Log-aesthetic curves: Similarity geometry, integrable discretization and variational principles

Inoguchi, Jun-ichi; Jikumaru, Yoshiki; Kajiwara, Kenji; Miura, Kenjiro T.; Schief, Wolfgang K.

doi:10.1016/j.cagd.2023.102233

Computer Aided Geometric Design

2023

DOI: 10.1016/j.cagd.2023.102233

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Log-aesthetic curves: Similarity geometry, integrable discretization and variational principles

Jun-ichi Inoguchi,

Yoshiki Jikumaru,

Kenji Kajiwara

et al.

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2024

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Cited by 1 publication

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Parametric generation of optimal structures through discrete exponential functions: unveiling connections between structural optimality and discrete isothermicity

Hayashi,

Jikumaru,

Yokosuka

et al. 2024

Struct Multidisc Optim

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This study discusses an equilibrium state of structures endowed with integrability and relates the structural optimality for Michell’s classic problem and the isothermicity in discrete differential geometry. This discussion leads to a new approach for the parametric generation of quasi-optimal layouts of bar members. The layout of bar members is determined by taking the diagonals of a quadrilateral mesh constructed from a discrete exponential function. The configuration of the planar layout can be changed by adjusting the parameters of a discrete exponential function. In addition, the inverse stereographic projection allows for obtaining spherical shapes from the planar layouts, and the Möbius transformations enable the generation of eccentric near-optimal shapes. It is also demonstrated that the structural layouts generated in this study are the exact optimal or near-optimal solution to Michell’s optimization problem.

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Parametric generation of optimal structures through discrete exponential functions: unveiling connections between structural optimality and discrete isothermicity

Hayashi,

Jikumaru,

Yokosuka

et al. 2024

Struct Multidisc Optim

View full text Add to dashboard Cite

show abstract

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Log-aesthetic curves: Similarity geometry, integrable discretization and variational principles

Cited by 1 publication

References 30 publications

Parametric generation of optimal structures through discrete exponential functions: unveiling connections between structural optimality and discrete isothermicity

Parametric generation of optimal structures through discrete exponential functions: unveiling connections between structural optimality and discrete isothermicity

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