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Author Wang, L.; Ratkowsky, D.A.; Gielis, J.; Ricci, P.E.; Shi, P. url  doi
openurl 
  Title Effects of the numerical values of the parameters in the Gielis equation on its geometries Type A1 Journal article
  Year 2022 Publication (up) Symmetry Abbreviated Journal Symmetry-Basel  
  Volume 14 Issue 12 Pages 2475-12  
  Keywords A1 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)  
  Abstract The Lamé curve is an extension of an ellipse, the latter being a special case. Dr. Johan Gielis further extended the Lamé curve in the polar coordinate system by introducing additional parameters (n1, n2, n3; m): rφ=1Acosm4φn2+1Bsinm4φn3−1/n1, which can be applied to model natural geometries. Here, r is the polar radius corresponding to the polar angle φ; A, B, n1, n2 and n3 are parameters to be estimated; m is the positive real number that determines the number of angles of the Gielis curve. Most prior studies on the Gielis equation focused mainly on its applications. However, the Gielis equation can also generate a large number of shapes that are rotationally symmetric and axisymmetric when A = B and n2 = n3, interrelated with the parameter m, with the parameters n1 and n2 determining the shapes of the curves. In this paper, we prove the relationship between m and the rotational symmetry and axial symmetry of the Gielis curve from a theoretical point of view with the condition A = B, n2 = n3. We also set n1 and n2 to take negative real numbers rather than only taking positive real numbers, then classify the curves based on extremal properties of r(φ) at φ = 0, π/m when n1 and n2 are in different intervals, and analyze how n1, n2 precisely affect the shapes of Gielis curves.  
  Address  
  Corporate Author Thesis  
  Publisher Place of Publication Editor  
  Language Wos 000904525700001 Publication Date 2022-11-23  
  Series Editor Series Title Abbreviated Series Title  
  Series Volume Series Issue Edition  
  ISSN 2073-8994 ISBN Additional Links UA library record; WoS full record  
  Impact Factor 2.7 Times cited Open Access OpenAccess  
  Notes Approved Most recent IF: 2.7  
  Call Number UA @ admin @ c:irua:191860 Serial 7301  
Permanent link to this record
 

 
Author Shi, P.; Ratkowsky, D.A.; Gielis, J. url  doi
openurl 
  Title The generalized Gielis geometric equation and its application Type A1 Journal article
  Year 2020 Publication (up) Symmetry-Basel Abbreviated Journal Symmetry-Basel  
  Volume 12 Issue 4 Pages 645-10  
  Keywords A1 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)  
  Abstract 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.  
  Address  
  Corporate Author Thesis  
  Publisher Place of Publication Editor  
  Language Wos 000540222200156 Publication Date 2020-04-21  
  Series Editor Series Title Abbreviated Series Title  
  Series Volume Series Issue Edition  
  ISSN 2073-8994 ISBN Additional Links UA library record; WoS full record; WoS citing articles  
  Impact Factor 2.7 Times cited 4 Open Access  
  Notes ; This research was funded by the Jiangsu Government Scholarship for Overseas Studies (grant number: JS-2018-038). ; Approved Most recent IF: 2.7; 2020 IF: 1.457  
  Call Number UA @ admin @ c:irua:168141 Serial 6526  
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Author Huang, W.; Li, Y.; Niklas, K.J.; Gielis, J.; Ding, Y.; Cao, L.; Shi, P. url  doi
openurl 
  Title A superellipse with deformation and its application in describing the cross-sectional shapes of a square bamboo Type A1 Journal article
  Year 2020 Publication (up) Symmetry-Basel Abbreviated Journal Symmetry-Basel  
  Volume 12 Issue 12 Pages 2073  
  Keywords A1 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)  
  Abstract Many cross-sectional shapes of plants have been found to approximate a superellipse rather than an ellipse. Square bamboos, belonging to the genus Chimonobambusa (Poaceae), are a group of plants with round-edged square-like culm cross sections. The initial application of superellipses to model these culm cross sections has focused on Chimonobambusa quadrangularis (Franceschi) Makino. However, there is a need for large scale empirical data to confirm this hypothesis. In this study, approximately 750 cross sections from 30 culms of C. utilis were scanned to obtain cross-sectional boundary coordinates. A superellipse exhibits a centrosymmetry, but in nature the cross sections of culms usually deviate from a standard circle, ellipse, or superellipse because of the influences of the environment and terrain, resulting in different bending and torsion forces during growth. Thus, more natural cross-sectional shapes appear to have the form of a deformed superellipse. The superellipse equation with a deformation parameter (SEDP) was used to fit boundary data. We find that the cross-sectional shapes (including outer and inner rings) of C. utilis can be well described by SEDP. The adjusted root-mean-square error of SEDP is smaller than that of the superellipse equation without a deformation parameter. A major finding is that the cross-sectional shapes can be divided into two types of superellipse curves: hyperellipses and hypoellipses, even for cross sections from the same culm. There are two proportional relationships between ring area and the product of ring length and width for both the outer and inner rings. The proportionality coefficients are significantly different, as a consequence of the two different superellipse types (i.e., hyperellipses and hypoellipses). The difference in the proportionality coefficients between hyperellipses and hypoellipses for outer rings is greater than that for inner rings. This work informs our understanding and quantifying of the longitudinal deformation of plant stems for future studies to assess the influences of the environment on stem development. This work is also informative for understanding the deviation of natural shapes from a strict rotational symmetry.  
