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Journal articles on the topic 'Triangulation'

Author: Grafiati

Published: 4 June 2021

Last updated: 25 July 2025

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1

Mitchell, Scott A. "Finding a Covering Triangulation Whose Maximum Angle is Provably Small." International Journal of Computational Geometry & Applications 07, no. 01n02 (1997): 5–20. http://dx.doi.org/10.1142/s021819599700003x.

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We consider the following problem: given a planar straight-line graph, find a covering triangulation whose maximum angle is as small as possible. A covering triangulation is a triangulation whose vertex set contains the input vertex set and whose edge set contains the input edge set. The covering triangulation problem differs from the usual Steiner triangulation problem in that we may not add a vertex on any input edge. Covering triangulations provide a convenient method for triangulating multiple regions sharing a common boundary, as each region can be triangulated independently. We give an e

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2

Wu, Bai Chao, Ai Ping Tang, and Lian Fa Wang. "A Constrained Delaunay Triangulation Algorithm Based on Incremental Points." Applied Mechanics and Materials 90-93 (September 2011): 3277–82. http://dx.doi.org/10.4028/www.scientific.net/amm.90-93.3277.

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The foundation ofdelaunay triangulationandconstrained delaunay triangulationis the basis of three dimensional geographical information system which is one of hot issues of the contemporary era; moreover it is widely applied in finite element methods, terrain modeling and object reconstruction, euclidean minimum spanning tree and other applications. An algorithm for generatingconstrained delaunay triangulationin two dimensional planes is presented. The algorithm permits constrained edges and polygons (possibly with holes) to be specified in the triangulations, and describes some data structures

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Levcopoulos, Christos, and Drago Krznaric. "Quasi-Greedy Triangulations Approximating the Minimum Weight Triangulation." Journal of Algorithms 27, no. 2 (1998): 303–38. http://dx.doi.org/10.1006/jagm.1997.0918.

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4

Keil, J. Mark, and Tzvetalin S. Vassilev. "Approximating the MaxMin and MinMax Area Triangulations using Angular Constraints." Serdica Journal of Computing 4, no. 3 (2010): 321–34. http://dx.doi.org/10.55630/sjc.2010.4.321-334.

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We consider sets of points in the two-dimensional Euclidean plane. For a planar point set in general position, i.e. no three points collinear, a triangulation is a maximal set of non-intersecting straight line segments with vertices in the given points. These segments, called edges, subdivide the convex hull of the set into triangular regions called faces or simply triangles. We study two triangulations that optimize the area of the individual triangles: MaxMin and MinMax area triangulation. MaxMin area triangulation is the triangulation that maximizes the area of the smallest area triangle in

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5

Stanchev, Bozhidar Angelov, and Hristo Ivanov Paraskevov. "CONSTRAINING TRIANGULATION TO LINE SEGMENTS: A FAST METHOD FOR CONSTRUCTING CONSTRAINED DELAUNAY TRIANGULATION." Annals of the Academy of Romanian Scientists Series on Mathematics and Its Application 12, no. 1-2 (2020): 164–78. http://dx.doi.org/10.56082/annalsarscimath.2020.1-2.164.

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"In this paper we present an edge swapping approach for incorporating line segments into triangulation. If the initial triangulation is Delaunay, the algorithm tends to produce optimal Constrained Delaunay triangulation by improving the triangles’ aspect ratios from the local area being constrained. There are two types of methods for constructing Constrained Delaunay Triangulation: straight-forward ones which take both points and line segments as source data and produce constrained triangulation from them at once; and post-processing ones which take an already constructed triangulation and inc

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6

Cavicchioli, Maddalena. "Acute Triangulations of Trapezoids and Pentagons." Journal of Mathematics 2013 (2013): 1–5. http://dx.doi.org/10.1155/2013/747128.

