Records |
Author |
Shi, P.; Gielis, J.; Quinn, B.K.; Niklas, K.J.; Ratkowsky, D.A.; Schrader, J.; Ruan, H.; Wang, L.; Niinemets, Ü.; Niinennets, U. |
Title |
‘biogeom’ : an R package for simulating and fitting natural shapes |
Type |
A1 Journal article |
Year |
2022 |
Publication |
Annals of the New York Academy of Sciences |
Abbreviated Journal |
Ann Ny Acad Sci |
Volume |
1516 |
Issue |
1 |
Pages |
123-134 |
Keywords |
A1 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL) |
Abstract |
Many natural objects exhibit radial or axial symmetry in a single plane. However, a universal tool for simulating and fitting the shapes of such objects is lacking. Herein, we present an R package called 'biogeom' that simulates and fits many shapes found in nature. The package incorporates novel universal parametric equations that generate the profiles of bird eggs, flowers, linear and lanceolate leaves, seeds, starfish, and tree-rings, and three growth-rate equations that generate the profiles of ovate leaves and the ontogenetic growth curves of animals and plants. 'biogeom' includes several empirical datasets comprising the boundary coordinates of bird eggs, fruits, lanceolate and ovate leaves, tree rings, seeds, and sea stars. The package can also be applied to other kinds of natural shapes similar to those in the datasets. In addition, the package includes sigmoid curves derived from the three growth-rate equations, which can be used to model animal and plant growth trajectories and predict the times associated with maximum growth rate. 'biogeom' can quantify the intra- or interspecific similarity of natural outlines, and it provides quantitative information of shape and ontogenetic modification of shape with important ecological and evolutionary implications for the growth and form of the living world. |
Address |
|
Corporate Author |
|
Thesis |
|
Publisher |
|
Place of Publication |
|
Editor |
|
Language |
|
Wos |
000829772300001 |
Publication Date |
2022-07-26 |
Series Editor |
|
Series Title |
|
Abbreviated Series Title |
|
Series Volume |
|
Series Issue |
|
Edition |
|
ISSN |
0077-8923; 1749-6632 |
ISBN |
|
Additional Links |
UA library record; WoS full record; WoS citing articles |
Impact Factor |
5.2 |
Times cited |
|
Open Access |
OpenAccess |
Notes |
|
Approved |
Most recent IF: 5.2 |
Call Number |
UA @ admin @ c:irua:189314 |
Serial |
7131 |
Permanent link to this record |
|
|
|
Author |
Lin, S.; Shao, L.; Hui, C.; Song, Y.; Reddy, G.V.P.; Gielis, J.; Li, F.; Ding, Y.; Wei, Q.; Shi, P.; Reddy, G.V.P. |
Title |
Why does not the leaf weight-area allometry of bamboos follow the 3/2-power law? |
Type |
A1 Journal article |
Year |
2018 |
Publication |
Frontiers in plant science |
Abbreviated Journal |
|
Volume |
9 |
Issue |
|
Pages |
583 |
Keywords |
A1 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL) |
Abstract |
The principle of similarity (Thompson, 1917) states that the weight of an organism follows the 3/2-power law of its surface area and is proportional to its volume on the condition that the density is constant. However, the allometric relationship between leaf weight and leaf area has been reported to greatly deviate from the 3/2-power law, with the irregularity of leaf density largely ignored for explaining this deviation. Here, we choose 11 bamboo species to explore the allometric relationships among leaf area (A), density (ρ), length (L), thickness (T), and weight (W). Because the edge of a bamboo leaf follows a simplified two-parameter Gielis equation, we could show that A ∝ L2 and that A ∝ T2. This then allowed us to derive the density-thickness allometry ρ ∝ Tb and the weight-area allometry W ∝ A(b+3)/2 ≈ A9/8, where b approximates −3/4. Leaf density is strikingly negatively associated with leaf thickness, and it is this inverse relationship that results in the weight-area allometry to deviate from the 3/2-power law. In conclusion, although plants are prone to invest less dry mass and thus produce thinner leaves when the leaf area is sufficient for photosynthesis, such leaf thinning needs to be accompanied with elevated density to ensure structural stability. The findings provide the insights on the evolutionary clue about the biomass investment and output of photosynthetic organs of plants. Because of the importance of leaves, plants could have enhanced the ratio of dry material per unit area of leaf in order to increase the efficiency of photosynthesis, relative the other parts of plants. Although the conclusion is drawn only based on 11 bamboo species, it should also be applicable to the other plants, especially considering previous works on the exponent of the weight-area relationship being less than 3/2 in plants. |
Address |
|
Corporate Author |
|
Thesis |
|
Publisher |
|
Place of Publication |
|
Editor |
|
Language |
|
Wos |
000431415100001 |
Publication Date |
2018-05-04 |
Series Editor |
|
Series Title |
|
Abbreviated Series Title |
|
Series Volume |
|
Series Issue |
|
Edition |
|
ISSN |
1664-462x |
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:150948 |
Serial |
8758 |
Permanent link to this record |
|
|
|
Author |
Gielis, J.; Caratelli, D.; Fougerolle, Y.; Ricci, P.E.; Tavkelidze, I.; Gerats, T. |
Title |
Universal natural shapes : from unifying shape description to simple methods for shape analysis and boundary value problems |
Type |
A1 Journal article |
Year |
2012 |
Publication |
PLoS ONE |
Abbreviated Journal |
|
Volume |
7 |
Issue |
9 |
Pages |
e29324-11 |
Keywords |
A1 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL) |
Abstract |
