and LCH can be obtained from [8] and reference therein.…”

Section: Introductionmentioning

confidence: 99%

Generation of Log-aesthetic curves using adaptive Runge–Kutta methods

Gobithaasan

Teh

Piah

et al. 2014

Applied Mathematics and Computation

Self Cite

View full text Add to dashboard Cite

“…In 2003, Kanaya et al simplified the formulation of LDDC to a simpler form, hence denoting it as Logarithmic Curvature Graph (LCG). Recently, Gobithaasan and Miura (2014) further proposed on using LCG as a shape interrogation tool for arbitrary curves.…”

Section: The Formulation Of Logarithmic Curvature Graph That Leads Tomentioning

confidence: 99%

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

Gobithaasan¹,

Miura²,

Yee³

et al. 2014

MAS

Self Cite

View full text Add to dashboard Cite

The quality of a curve for industrial design and computer graphics can be interrogated using Logarithmic Curvature Graph (LCG) and Logarithmic Torsion Graph (LTG). A curve is said to be aesthetic if it depicts linear LCG and LTG function. The Log-aesthetic curve (LAC) was developed bearing this notion and it was later extended to a Generalized Log-aesthetic curve (GLAC) using the -shift and -shift approach. This paper reformulates GLAC by representing the Logarithmic Curvature and Torsion graph's gradient function as a nonlinear ordinary differential equation (ODE) with boundary conditions. The outputs of solving the ODEs result in a well defined Cesaro equation in the form of curvature function that is able to produce both planar as well as spatial curves with promising entities for industrial product design, computer graphics and more.

show abstract

“…It is the same for aesthetic designs in CAGD. However, lines and circles are considered fair or beautiful because of their simplicity [2]. The definition of a fair curve still remains subjective and unclear, which makes the condition required for ending a fairing process seems rather ambiguous.…”

Section: Introductionmentioning

confidence: 99%

Log-Aesthetic Magnetic Curves and Their Application for CAD Systems

Gobithaasan

Miura

2014

Mathematical Problems in Engineering

Self Cite

View full text Add to dashboard Cite

Curves are the building blocks of shapes and designs in computer aided geometric design (CAGD). It is important to ensure these curves are both visually and geometrically aesthetic to meet the high aesthetic need for successful product marketing. Recently, magnetic curves that have been proposed for computer graphics purposes are a particle tracing technique that generates a wide variety of curves and spirals under the influence of a magnetic field. The contributions of this paper are threefold, where the first part reformulates magnetic curves in the form of log-aesthetic curve (LAC) denoting it as log-aesthetic magnetic curves (LMC) and log-aesthetic magnetic space curves (LMSC), the second part elucidates vital properties of LMCs, and the final part proposes G2LMC design for CAD applications. The final section shows two examples of LMC surface generation along with its zebra maps. LMC holds great potential in overcoming the weaknesses found in current interactive LAC mechanism where matching a single segment with G2Hermite data is still a cumbersome task.

show abstract

Logarithmic curvature graph as a shape interrogation tool

Cited by 11 publications

References 8 publications

Generation of Log-aesthetic curves using adaptive Runge–Kutta methods

Generation of Log-aesthetic curves using adaptive Runge–Kutta methods

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

Log-Aesthetic Magnetic Curves and Their Application for CAD Systems

Contact Info

Product

Resources

About