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An acute triangulation of a polygon is a triangulation whose triangles have all their angles less than . The number of triangles in a triangulation is called the size of it. In this paper, we investigate acute triangulations of trapezoids and convex pentagons and prove new results about such triangulations with minimum size. This completes and improves in some cases the results obtained in two papers of Yuan (2010).

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7

Mirzoev, Tigran, and Tzvetalin S. Vassilev. "Quadratic Time Computable Instances of MaxMin and MinMax Area Triangulations of Convex Polygons." Serdica Journal of Computing 4, no. 3 (2010): 335–48. http://dx.doi.org/10.55630/sjc.2010.4.335-348.

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We consider the problems of finding two optimal triangulations of a convex polygon: MaxMin area and MinMax area. These are the triangulations that maximize the area of the smallest area triangle in a triangulation, and respectively minimize the area of the largest area triangle in a triangulation, over all possible triangulations. The problem was originally solved by Klincsek by dynamic programming in cubic time [2]. Later, Keil and Vassilev devised an algorithm that runs in O(n^2 log n) time [1]. In this paper we describe new geometric findings on the structure of MaxMin and MinMax Area trian

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8

BURTON, BENJAMIN A. "FACE PAIRING GRAPHS AND 3-MANIFOLD ENUMERATION." Journal of Knot Theory and Its Ramifications 13, no. 08 (2004): 1057–101. http://dx.doi.org/10.1142/s0218216504003627.

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The face pairing graph of a 3-manifold triangulation is a 4-valent graph denoting which tetrahedron faces are identified with which others. We present a series of properties that must be satisfied by the face pairing graph of a closed minimal ℙ2-irreducible triangulation. In addition we present constraints upon the combinatorial structure of such a triangulation that can be deduced from its face pairing graph. These results are then applied to the enumeration of closed minimal ℙ2-irreducible 3-manifold triangulations, leading to a significant improvement in the performance of the enumeration a

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9

Ramprogus, Vince. "Triangulation." Nurse Researcher 12, no. 4 (2005): 4–6. http://dx.doi.org/10.7748/nr2005.04.12.4.4.c5954.

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10

Singh, Surinder. "Triangulation." London Journal of Primary Care 2, no. 1 (2009): 86–87. http://dx.doi.org/10.1080/17571472.2009.11493257.

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11

KIMCHI, JUDITH, BARBARA POLIVKA, and JOANNE SABOL STEVENSON. "Triangulation." Nursing Research 40, no. 6 (1991): 364???366. http://dx.doi.org/10.1097/00006199-199111000-00009.

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12

Dzenovska, Dace. "Triangulation." HAU: Journal of Ethnographic Theory 14, no. 2 (2024): 483–86. http://dx.doi.org/10.1086/730772.

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13

Jackson, Emerson Abraham. "Triangulation." African Journal of Economic and Management Studies 9, no. 2 (2018): 266–71. http://dx.doi.org/10.1108/ajems-01-2018-0034.

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Purpose The purpose of this paper is to provide forum for critical discourses in the area of retroduction thinking in the re-orientation of social sciences research at the Bank of Sierra Leone. It is acknowledged that economic research at the bank is more oriented towards the orthodox approach (Keynesian, etc.), while that of the un-orthodox (heterodox) view is being blighted by the need to prove economic theory application without much consideration given to the imperfect market economic conditions faced in the country. Design/methodology/approach The methodology of the paper is based on crit

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14

Manning, Louise. "Triangulation." Worldwide Hospitality and Tourism Themes 10, no. 3 (2018): 297–312. http://dx.doi.org/10.1108/whatt-02-2018-0009.

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PurposeThe purpose of this paper is to critique the existing and emerging alternative approaches being used by regulators and industry to verify the presence and efficacy of food safety management systems (FSMS). It is the second paper in a theme issue of Worldwide Hospitality and Tourism Themes, discussing the importance of measuring food safety and quality culture.Design/methodology/approachThis paper, primarily focused on UK examples, examines academic and grey literature to consider the options for effective verification of FSMS with emphasis on the hospitality sector including the use of

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15

Wilson, Chauncey E. "Triangulation." Interactions 13, no. 6 (2006): 46. http://dx.doi.org/10.1145/1167948.1167980.