Gielis curves and surfaces can describe a wide range of natural shapes and they have been used in various studies in biology and physics as descriptive tool. This has stimulated the generalization of widely used computational methods. Here we show that proper normalization of the Levenberg-Marquardt algorithm allows for efficient and robust reconstruction of Gielis curves, including self-intersecting and asymmetric curves, without increasing the overall complexity of the algorithm. Then, we show how complex curves of k-type can be constructed and how solutions to the Dirichlet problem for the Laplace equation on these complex domains can be derived using a semi-Fourier method. In all three methods, descriptive and computational power and efficiency is obtained in a surprisingly simple way. |
Address |
|
Corporate Author |
|
Thesis |
|
Publisher |
|
Place of Publication |
|
Editor |
|
Language |
|
Wos |
000309517500001 |
Publication Date |
2012-09-30 |
Series Editor |
|
Series Title |
|
Abbreviated Series Title |
|
Series Volume |
|
Series Issue |
|
Edition |
|
ISSN |
1932-6203 |
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:102202 |
Serial |
8711 |
Permanent link to this record |
|
|
|
Author |
Gielis, J.; Shi, P.; Caratelli, D. |
Title |
Universal equations : a fresh perspective |
Type |
A1 Journal article |
Year |
2022 |
Publication |
Growth and Form |
Abbreviated Journal |
|
Volume |
|
Issue |
|
Pages |
|
Keywords |
A1 Journal article; Sustainable Energy, Air and Water Technology (DuEL) |
Abstract |
A uniform description of natural shapes and phenomena is an important goal in science. Such description should check some basic principles, related to 1) the complexity of the model, 2) how well its fits real objects, phenomena and data, and 3) ia direct connection with optimization principles and the calculus of variations. In this article, we present nine principles, three for each group, and we compare some models with a claim to universality. It is also shown that Gielis Transformations and power laws have a common origin in conic sections |
Address |
|
Corporate Author |
|
Thesis |
|
Publisher |
|
Place of Publication |
|
Editor |
|
Language |
|
Wos |
|
Publication Date |
|
Series Editor |
|
Series Title |
|
Abbreviated Series Title |
|
Series Volume |
|
Series Issue |
|
Edition |
|
ISSN |
|
ISBN |
|
Additional Links |
UA library record |
Impact Factor |
|
Times cited |
|
Open Access |
|
Notes |
|
Approved |
Most recent IF: NA |
Call Number |
UA @ admin @ c:irua:189317 |
Serial |
7224 |
Permanent link to this record |
|
|
|
Author |
Gielis, J.; Ding, Y.; Shi, P. |
Title |
Towards a geometrical theory of morphology and morphogenesis |
Type |
P3 Proceeding |
Year |
2016 |
Publication |
|
Abbreviated Journal |
|
Volume |
|
Issue |
|
Pages |
|
Keywords |
P3 Proceeding; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL) |
Abstract |
|
Address |
|
Corporate Author |
|
Thesis |
|
Publisher |
|
Place of Publication |
|
Editor |
|
Language |
|
Wos |
|
Publication Date |
|
Series Editor |
|
Series Title |
|
Abbreviated Series Title |
|
Series Volume |
|
Series Issue |
|
Edition |
|
ISSN |
|
ISBN |
|
Additional Links |
UA library record |
Impact Factor |
|
Times cited |
|
Open Access |
|
Notes |
|
Approved |
no |
Call Number |
UA @ admin @ c:irua:144548 |
Serial |
8677 |
Permanent link to this record |
|
|
|
Author |
Huang, W.; Su, X.; Ratkowsky, D.A.; Niklas, K.J.; Gielis, J.; Shi, P. |
Title |
The scaling relationships of leaf biomass vs. leaf surface area of 12 bamboo species |
Type |
A1 Journal article |
Year |
2019 |
Publication |
Global ecology and conservation |
Abbreviated Journal |
|
Volume |
20 |
Issue |
|
Pages |
e00793 |
Keywords |
A1 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL) |
Abstract |
There is convincing evidence for a scaling relationship between leaf dry weight (DW) and leaf surface area (A) for broad-leaved plants, and most estimates of the scaling exponent of DW vs. A are greater than unity. However, the scaling relationship of leaf fresh weight (FW) vs. A has been largely neglected. In the present study, we examined whether there is a statistically strong scaling relationship between FW and A and compared the goodness of fit to that of DW vs. A. Between 250 and 520 leaves from each of 12 bamboo species within 2 genera (Phyllostachys and Pleioblastus) were investigated. The reduced major axis regression protocols were used to determine scaling relationships. The fit for the linearized scaling relationship of FW vs. A was compared with that of DW vs. A using the coefficient of determination (i.e., r2). A stronger scaling relationship between FW and A than that between DW and A was observed for each of the 12 bamboo species investigated. Among the 12 species examined, five had significantly smaller scaling exponents of FW vs. A compared to those of DW vs. A; only one species had a scaling exponent of FW vs. A greater than that of DW vs. A. No significant difference between the two scaling exponents was observed for the remaining 6 species. Researchers conducting future studies might be well advised to consider the influence of leaf fresh weight when exploring the scaling relationships of foliar biomass allocation patterns. |
Address |
|
Corporate Author |
|
Thesis |
|
Publisher |
|
Place of Publication |
|
Editor |
|
Language |
|
Wos |
000498226800095 |
Publication Date |
2019-09-19 |
Series Editor |
|
Series Title |
|
Abbreviated Series Title |
|
Series Volume |
|
Series Issue |
|
Edition |
|
ISSN |
2351-9894; 2351-9894 |
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:162954 |
Serial |
8497 |
Permanent link to this record |
|
|
|
Author |
Caratelli, D.; Gielis, J.; Natalini, P.; Ricci, P.E.; Tavkhelidze, I. |
Title |
