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Author |
Shi, P.; Wang, L.; Quinn, B.K.K.; Gielis, J. |
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Title |
A new program to estimate the parameters of Preston's equation, a general formula for describing the egg shape of birds |
Type |
A1 Journal article |
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Year  |
2023 |
Publication |
Symmetry |
Abbreviated Journal |
Symmetry-Basel |
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Volume |
15 |
Issue |
1 |
Pages |
231-10 |
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Keywords |
A1 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL) |
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Abstract |
Preston's equation is a general model describing the egg shape of birds. The parameters of Preston's equation are usually estimated after re-expressing it as the Todd-Smart equation and scaling the egg's actual length to two. This method assumes that the straight line through the two points on an egg's profile separated by the maximum distance (i.e., the longest axis of an egg's profile) is the mid-line. It hypothesizes that the photographed egg's profile is perfectly bilaterally symmetrical, which seldom holds true because of photographic errors and placement errors. The existing parameter estimation method for Preston's equation considers an angle of deviation for the longest axis of an egg's profile from the mid-line, which decreases prediction errors to a certain degree. Nevertheless, this method cannot provide an accurate estimate of the coordinates of the egg's center, and it leads to sub-optimal parameter estimation. Thus, it is better to account for the possible asymmetry between the two sides of an egg's profile along its mid-line when fitting egg-shape data. In this paper, we propose a method based on the optimization algorithm (optimPE) to fit egg-shape data and better estimate the parameters of Preston's equation by automatically searching for the optimal mid-line of an egg's profile and testing its validity using profiles of 59 bird eggs spanning a wide range of existing egg shapes. We further compared this method with the existing one based on multiple linear regression (lmPE). This study demonstrated the ability of the optimPE method to estimate numerical values of the parameters of Preston's equation and provide the theoretical egg length (i.e., the distance between two ends of the mid-line of an egg's profile) and the egg's maximum breadth. This provides a valuable approach for comparing egg shapes among conspecifics or across different species, or even different classes (e.g., birds and reptiles), in future investigations. |
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Wos |
000927531000001 |
Publication Date |
2023-01-13 |
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Edition |
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ISSN |
2073-8994 |
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Additional Links |
UA library record; WoS full record; WoS citing articles |
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Impact Factor |
2.7 |
Times cited |
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Open Access |
OpenAccess |
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Notes |
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Approved |
Most recent IF: 2.7; 2023 IF: 1.457 |
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Call Number |
UA @ admin @ c:irua:195347 |
Serial |
7279 |
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Author |
Li, Y.; Quinn, B.K.; Gielis, J.; Li, Y.; Shi, P. |
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Title |
Evidence that supertriangles exist in nature from the vertical projections of Koelreuteria paniculata fruit |
Type |
A1 Journal article |
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Year |
2022 |
Publication |
Symmetry |
Abbreviated Journal |
Symmetry-Basel |
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Volume |
14 |
Issue |
1 |
Pages |
23 |
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Keywords |
A1 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL) |
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Abstract |
Many natural radial symmetrical shapes (e.g., sea stars) follow the Gielis equation (GE) or its twin equation (TGE). A supertriangle (three triangles arranged around a central polygon) represents such a shape, but no study has tested whether natural shapes can be represented as/are supertriangles or whether the GE or TGE can describe their shape. We collected 100 pieces of Koelreuteria paniculata fruit, which have a supertriangular shape, extracted the boundary coordinates for their vertical projections, and then fitted them with the GE and TGE. The adjusted root mean square errors (RMSEadj) of the two equations were always less than 0.08, and >70% were less than 0.05. For 57/100 fruit projections, the GE had a lower RMSEadj than the TGE, although overall differences in the goodness of fit were non-significant. However, the TGE produces more symmetrical shapes than the GE as the two parameters controlling the extent of symmetry in it are approximately equal. This work demonstrates that natural supertriangles exist, validates the use of the GE and TGE to model their shapes, and suggests that different complex radially symmetrical shapes can be generated by the same equation, implying that different types of biological symmetry may result from the same biophysical mechanisms. |
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Wos |
000746030100001 |
Publication Date |
2021-12-27 |
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Edition |
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ISSN |
2073-8994 |
ISBN |
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Additional Links |
UA library record; WoS full record; WoS citing articles |
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Impact Factor |
2.7 |
Times cited |
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Open Access |
OpenAccess |
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Notes |
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Approved |
Most recent IF: 2.7 |
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Call Number |
UA @ admin @ c:irua:186453 |
Serial |
7158 |
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Author |
Wang, L.; Ratkowsky, D.A.; Gielis, J.; Ricci, P.E.; Shi, P. |
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Title |
Effects of the numerical values of the parameters in the Gielis equation on its geometries |
Type |
A1 Journal article |
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Year |
2022 |
Publication |
Symmetry |
Abbreviated Journal |
Symmetry-Basel |
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Volume |
14 |
Issue |
12 |
Pages |
2475-12 |
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Keywords |
A1 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL) |
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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. |
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Wos |
000904525700001 |
Publication Date |
2022-11-23 |
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Abbreviated Series Title |
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Series Volume |
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Series Issue |
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Edition |
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ISSN |
2073-8994 |
ISBN |
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Additional Links |
UA library record; WoS full record |
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Impact Factor |
2.7 |
Times cited |
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Open Access |
OpenAccess |
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Notes |
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Approved |
Most recent IF: 2.7 |
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Call Number |
UA @ admin @ c:irua:191860 |
Serial |
7301 |
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