Designing Log-aesthetic Splines with<i>G<sup>2</sup></i>Continuity

Miura, Kenjiro T.; Shibuya, Dai; Gobithaasan, R. U.; Usuki, Satoshi

doi:10.3722/cadaps.2013.1021-1032

Cited by 31 publications

(18 citation statements)

References 15 publications

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“…This Fuzzy Linguistic Control Point was redefined to solve the uncertainty and linguistic data. The model presented can be used in other spline model such as B-Spines, NURBS (Non-Uniform Rational B-Spline) and LogAesthetic [18][19][20] for industrial method.…”

Section: Resultsmentioning

confidence: 99%

A new types of spline modeling using fuzzy linguistic approach

Wahab¹,

Husain²

2016

AIP Conference Proceedings

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Abstract. The problem of fuzzy linguistic data is difficult to analyze. By the existing approaches are not be able to describe the data in the form of a generic figure which smooth and continuous. This is because the generalization of the problems of linguistic data in the form of curves and surfaces require a new of the models which characterized by a fuzzy linguistic. In this paper introduces new types of fuzzy spline models such as Fuzzy Linguistic Bezier and Fuzzy Linguistic B-Splines by using the definition of fuzzy linguistic control points. For the effectives of the model, some numerical examples are given at the end of this paper.

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Section: Resultsmentioning

confidence: 99%

A new types of spline modeling using fuzzy linguistic approach

Wahab¹,

Husain²

2016

AIP Conference Proceedings

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“…Moreover, the truncation error of classical RK method is substantially small. A noticeable speed can be experienced when one renders a piecewise LAC similar to techniques stated in [8,20], using LAC as a fairing method [15] and extending LACs to form aesthetic surfaces. Our next workin-progress includes automated control of stepsize with defined accuracy using adaptive Runge-Kutta methods.…”

Section: Discussionmentioning

confidence: 99%

“…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.…”

Section: Introductionmentioning

confidence: 99%

Rendering log aesthetic curves via Runge-Kutta method

Gobithaasan¹,

Meng²,

Piah³

et al. 2014

AIP Conference Proceedings

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Abstract. Log Aesthetic Curves (LAC) are visually pleasing curves which has been developed using monotonic curvature profile. Hence, it can be easily implemented in product design environment, e.g, Rhino 3D CAD systems. LAC is generally represented in an integral form of its turning angle. Traditionally, Gaussian-Kronrod method has been used to render this curve which consumes less than one second for a given interval. Recently, Incomplete Gamma Function was proposed to represent LAC analytically which decreases the computation time up to 13 times. However, only certain value of shape parameters (denoted as α) which dictates the types of curves generated for LAC, can be used to compute LAC. In this paper, the classical Runge-Kutta (RK4) method is proposed to evaluate LAC numerically to reduce the LAC computation time for arbitrary, α. The preliminary result looks promising where the evaluation time is decreased tremendously. This paper also demonstrates the accuracy control of LAC by reducing the stepsize of RK4. The computation time and the accuracy for various α, are also illustrated in the last section of this paper.

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“…Recently, Miura et al proposed an algorithm to design LAC spline with G 2 continuity and it was made into a plugin for Rhino 3D CAD system. They further illustrated the maturity of this algorithm by showing its application in automobile design [14]. Readers are referred to an extensive review on aesthetic curves and surfaces [15].…”

Section: Introductionmentioning

confidence: 99%