The Robin problem for the Helmholtz equation in a starlike planar domain |
Type |
A1 Journal article |
Year |
2011 |
Publication |
Georgian mathematical journal |
Abbreviated Journal |
|
Volume |
18 |
Issue |
3 |
Pages |
465-479 |
Keywords |
A1 Journal article; Sustainable Energy, Air and Water Technology (DuEL) |
Abstract |
The interior and exterior Robin problems for the Helmholtz equation in starlike planar domains are addressed by using a suitable Fourier-like technique. Attention is in particular focused on normal-polar domains whose boundaries are defined by the so-called superformula introduced by J. Gielis. A dedicated numerical procedure based on the computer algebra system Mathematica© is developed in order to validate the proposed approach. In this way, highly accurate approximations of the solution, featuring properties similar to the classical ones, are obtained. The computed results are found to be in good agreement with the theoretical findings on Fourier series expansion presented by L. Carleson. |
Address |
|
Corporate Author |
|
Thesis |
|
Publisher |
|
Place of Publication |
|
Editor |
|
Language |
|
Wos |
000296166100004 |
Publication Date |
2021-02-28 |
Series Editor |
|
Series Title |
|
Abbreviated Series Title |
|
Series Volume |
|
Series Issue |
|
Edition |
|
ISSN |
1072-947x |
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:91086 |
Serial |
8658 |
Permanent link to this record |
|
|
|
Author |
Tavkhelidze, I.; Gielis, J. |
Title |
The process of cutting GMLmn bodies with dm-knives |
Type |
A3 Journal article |
Year |
2018 |
Publication |
Sn – 1512-0066 |
Abbreviated Journal |
|
Volume |
32 |
Issue |
|
Pages |
67-70 |
Keywords |
A3 Journal article; Sustainable Energy, Air and Water Technology (DuEL) |
Abstract |
|
Address |
|
Corporate Author |
|
Thesis |
|
Publisher |
|
Place of Publication |
|
Editor |
|
Language |
|
Wos |
|
Publication Date |
|
Series Editor |
|
Series Title |
|
Abbreviated Series Title |
|
Series Volume |
|
Series Issue |
|
Edition |
|
ISSN |
|
ISBN |
|
Additional Links |
UA library record |
Impact Factor |
|
Times cited |
|
Open Access |
|
Notes |
|
Approved |
no |
Call Number |
UA @ admin @ c:irua:159971 |
Serial |
8417 |
Permanent link to this record |
|
|
|
Author |
Gielis, J.; Tavkhelidze, I. |
Title |
The Mӧbius phenomenon in Generalized Mӧbius-Listing bodies with cross sections of odd and even polygons |
Type |
A3 Journal article |
Year |
2020 |
Publication |
Sn – 1512-0066 |
Abbreviated Journal |
|
Volume |
34 |
Issue |
|
Pages |
23-26 |
Keywords |
A3 Journal article; Sustainable Energy, Air and Water Technology (DuEL) |
Abstract |
|
Address |
|
Corporate Author |
|
Thesis |
|
Publisher |
|
Place of Publication |
|
Editor |
|
Language |
|
Wos |
|
Publication Date |
|
Series Editor |
|
Series Title |
|
Abbreviated Series Title |
|
Series Volume |
|
Series Issue |
|
Edition |
|
ISSN |
|
ISBN |
|
Additional Links |
UA library record |
Impact Factor |
|
Times cited |
|
Open Access |
|
Notes |
|
Approved |
Most recent IF: NA |
Call Number |
UA @ admin @ c:irua:174474 |
Serial |
8257 |
Permanent link to this record |
|
|
|
Author |
Gielis, J.; Ricci, P.E.; Tavkhelidze, I. |
Title |
The Möbius phenomenon in Generalized Möbius-Listing surfaces and bodies, and Arnold's Cat phenomenon |
Type |
A1 Journal article |
Year |
2021 |
Publication |
Advanced Studies : Euro-Tbilisi Mathematical Journal |
Abbreviated Journal |
|
Volume |
14 |
Issue |
4 |
Pages |
17-35 |
Keywords |
A1 Journal article; Sustainable Energy, Air and Water Technology (DuEL) |
Abstract |
Möbius bands have been studied extensively, mainly in topology. Generalized Möbius-Listing surfaces and bodies providing a full geometrical generalization, is a quite new field, motivated originally by solutions of boundary value problems. Analogous to cutting of the original Möbius band, for this class of surfaces and bodies, results have been obtained when cutting such bodies or surfaces. In general, cutting leads to interlinked and intertwined different surfaces or bodies, resulting in very complex systems. However, under certain conditions, the result of cutting can be a single surface or body, which reduces complexity considerably. Our research is motivated by this reduction of complexity. In the study of cutting Generalized Möbius-Listing bodies with polygons as cross section, the conditions under which a single body results, displaying the Möbius phenomenon of a one-sided body, have been determined for even and odd polygons. These conditions are based on congruence and rotational symmetry of the resulting cross sections after cutting, and on the knife cutting the origin. The Möbius phenomenon is important, since the process of cutting (or separation of zones in a GML body in general) then results in a single body, not in different, intertwined domains. In all previous works it was assumed that the cross section of the GML bodies is constant, but the main result of this paper is that it is sufficient that only one cross section on the whole GML structure meets the conditions for the Möbius phenomenon to occur. Several examples are given to illustrate this. |
Address |
|
Corporate Author |
|
Thesis |
|
Publisher |
|
Place of Publication |
|
Editor |
|
Language |
|
Wos |
000774655100002 |
Publication Date |
|
Series Editor |
|
Series Title |
|
Abbreviated Series Title |
|
Series Volume |
|
Series Issue |
|
Edition |
|
ISSN |
|
ISBN |
|
Additional Links |
UA library record; WoS full record |
Impact Factor |
|
Times cited |
|
Open Access |
OpenAccess |
Notes |
|
Approved |
Most recent IF: NA |
Call Number |
UA @ admin @ c:irua:183081 |
Serial |
8258 |
Permanent link to this record |
|
|
