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RISS 인기검색어
- 검색키워드
- 저자 : Kenjiro T. Miura (검색결과 5 건)
- 무료
- 기관 내 무료
- 유료
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τ-curve: introduction of cusps to aesthetic curves
Kenjiro T. Miura,Sho Suzuki,Shin Usuki,R.U. Gobithaasan 한국CDE학회 2020 Journal of computational design and engineering Vol.7 No.2
Yan, Schiller, Wilensky, Carr, and Schaefer pointed out that one of the demerits of clothoid interpolation is a jumping behavior during the deformation of the curve. This phenomenon occurs because the clothoid curve cannot have a cusp, where the curve is kinked or the direction of the curve is abruptly changed. We discuss how to introduce cusps for the log-aesthetic curve including the clothoid curve and propose to use for the representation of a curve the direction angle instead of curvature and define a new curve named τ-curve, which is defined by the direction angle of the curve.
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Robot Trajectory Generation with Smoothly Changing Curvature Using the Clothoid Spline
Dai Shibuya,Shin Usuki,Kenjiro T. Miura (사)한국CDE학회 2013 한국CAD/CAM학회 국제학술발표 논문집 Vol.2010 No.8
In this paper we propose optimization methods for trajectory design using the clothoid spline, which consists of several clothoid curve segments with some parametric or geometric continuity, in two-dimensional space. As a trajectory path, the clothoid curve is superior to other ones because its curvature varies linearly with its arc length. However, a single clothoid segment cannot generally satisfies both tangent and curvature conditions at its end points because the number of parameters, i.e. its degree of freedom is insufficient. In order to solve the problem mentioned above, “the triple-clothoid”[1], which is a clothoid spline consisting of three clothoid segments, was introduced to match both tangent and curvature boundary conditions. It has sufficient parameters needed for tangent and curvature matching at its end point. The clothoid spline with three segments were used to construct a smooth transition passing through arbitrary point sequence. The resultant trajectory possesses curvature continuity, i.e. G2 continuity and matches all tangent and curvature specifications at the giving points. However, the clothoid spline with three segments that passes through specified points is not uniquely determined. Therefore we propose optimization methods to minimize the trajectory path length and an energy consumption measure in this paper.
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Log-aesthetic curves and their relation to fluid flow patterns in terms of streamlines
Mei Seen Wo,R.U. Gobithaasan,Kenjiro T. Miura,Kak Choon Loy,Sadaf Yasmeen,Fatimah Noor Harun 한국CDE학회 2021 Journal of computational design and engineering Vol.8 No.1
The log-aesthetic curve (LAC) is a family of aesthetic curves with linear logarithmic curvature graphs (LCGs). It encompasses well-known aesthetic curves such as clothoid, logarithmic spiral, and circle involute. LAC has been playing a pivotal role in aesthetic design. However, its application for functional design is an uncharted territory, e.g. the relationship between LAC and fluid flow patterns may aid in designing better ship hulls and breakwaters. We address this problem by elucidating the relationship between LAC and flow patterns in terms of streamlines at a steady state. We discussed how LAC pathlines form under the influence of pressure gradient via Euler’s equation and how LAC streamlines are formed in a special case. LCG gradient (α) for implicit and explicit functions is derived, and it is proven that the LCG gradient at the inflection points of explicit functions is always 0 when its third derivative is nonzero. Due to the complexity of the parametric representation of LAC, it is almost impossible to derive the general representation of LAC streamlines. We address this by analyzing the streamlines formed by incompressible flow around an airfoil-like obstacle generated with LAC having various shapes, αr = {−20, − 5, − 1, − 0.5, − 0.15, 0, 1, 2, 3, 4, 20}, and simulating the streamlines using FreeFem++ reaching a steady state. We found that the LCG gradient of the resultant streamlines is close to that of a clothoid. When the obstacle shape is almost the same as that of a circle (α = 20), the streamlines adjacent to the obstacles have numerous curvature extrema despite nearing steady state. The flow speed variation is the lowest for α = −1.43 and gets higher as α is increased or decreased from α = −1.43.
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Minimum variation log-aesthetic surfaces and their applications for smoothing free-form shapes
Sho Suzuki,R.U. Gobithaasan,Péter Salvi,Shin Usuki,Kenjiro T. Miura 한국CDE학회 2018 Journal of computational design and engineering Vol.5 No.2
The log-aesthetic curve, which includes the logarithmic (equiangular) spiral, clothoid, and involute of a circle, achieves a control over curvature distribution by defining its shape as an integral form of its curvature and they are expected to be utilized for the field of design. However, it is very difficult to extend it to surfaces and the existing formulations have some problems that they cannot use arbitrary boundary curves. In this paper, we propose ‘‘minimum variation log-aesthetic surface” as a new formulation for the log-aesthetic surface. Based on variational principle our method can generate surfaces by minimizing the objective function newly proposed in this paper for given arbitrary boundary curves.
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Minimum variation log-aesthetic surfaces and their applications for smoothing free-form shapes
Suzuki, Sho,Gobithaasan, R.U.,Salvi, Peter,Usuki, Shin,Miura, Kenjiro T. Society for Computational Design and Engineering 2018 Journal of computational design and engineering Vol.5 No.2
The log-aesthetic curve, which includes the logarithmic (equiangular) spiral, clothoid, and involute of a circle, achieves a control over curvature distribution by defining its shape as an integral form of its curvature and they are expected to be utilized for the field of design. However, it is very difficult to extend it to surfaces and the existing formulations have some problems that they cannot use arbitrary boundary curves. In this paper, we propose ''minimum variation log-aesthetic surface" as a new formulation for the log-aesthetic surface. Based on variational principle our method can generate surfaces by minimizing the objective function newly proposed in this paper for given arbitrary boundary curves.
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