The Geometrical Beauty of Plants

Gielis, Johan

doi:10.2991/978-94-6239-151-2

Cited by 48 publications

(97 citation statements)

References 11 publications

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“…These geometries naturally exist in plants [35]. Herein, three kinds of SNPs are assumed to names of curved NPs ( Fig.1a1-1a6), pod NPs ( Fig.1b1-1b6) and starfish NPs(( Fig.1c1-1c6)).…”

Section: Resultsmentioning

confidence: 99%

Supershape Nanoparticle Plasmons

2017

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In this work, we proposed new shape nanoparticles in the name of supershape nanoparticles by manipulation in the morphology of a disk nanoparticle. The electric field distribution of supershape nanoparticles were investigated at resonance wavelength of particle plasmons. The effects of dispersed medium and different sensory materials on particle plasmons were reported. The obtained results showed that there exist the multiple plasmonics modes in supershape nanoparticles. We found that the high sensitivity factor is available in the supershape nanoparticles. This study can be a base for the characterization of multiple particle plasmons in plasmonic devices for sensing applications.

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“…These geometries naturally exist in plants [35]. Herein, three kinds of SNPs are assumed to names of curved NPs ( Fig.1a1-1a6), pod NPs ( Fig.1b1-1b6) and starfish NPs(( Fig.1c1-1c6)).…”

Section: Resultsmentioning

confidence: 99%

Supershape Nanoparticle Plasmons

2017

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“…The values of a and b control the size, and the exponents n 1 , n 2 and n 3 control the curvature of the sides. The superformula can produce a wide range of shapes, including many shapes found in nature; the reader is referred to Gielis (2003;2017) for more examples.…”

Section: Supershapesmentioning

confidence: 99%

“…Section 3 describes the projection of the supershapes onto a density field for the analysis. The computation of the signed distance to (Bell et al 2012(Norato et al 2015, 2016 (Zhang et al 2016a) Union of rectangular bars with straight (Bell et al 2012) or semicircular (Norato et al 2015) (Guo et al 2014b), 2016a (Zhang et al 2016b), 2016b (Guo et al 2016), 2017(Zhang et al 2017b Union of rectangles approximated as superellipses (Guo et al 2014b), or curved quadrilaterals with polynomial or trigonometric sides (Zhang et al 2016b;Guo et al 2016) Positions and orientation of discrete elements, dimensions (Guo et al 2014b) and curve parameters (Zhang et al 2016b;Guo et al 2016) Maximum of Heaviside function of individual geometric components XFEM to follow level set (Guo et al 2014b;Zhang et al 2016b), ersatz material from average of nodal smooth Heaviside (Guo et al 2016) Through union of Heavisides (bars merge, separate and are engulfed in other bars); no component insertion XFEM (Guo et al 2014b;…”

Section: Introductionmentioning

confidence: 99%

Topology optimization with supershapes

Norato

2018

Struct Multidisc Optim

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This work presents a method for the continuum-based topology optimization of structures whereby the structure is represented by the union of supershapes. Supershapes are an extension of superellipses that can exhibit variable symmetry as well as asymmetry and that can describe through a single equation, the so-called superformula, a wide variety of shapes, including geometric primitives. As demonstrated by the author and his collaborators and by others in previous work, the availability of a feature-based description of the geometry opens the possibility to impose geometric constraints that are otherwise difficult to impose in density-based or level set-based approaches. Moreover, such description lends itself to direct translation to computer aided design systems. This work is an extension of the author's group previous work, where it was desired for the discrete geometric elements that describe the structure to have a fixed shape (but variable dimensions) in order to design structures made of stock material, such as bars and plates. The use of supershapes provides a more general geometry description that, using a single formulation, can render a structure made exclusively of the union of geometric primitives. It is also desirable to retain hallmark advantages of existing methods, namely the ability to employ a fixed grid for the analysis to circumvent re-meshing and the availability of sensitivities to use robust and efficient gradient-based optimization methods. The conduit between the geometric representation of the supershapes and the fixed analysis discretization is, as in previous work, a differentiable geometry projection that maps the supershapes parameters onto a density field. The proposed approach is demonstrated on classical problems of 2-dimensional compliance-based topology optimization.

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“…where A and B (A ≥ B > 0) represent the major and minor axis semi-diameters, respectively. Interestingly, circles and ellipses, as well as squares and rectangles, can be regarded as special cases of Lamé curves [1,2], whose mathematical expression is listed as…”

Section: Introductionmentioning

confidence: 99%

“…where n is a real number. This equation has been shown to be valid for describing the actual cross-sections of tree rings and bamboo shoots [2][3][4][5]. Equation (3) in polar coordinates can be rewritten as…”

Section: Introductionmentioning

confidence: 99%

The Generalized Gielis Geometric Equation and Its Application

2020

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Many natural shapes exhibit surprising symmetry and can be described by the Gielis equation, which has several classical geometric equations (for example, the circle, ellipse and superellipse) as special cases. However, the original Gielis equation cannot reflect some diverse shapes due to limitations of its power-law hypothesis. In the present study, we propose a generalized version by introducing a link function. Thus, the original Gielis equation can be deemed to be a special case of the generalized Gielis equation (GGE) with a power-law link function. The link function can be based on the morphological features of different objects so that the GGE is more flexible in fitting the data of the shape than its original version. The GGE is shown to be valid in depicting the shapes of some starfish and plant leaves.

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The Geometrical Beauty of Plants

Cited by 48 publications

References 11 publications

Supershape Nanoparticle Plasmons

Supershape Nanoparticle Plasmons

Topology optimization with supershapes

The Generalized Gielis Geometric Equation and Its Application

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