|
Author |
Gielis, J. |
Title |
The geometrical beauty of plants |
Type |
MA3 Book as author |
Year |
2017 |
Publication |
|
Abbreviated Journal |
|
Volume |
|
Issue |
|
Pages |
229 p. |
Keywords |
MA3 Book as author; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL) |
Abstract |
|
Address |
|
Corporate Author |
|
Thesis |
|
Publisher |
|
Place of Publication |
|
Editor |
|
Language |
|
Wos |
|
Publication Date |
2017-06-01 |
Series Editor |
|
Series Title |
|
Abbreviated Series Title |
|
Series Volume |
|
Series Issue |
|
Edition |
|
ISSN |
|
ISBN |
978-94-6239-150-5; 978-94-6239-151-2 |
Additional Links |
UA library record |
Impact Factor |
|
Times cited |
|
Open Access |
|
Notes |
|
Approved |
no |
Call Number |
UA @ admin @ c:irua:144554 |
Serial |
7997 |
Permanent link to this record |
|
|
|
Author |
Shi, P.; Ratkowsky, D.A.; Gielis, J. |
Title |
The generalized Gielis geometric equation and its application |
Type |
A1 Journal article |
Year |
2020 |
Publication |
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 |
Permanent link to this record |
|
|
|
Author |
Gielis, J.; Tavkhelidze, I. |
Title |
The general case of cutting of Generalized Möbius-Listing surfaces and bodies |
Type |
A1 Journal article |
Year |
2020 |
Publication |
4Open |
Abbreviated Journal |
|
Volume |
3 |
Issue |
|
Pages |
7-48 |
Keywords |
A1 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL) |
Abstract |
The original motivation to study Generalized Möbius-Listing GML surfaces and bodies was the observation that the solution of boundary value problems greatly depends on the domains. Since around 2010 GML’s were merged with (continuous) Gielis Transformations, which provide a unifying description of geometrical shapes, as a generalization of the Pythagorean Theorem. The resulting geometrical objects can be used for modeling a wide range of natural shapes and phenomena. The cutting of GML bodies and surfaces, with the Möbius strip as one special case, is related to the field of knots and links, and classifications were obtained for GML with cross sectional symmetry of 2, 3, 4, 5 and 6. The general case of cutting GML bodies and surfaces, in particular the number of ways of cutting, could be solved by reducing the 3D problem to planar geometry. This also unveiled a range of connections with topology, combinatorics, elasticity theory and theoretical physics. |
Address |
|
Corporate Author |
|
Thesis |
|
Publisher |
|
Place of Publication |
|
Editor |
|
Language |
|
Wos |
|
Publication Date |
2020-08-31 |
Series Editor |
|
Series Title |
|
Abbreviated Series Title |
|
Series Volume |
|
Series Issue |
|
Edition |
|
ISSN |
2557-0250 |
ISBN |
|
Additional Links |
UA library record |
Impact Factor |
|
Times cited |
|
Open Access |
|
Notes |
|
Approved |
Most recent IF: NA |
Call Number |
UA @ admin @ c:irua:174471 |
Serial |
7992 |
Permanent link to this record |
|
|
|
Author |
Gielis, J.; Caratelli, D.; Tavkhelidze, I. |
Title |
The general case of cutting GML bodies : the geometrical solution |
Type |
H1 Book chapter |
Year |
2020 |
Publication |
|
Abbreviated Journal |
|
Volume |
|
Issue |
|
Pages |
397-411
T2 - Differential and difference equations |
Keywords |
H1 Book chapter; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL) |
Abstract |
|
Address |
|
Corporate Author |
|
Thesis |
|
Publisher |
|
Place of Publication |
|
Editor |
|
Language |
|
Wos |
|
Publication Date |
2020-10-21 |
Series Editor |
|
Series Title |
|
Abbreviated Series Title |
|
Series Volume |
|
Series Issue |
|
Edition |
|
ISSN |
|
ISBN |
978-3-030-56322-6 |
Additional Links |
UA library record |
Impact Factor |
|
Times cited |
|
Open Access |
|
Notes |
|
Approved |
Most recent IF: NA |
Call Number |
UA @ admin @ c:irua:174477 |
Serial |
7991 |
Permanent link to this record |
|
|
|
Author |
Caratelli, D.; Gielis, J.; Tavkhelidze, I.; Ricci, P.E. |
Title |
The Dirichlet problem for the Laplace equation in supershaped annuli |
Type |
A1 Journal article |
Year |
2013 |
Publication |
Boundary value problems |
Abbreviated Journal |
|
Volume |
|
Issue |
|
Pages |
113-10 |
Keywords |
A1 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL) |
Abstract |
The Dirichlet problem for the Laplace equation in normal-polar annuli is addressed by using a suitable Fourier-like technique. Attention is in particular focused on the wide class of domains whose boundaries are defined by the so-called superformula introduced by Gielis. A dedicated numerical procedure based on the computer algebra system Mathematica© is developed in order to validate the proposed methodology. In this way, highly accurate approximations of the solution, featuring properties similar to the classical ones, are obtained. |
Address |
|
Corporate Author |
|
Thesis |
|
Publisher |
|
Place of Publication |
|
Editor |
|
Language |
|
Wos |
000325760900002&DestLinkType=CitingArticles&DestApp=ALL_WOS&UsrCustomerID=ef845e08c439e550330acc77c7 |
Publication Date |
2013-05-03 |
Series Editor |
|
Series Title |
|
Abbreviated Series Title |
|
Series Volume |
|
Series Issue |
|
Edition |
|
ISSN |
1687-2762; 1687-2770 |
ISBN |
|
Additional Links |
UA library record; WoS citing articles; WoS full record |
Impact Factor |
|
Times cited |
|
Open Access |
|
Notes |
|
Approved |
no |
Call Number |
UA @ admin @ c:irua:108644 |
Serial |
7812 |
Permanent link to this record |
|
|
|
Author |
Gielis, J.; Caratelli, D.; de Jong van Coevorden, M.; Ricci, P.E. |
Title |
The common descent of biological shape description and special functions |
Type |
H1 Book chapter |
Year |
2018 |
Publication |
|
Abbreviated Journal |
|
Volume |
230 |
Issue |
|
Pages |
119-131
T2 - Differential and difference equations |