  Address  
  Corporate Author Thesis  
  Publisher Place of Publication Editor  
  Language Wos 000602546300001 Publication Date 2020-12-15  
  Series Editor Series Title Abbreviated Series Title  
  Series Volume Series Issue Edition  
  ISSN 2073-8994 ISBN Additional Links UA library record; WoS full record; WoS citing articles  
  Impact Factor 2.7 Times cited Open Access  
  Notes Approved Most recent IF: 2.7; 2020 IF: 1.457  
  Call Number UA @ admin @ c:irua:174472 Serial 8622  
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Author Shi, P.; Liu, M.; Ratkowsky, D.A.; Gielis, J.; Su, J.; Yu, X.; Wang, P.; Zhang, L.; Lin, Z.; Schrader, J. pdf  url
doi  openurl
  Title Leaf area-length allometry and its implications in leaf shape evolution Type A1 Journal article
  Year 2019 Publication (up) Trees: structure and function Abbreviated Journal  
  Volume 33 Issue 4 Pages 1073-1085  
  Keywords A1 Journal article; Sustainable Energy, Air and Water Technology (DuEL)  
  Abstract According to Thompson’s principle of similarity, the area of an object should be proportional to its length squared. However, leaf area–length data of some plants have been demonstrated not to follow the principle of similarity. We explore the reasons why the leaf area–length allometry deviates from the principle of similarity and examine whether there is a general model describing the relationship among leaf area, width and length. We sampled more than 11,800 leaves from six classes of woody and herbaceous plants and tested the leaf area–length allometry. We compared six mathematical models based on root-mean-square error as the measure of goodness-of-fit. The best supported model described a proportional relationship between leaf area and the product of leaf width and length (i.e., the Montgomery model). We found that the extent to which the leaf area–length allometry deviates from the principle of similarity depends upon the extent of variation of the ratio of leaf width to length. Estimates of the parameter of the Montgomery model ranged between 1/2, which corresponds to a triangular leaf with leaf length as its height and leaf width as its base, and π/4, which corresponds to an elliptical leaf with leaf length as its major axis and leaf width as its minor axis, for the six classes of plants. The narrow range in practice of the Montgomery parameter implies an evolutionary stability for the leaf area of large-leaved plants despite the fact that leaf shapes of these plants are rather different.  
  Address  
  Corporate Author Thesis  
  Publisher Place of Publication Editor  
  Language Wos 000475992600010 Publication Date 2019-04-04  
  Series Editor Series Title Abbreviated Series Title  
  Series Volume Series Issue Edition  
  ISSN 0931-1890; 1432-2285 ISBN Additional Links UA library record; WoS full record; WoS citing articles  
  Impact Factor Times cited Open Access  
  Notes Approved no  
  Call Number UA @ admin @ c:irua:159970 Serial 8170  
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Author Lian, M.; Shi, P.; Zhang, L.; Yao, W.; Gielis, J.; Niklas, K.J. pdf  url
doi  openurl
  Title A generalized performance equation and its application in measuring the Gini index of leaf size inequality Type A1 Journal article
  Year 2023 Publication (up) Trees: structure and function Abbreviated Journal  
  Volume 37 Issue Pages 1555-1565  
  Keywords A1 Journal article; Sustainable Energy, Air and Water Technology (DuEL)  
  Abstract The goal of this study is to provide a rigorous tool to quantify the inequality of the leaf size distribution of an individual plant, thereby serving as a reference trait for quantifying plant adaptations to local environmental conditions. The tool to be presented and tested employs three components: (1) a performance equation (PE), which can produce flexible asymmetrical and symmetrical bell-shaped curves, (2) the Lorenz curve (i.e., the cumulative proportion of leaf size vs. the cumulative proportion of number of leaves), which is the basis for calculating, and (3) the Gini index, which measures the inequality of leaf size distribution. We sampled 12 individual plants of a dwarf bamboo and measured the area and dry mass of each leaf of each plant. We then developed a generalized performance equation (GPE) of which the PE is a special case and fitted the Lorenz curve to leaf size distribution using the GPE and PE. The GPE performed better than the PE in fitting the Lorenz curve. We compared the Gini index of leaf area distribution with that of leaf dry mass distribution and found that there was a significant difference between the two indices that might emerge from the scaling relationship between leaf dry mass and area. Nevertheless, there was a strong correlation between the two Gini indices (r2 = 0.9846). This study provides a promising tool based on the GPE for quantifying the inequality of leaf size distributions across individual plants and can be used to quantify plant adaptations to local environmental conditions.  
  Address  
  Corporate Author Thesis  
  Publisher Place of Publication Editor  
  Language Wos 001069570200001 Publication Date 2023-08-26  
  Series Editor Series Title Abbreviated Series Title  
  Series Volume Series Issue Edition  
  ISSN 0931-1890; 1432-2285 ISBN Additional Links UA library record; WoS full record; WoS citing articles  
  Impact Factor 2.3 Times cited Open Access Not_Open_Access: Available from 26.02.2024  
  Notes Approved Most recent IF: 2.3; 2023 IF: 1.842  
  Call Number UA @ admin @ c:irua:199562 Serial 8874  
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