Keywords |
H1 Book chapter; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL) |
Abstract |
Gielis transformations, with their origin in botany, are used to define square waves and trigonometric functions of higher order. They are rewritten in terms of Chebyshev polynomials. The origin of both, a uniform descriptor and the origin of orthogonal polynomials, can be traced back to a letter of Guido Grandi to Leibniz in 1713 on the mathematical description of the shape of flowers. In this way geometrical description and analytical tools are seamlessly combined. |
Address |
|
Corporate Author |
|
Thesis |
|
Publisher |
|
Place of Publication |
|
Editor |
|
Language |
|
Wos |
000451375900010 |
Publication Date |
2018-05-08 |
Series Editor |
|
Series Title |
|
Abbreviated Series Title |
|
Series Volume |
|
Series Issue |
|
Edition |
|
ISSN |
|
ISBN |
978-3-319-75646-2; 2194-1009; 978-3-319-75647-9; 978-3-319-75646-2 |
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:150949 |
Serial |
7685 |
Permanent link to this record |
|
|
|
Author |
Gielis, J.; Brasili, S. |
Title |
The apeirogon and dual numbers |
Type |
A1 Journal article |
Year |
2021 |
Publication |
Symmetry : culture and science |
Abbreviated Journal |
|
Volume |
32 |
Issue |
2 |
Pages |
157-160 |
Keywords |
A1 Journal article; Sustainable Energy, Air and Water Technology (DuEL) |
Abstract |
The richness, diversity, connection, depth and pleasure of studying symmetry continue to open doors. Here we report a connection between Coxeter's Apeirogon and the geometry associated with pictorial space, parabolic rotation and dual numbers. |
Address |
|
Corporate Author |
|
Thesis |
|
Publisher |
|
Place of Publication |
|
Editor |
|
Language |
|
Wos |
000670122100011 |
Publication Date |
2021-07-02 |
Series Editor |
|
Series Title |
|
Abbreviated Series Title |
|
Series Volume |
|
Series Issue |
|
Edition |
|
ISSN |
0865-4824 |
ISBN |
|
Additional Links |
UA library record; WoS full record |
Impact Factor |
|
Times cited |
|
Open Access |
Not_Open_Access |
Notes |
|
Approved |
Most recent IF: NA |
Call Number |
UA @ admin @ c:irua:179759 |
Serial |
8652 |
Permanent link to this record |
|
|
|
Author |
Gielis, J. |
Title |
Temperate bamboos in ornamental horticulture: differentiators and spillover effects into the 21st century |
Type |
H3 Book chapter |
Year |
2012 |
Publication |
|
Abbreviated Journal |
|
Volume |
|
Issue |
|
Pages |
603-623
T2 - Proceedings of the 9th World Bamboo C |
Keywords |
H3 Book chapter; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL) |
Abstract |
|
Address |
|
Corporate Author |
|
Thesis |
|
Publisher |
|
Place of Publication |
|
Editor |
|
Language |
|
Wos |
|
Publication Date |
|
Series Editor |
|
Series Title |
|
Abbreviated Series Title |
|
Series Volume |
|
Series Issue |
|
Edition |
|
ISSN |
|
ISBN |
|
Additional Links |
UA library record |
Impact Factor |
|
Times cited |
|
Open Access |
|
Notes |
|
Approved |
no |
Call Number |
UA @ admin @ c:irua:97755 |
Serial |
8644 |
Permanent link to this record |
|
|
|
Author |
Tavkhelidze, I.; Gielis, J. |
Title |
Structure of the dm knives and process of cutting of GML(man) or GRT(man) bodies |
Type |
A3 Journal article |
Year |
2019 |
Publication |
Sn – 1512-0066 |
Abbreviated Journal |
|
Volume |
33 |
Issue |
|
Pages |
|
Keywords |
A3 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL) |
Abstract |
|
Address |
|
Corporate Author |
|
Thesis |
|
Publisher |
|
Place of Publication |
|
Editor |
|
Language |
|
Wos |
|
Publication Date |
|
Series Editor |
|
Series Title |
|
Abbreviated Series Title |
|
Series Volume |
|
Series Issue |
|
Edition |
|
ISSN |
|
ISBN |
|
Additional Links |
UA library record |
Impact Factor |
|
Times cited |
|
Open Access |
|
Notes |
|
Approved |
no |
Call Number |
UA @ admin @ c:irua:164897 |
Serial |
8588 |
Permanent link to this record |
|
|
|
Author |
Li, Q.; Niklas, K.J.J.; Niinemets, U.; Zhang, L.; Yu, K.; Gielis, J.; Gao, J.; Shi, P. |
Title |
Stomatal shape described by a superellipse in four Magnoliaceae species |
Type |
A1 Journal article |
Year |
2023 |
Publication |
Botany letters |
Abbreviated Journal |
|
Volume |
|
Issue |
|
Pages |
1-9 |
Keywords |
A1 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL) |
Abstract |
Stomata are essential for the exchange of water vapour and atmospheric gases between vascular plants and their external environments. The stomatal geometries of many plants appear to be elliptical. However, prior studies have not tested whether this is a mathematical reality, particularly since many natural shapes that appear to be ellipses are superellipses with greater or smaller edge curvature than predicted for an ellipse. Compared with the ellipse equation, the superellipse equation includes an additional parameter that allows generation of a larger range of shapes. We randomly selected 240 stomata from each of four Magnoliaceae species to test whether the stomatal geometries are superellipses or ellipses. The stomatal geometries for most stomata (943/960) were found to be described better using the superellipse equation. The traditional “elliptical stomata hypothesis” resulted in an underestimation of the area of stomata, whereas the superellipse equation accurately predicted stomatal area. This finding has important implications for the estimation of stomatal area in studies looking at stomatal shape, geometry, and function. |
Address |
|
Corporate Author |
|
Thesis |
|
Publisher |
|
Place of Publication |
|
Editor |
|
Language |
|
Wos |
001024190300001 |
Publication Date |
2023-07-12 |
Series Editor |
|
Series Title |
|
Abbreviated Series Title |
|
Series Volume |
|
Series Issue |
|
Edition |
|
ISSN |
2381-8107; 2381-8115 |
ISBN |
|
Additional Links |
UA library record; WoS full record |
Impact Factor |
1.5 |
Times cited |
|
Open Access |
Not_Open_Access: Available from 12.01.2024 |
Notes |
|
Approved |
Most recent IF: 1.5; 2023 IF: NA |
Call Number |
UA @ admin @ c:irua:197847 |
Serial |
8935 |
Permanent link to this record |
|
|
|
Author |
Caratelli, D.; Gielis, J.; Tavkhelidze, I.; Ricci, P.E. |
Title |
Spherical harmonic solution of the Robin problem for the Helmholtz equation in a supershaped shell |
Type |
A1 Journal article |
Year |
2013 |
Publication |
Applied mathematics |
Abbreviated Journal |
|
Volume |
4 |
Issue |
1a |
Pages |
263-270 |
Keywords |
A1 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL) |
Abstract |
The Robin problem for the Helmholtz equation in normal-polar shells is addressed by using a suitable spherical harmonic expansion technique. Attention is in particular focused on the wide class of domains whose boundaries are defined by a generalized version of the so-called superformula introduced by Gielis. A dedicated numerical procedure based on the computer algebra system Mathematica? is developed in order to validate the proposed methodology. In this way, highly accurate approximations of the solution, featuring properties similar to the classical ones, are obtained. |
Address |
|
Corporate Author |
|
Thesis |
|
Publisher |
|
Place of Publication |
|
Editor |
|
Language |
|
Wos |
|
Publication Date |
2013-01-30 |
Series Editor |
|
Series Title |
|
Abbreviated Series Title |
|
Series Volume |
|
Series Issue |
|
Edition |
|
ISSN |
2152-7385 |
ISBN |
|
Additional Links |
UA library record |
Impact Factor |
|
Times cited |
|
Open Access |
|
Notes |
|
Approved |
no |
Call Number |
UA @ admin @ c:irua:107177 |
Serial |
8576 |
Permanent link to this record |
|
|
|
Author |
Caratelli, D.; Gielis, J.; Ricci, P.E.; Tavkhelidze, I. |
Title |
Some properties of “bulky” links, generated by Generalized Möbius Listing's bodies GML4n |
Type |
A2 Journal article |
Year |
2016 |
Publication |
Journal of mathematical sciences |
Abbreviated Journal |
|
Volume |
216 |
Issue |
4 |
Pages |
509-518 |
Keywords |
A2 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL) |
Abstract |
In the present paper, we consider the bulky knots and bulky links that appear after cutting of generalized MöbiusListing GML 4 n bodies (with corresponding radial cross sections square) along different generalized MöbiusListing surfaces GML 2 n situated in it. The aim of this article is to examine the number and geometric structure of independent objects that appear after such a cutting process of GML 4 n bodies. In most cases, we are able to count the indices of the resulting mathematical objects according to the known tabulation for knots and links of small complexity. |
Address |
|
Corporate Author |
|
Thesis |
|
Publisher |
|
Place of Publication |
|
Editor |
|
Language |
|
Wos |
|
Publication Date |
2016-06-10 |
Series Editor |
|
Series Title |
|
Abbreviated Series Title |
|
Series Volume |
|
Series Issue |
|
Edition |
|
ISSN |
1072-3374; 1573-8795 |
ISBN |
|
Additional Links |
UA library record |
Impact Factor |
|
Times cited |
|
Open Access |
|
Notes |
|
Approved |
no |
Call Number |
UA @ admin @ c:irua:133948 |
Serial |
8554 |
Permanent link to this record |
|
|
|
Author |
Caratelli, D.; Gielis, J.; Ricci, P.E.; Tavkhelidze, I. |
Title |
Some properties of “bulky” links, generated by Generalized Möbius Listing's bodies GML4n |
Type |
P3 Proceeding |
Year |
2013 |
Publication |
|
Abbreviated Journal |
|
Volume |
|
Issue |
|
Pages |
|
Keywords |
P3 Proceeding; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL) |
Abstract |
|
Address |
|
Corporate Author |
|
Thesis |
|
Publisher |
|
Place of Publication |
|
Editor |
|
Language |
|
Wos |
|
Publication Date |
|
Series Editor |
|
Series Title |
|
Abbreviated Series Title |
|
Series Volume |
|
Series Issue |
|
Edition |
|
ISSN |
|
ISBN |
|
Additional Links |
UA library record |
Impact Factor |
|
Times cited |
|
Open Access |
|
Notes |
|
Approved |
no |
Call Number |
UA @ admin @ c:irua:108672 |
Serial |
8555 |
Permanent link to this record |
|
|
|
Author |
Gielis, J. |
Title |
Simon Stevin as a central figure in the development of abstract algebra and generic programming |
Type |
A1 Journal article |
Year |
2023 |
Publication |
Symmetry : culture and science |
Abbreviated Journal |
|
Volume |
34 |
Issue |
2 |
Pages |
155-168 |
Keywords |
A1 Journal article; Sustainable Energy, Air and Water Technology (DuEL) |
Abstract |
Simon Stevin (1548-1620) is mainly known for the decimal system and his Clootkrans proof. His influence is also profound in infinitesimal calculus, mechanics, and even in abstract algebra and today’s conception of polynomials, algorithms, and generic programming. Here we review his influence as assessed in generic programming. According to Dr. Stepanov, one of the most influential researchers in generic programming, Stevin’s work on polynomials can be regarded as the essence of generic programming: an algorithm from one domain can be applied in another similar domain. |
Address |
|
Corporate Author |
|
Thesis |
|
Publisher |
|
Place of Publication |
|
Editor |
|
Language |
|
Wos |
001068714100003 |
Publication Date |
2023-07-11 |
Series Editor |
|
Series Title |
|
Abbreviated Series Title |
|
Series Volume |
|
Series Issue |
|
Edition |
|
ISSN |
0865-4824 |
ISBN |
|
Additional Links |
UA library record; WoS full record |
Impact Factor |
|
Times cited |
|
Open Access |
Not_Open_Access: Available from 08.02.2024 |
Notes |
|
Approved |
Most recent IF: NA |
Call Number |
UA @ admin @ c:irua:198000 |
Serial |
8929 |
Permanent link to this record |
|
|
|
Author |
Mescia, L.; Chiapperino, M.A.; Bia, P.; Lamacchia, C.M.; Gielis, J.; Caratelli, D. |
Title |
Relevance of the cell membrane modelling for accurate analysis of the pulsed electric field-induced electroporation |
Type |
P1 Proceeding |
Year |
2019 |
Publication |
Progress in Electromagnetic Research Symposium (PIERS)
T2 – 2019 PhotonIcs & Electromagnetics Research Symposium – Spring (PIERS-Spring), 17-20 June 2019, Rome, Italy |
Abbreviated Journal |
|
Volume |
|
Issue |
|
Pages |
2985-2991 |
Keywords |
P1 Proceeding; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL) |
Abstract |
In this work, a nonlinear dispersive multiphysic model based on Maxwell and asymptotic Smoluchowsky equations has been developed to analyze the electroporation phenomenon induced by pulsed electric field on biological cells. The irregular plasma membrane geometry has been modeled by incorporating in the numerical algorithm the Gielis superformula as well as the dielectric dispersion of the plasma membrane has been modeled using the multi-relaxation Debye-based relationship. The study has been carried out with the aim to compare our model implementing a thin plasma membrane with the simplified model in which the plasma membrane is modeled as a distributed impedance boundary condition. The numerical analysis has been performed exposing the cell to external electric pulses having rectangular shapes. By an inspection of the obtained results, significant differences can be highlighted between the two models confirming the need to incorporate the effective thin membrane into the numerical algorithm to well predict the cell response to the pulsed electric fields in terms of transmembrane voltages and pore densities, especially when the cell is exposed to external nanosecond pulses. |
Address |
|
Corporate Author |
|
Thesis |
|
Publisher |
|
Place of Publication |
|
Editor |
|
Language |
|
Wos |
000550769302158 |
Publication Date |
2020-03-03 |
Series Editor |
|
Series Title |
|
Abbreviated Series Title |
|
Series Volume |
|
Series Issue |
|
Edition |
|
ISSN |
978-1-72813-404-8; 978-1-72813-403-1 |
ISBN |
|
Additional Links |
UA library record; WoS full record |
Impact Factor |
|
Times cited |
|
Open Access |
|
Notes |
|
Approved |
no |
Call Number |
UA @ admin @ c:irua:169171 |
Serial |
8469 |
Permanent link to this record |
|
|
|
Author |
Wang, L.; Miao, Q.; Niinemets, Ü.; Gielis, J.; Shi, P. |
Title |
Quantifying the variation in the geometries of the outer rims of corolla tubes of Vinca major L |
Type |
A1 Journal article |
Year |
2022 |
Publication |
Plants |
Abbreviated Journal |
|
Volume |
11 |
Issue |
15 |
Pages |
1987-12 |
Keywords |
A1 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL) |
Abstract |
Many geometries of plant organs can be described by the Gielis equation, a polar coordinate equation extended from the superellipse equation, . Here, r is the polar radius corresponding to the polar angle φ; m is a positive integer that determines the number of angles of the Gielis curve when φ ∈ [0 to 2π); and the rest of the symbols are parameters to be estimated. The pentagonal radial symmetry of calyxes and corolla tubes in top view is a common feature in the flowers of many eudicots. However, prior studies have not tested whether the Gielis equation can depict the shapes of corolla tubes. We sampled randomly 366 flowers of Vinca major L., among which 360 had five petals and pentagonal corolla tubes, and six had four petals and quadrangular corolla tubes. We extracted the planar coordinates of the outer rims of corolla tubes (in top view) (ORCTs), and then fitted the data with two simplified versions of the Gielis equation with k = 1 and m = 5: (Model 1), and (Model 2). The adjusted root mean square error (RMSEadj) was used to evaluate the goodness of fit of each model. In addition, to test whether ORCTs are radially symmetrical, we correlated the estimates of n2 and n3 in Model 1 on a log-log scale. The results validated the two simplified Gielis equations. The RMSEadj values for all corolla tubes were smaller than 0.05 for both models. The numerical values of n2 and n3 were demonstrated to be statistically equal based on the regression analysis, which suggested that the ORCTs of V. major are radially symmetrical. It suggests that Model 1 can be replaced by the simpler Model 2 for fitting the ORCT in this species. This work indicates that the pentagonal or quadrangular corolla tubes (in top view) can both be modeled by the Gielis equation and demonstrates that the pentagonal or quadrangular corolla tubes of plants tend to form radial symmetrical geometries during their development and growth. |
Address |
|
Corporate Author |
|
Thesis |
|
Publisher |
|
Place of Publication |
|
Editor |
|
Language |
|
Wos |
000839115100001 |
Publication Date |
2022-08-01 |
Series Editor |
|
Series Title |
|
Abbreviated Series Title |
|
Series Volume |
|
Series Issue |
|
Edition |
|
ISSN |
2223-7747 |
ISBN |
|
Additional Links |
UA library record; WoS full record; WoS citing articles |
Impact Factor |
|
Times cited |
|
Open Access |
OpenAccess |
Notes |
|
Approved |
Most recent IF: NA |
Call Number |
UA @ admin @ c:irua:189315 |
Serial |
7200 |
Permanent link to this record |
|
|
|
Author |
Shi, P.; Liu, M.; Yu, X.; Gielis, J.; Ratkowsky, D.A. |
Title |
Proportional relationship between leaf area and the product of leaf length and width of four types of special leaf shapes |
Type |
A1 Journal article |
Year |
2019 |
Publication |
Forests (19994907) |
Abbreviated Journal |
|
Volume |
10 |
Issue |
2 |
Pages |
178 |
Keywords |
A1 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL) |
Abstract |
The leaf area, as an important leaf functional trait, is thought to be related to leaf length and width. Our recent study showed that the Montgomery equation, which assumes that leaf area is proportional to the product of leaf length and width, applied to different leaf shapes, and the coefficient of proportionality (namely the Montgomery parameter) range from 1/2 to π/4. However, no relevant geometrical evidence has previously been provided to support the above findings. Here, four types of representative leaf shapes (the elliptical, sectorial, linear, and triangular shapes) were studied. We derived the range of the estimate of the Montgomery parameter for every type. For the elliptical and triangular leaf shapes, the estimates are π/4 and 1/2, respectively; for the linear leaf shape, especially for the plants of Poaceae that can be described by the simplified Gielis equation, the estimate ranges from 0.6795 to π/4; for the sectorial leaf shape, the estimate ranges from 1/2 to π/4. The estimates based on the observations of actual leaves support the above theoretical results. The results obtained here show that the coefficient of proportionality of leaf area versus the product of leaf length and width only varies in a small range, maintaining the allometric relationship for leaf area and thereby suggesting that the proportional relationship between leaf area and the product of leaf length and width broadly remains stable during leaf evolution. |
Address |
|
Corporate Author |
|
Thesis |
|
Publisher |
|
Place of Publication |
|
Editor |
|
Language |
|
Wos |
000460744000102 |
Publication Date |
2019-02-20 |
Series Editor |
|
Series Title |
|
Abbreviated Series Title |
|
Series Volume |
|
Series Issue |
|
Edition |
|
ISSN |
1999-4907 |
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:157200 |
Serial |
8427 |
Permanent link to this record |
|
|
|
Author |
Gielis, J.; Potters, G. |
Title |
Proceedings of the 9th World Bamboo Congress, Antwerp 2012 |
Type |
P3 Proceeding |
Year |
2012 |
Publication |
|
Abbreviated Journal |
|
Volume |
|
Issue |
|
Pages |
|
Keywords |
P3 Proceeding; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL) |
Abstract |
|
Address |
|
Corporate Author |
|
Thesis |
|
Publisher |
|
Place of Publication |
|
Editor |
|
Language |
|
Wos |
|
Publication Date |
|
Series Editor |
|
Series Title |
|
Abbreviated Series Title |
|
Series Volume |
|
Series Issue |
|
Edition |
|
ISSN |
|
ISBN |
|
Additional Links |
UA library record |
Impact Factor |
|
Times cited |
|
Open Access |
|
Notes |
|
Approved |
no |
Call Number |
UA @ admin @ c:irua:97756 |
Serial |
8413 |
Permanent link to this record |
|
|
|
Author |
Gielis, J.; Brasili, S. |
Title |
Proceedings of the 1st International Symposium on Square Bamboos and the Geometree (ISSBG 2022) |
Type |
ME3 Book as editor |
Year |
2023 |
Publication |
|
Abbreviated Journal |
|
Volume |
|
Issue |
|
Pages |
xi, 175 p. |
Keywords |
ME3 Book as editor; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL) |
Abstract |
|
Address |
|
Corporate Author |
|
Thesis |
|
Publisher |
|
Place of Publication |
|
Editor |
|
Language |
|
Wos |
|
Publication Date |
2023-11-29 |
Series Editor |
|
Series Title |
|
Abbreviated Series Title |
|
Series Volume |
|
Series Issue |
|
Edition |
|
ISSN |
|
ISBN |
978-90-833839-0-3 |
Additional Links |
UA library record |
Impact Factor |
|
Times cited |
|
Open Access |
|
Notes |
|
Approved |
Most recent IF: NA |
Call Number |
UA @ admin @ c:irua:201049 |
Serial |
9077 |
Permanent link to this record |
|
|
|
Author |
Fougerolle, Y.; Truchetet, F.; Gielis, J. |
Title |
Potential fields of self intersecting Gielis curves for modeling and generalized blending techniques |
Type |
P1 Proceeding |
Year |
2017 |
Publication |
Modeling In Mathematics |
Abbreviated Journal |
|
Volume |
2 |
Issue |
|
Pages |
67-81
T2 - |
Keywords |
P1 Proceeding; Sustainable Energy, Air and Water Technology (DuEL) |
Abstract |
The definition of Gielis curves allows for the representation of self intersecting curves. The analysis and the understanding of these representations is of major interest for the analytical representation of sectors bounded by multiple subsets of curves (or surfaces), as this occurs for instance in many natural objects. We present a construction scheme based on R-functions to build signed potential fields with guaranteed differential properties, such that their zero-set corresponds to the outer, the inner envelop, or combined subparts of the curve. Our framework is designed to allow for the definition of composed domains built upon Boolean operations between several distinct objects or some subpart of self-intersecting curves, but also provides a representation for soft blending techniques in which the traditional Boolean union and intersection become special cases of linear combinations between the objects' potential fields. Finally, by establishing a connection between R-functions and Lame curves, we can extend the domain of the p parameter within the R-p-function from the set of the even positive numbers to the real numbers strictly greater than 1, i.e. p is an element of]1, +infinity[. |
Address |
|
Corporate Author |
|
Thesis |
|
Publisher |
|
Place of Publication |
|
Editor |
|
Language |
|
Wos |
000442076400006 |
Publication Date |
2017-04-20 |
Series Editor |
|
Series Title |
|
Abbreviated Series Title |
|
Series Volume |
|
Series Issue |
|
Edition |
|
ISSN |
978-94-6239-261-8; 978-94-6239-260-1; 978-94-6239-260-1 |
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:153801 |
Serial |
8395 |
Permanent link to this record |