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16

Hartley, Richard I., and Peter Sturm. "Triangulation." Computer Vision and Image Understanding 68, no. 2 (1997): 146–57. http://dx.doi.org/10.1006/cviu.1997.0547.

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17

Landman, Claude. "Triangulation." Journal français de psychiatrie 53, no. 2 (2024): 53–56. http://dx.doi.org/10.3917/jfp.053.0053.

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18

NARASIMHAN, GIRI. "ON HAMILTONIAN TRIANGULATIONS IN SIMPLE POLYGONS." International Journal of Computational Geometry & Applications 09, no. 03 (1999): 261–75. http://dx.doi.org/10.1142/s0218195999000182.

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An n-vertex simple polygon P is said to have a Hamiltonian Triangulation if it has a triangulation whose dual graph contains a hamiltonian path. Such triangulations are useful in fast rendering engines in Computer Graphics. We give a new characterization of polygons with hamiltonian triangulations and use it to devise O(n log n)-time algorithms to recognize such polygons. We also give efficient algorithms for several related problems.

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19

Dyshkant, N. F. "About Some Localization Problems in Delaunay Triangulations." Modeling and Analysis of Information Systems 19, no. 6 (2015): 112–26. http://dx.doi.org/10.18255/1818-1015-2012-6-112-126.

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We study some problems of nodes localization in a Delaunay triangulation and problem-solving procedures. For the problem of the set of nodes the computationally efficient approach that uses Euclidean minimum spanning tree of Delaunay triangulation is proposed. Efficient estimations for computational comlexity of the proposed methods in the average and in the worst cases are proved.computational geometry, geometric search, Delaunay triangulation, merging of overlapping triangulations, unregular discrete mesh, computational complexity

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20

Davies, David. "A Moderately Pessimistic Perspective on “Cooperative Naturalism”." Projections 12, no. 2 (2018): 9–18. http://dx.doi.org/10.3167/proj.2018.120203.

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Murray Smith’s plea for a “cooperative naturalism” that adopts a “triangulational” approach to issues in film studies is both timely and well-defended. I raise three concerns, however: one is external, relating to this strategy’s limitations, and two are internal, relating to Smith’s application of the strategy. While triangulation seems appropriate when we ask about the nature of film experience, other philosophical questions about film have an ineliminable normative dimension that triangulation cannot address. Empirically informed philosophical reflection upon the arts must be “moderately pe

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21

Grigis, Alain. "Triangulation de Delaunay et Triangulation des Tores." Geometriae Dedicata 143, no. 1 (2009): 81–88. http://dx.doi.org/10.1007/s10711-009-9374-1.

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22

GALTIER, JERÔME, FERRAN HURTADO, MARC NOY, STÉPHANE PÉRENNES, and JORGE URRUTIA. "SIMULTANEOUS EDGE FLIPPING IN TRIANGULATIONS." International Journal of Computational Geometry & Applications 13, no. 02 (2003): 113–33. http://dx.doi.org/10.1142/s0218195903001098.

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We generalize the operation of flipping an edge in a triangulation to that of flipping several edges simultaneously. Our main result is an optimal upper bound on the number of simultaneous flips that are needed to transform a triangulation into another. Our results hold for triangulations of point sets and for polygons.

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23

Rakotosaona, Marie-Julie, Noam Aigerman, Niloy J. Mitra, Maks Ovsjanikov, and Paul Guerrero. "Differentiable surface triangulation." ACM Transactions on Graphics 40, no. 6 (2021): 1–13. http://dx.doi.org/10.1145/3478513.3480554.

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Triangle meshes remain the most popular data representation for surface geometry. This ubiquitous representation is essentially a hybrid one that decouples continuous vertex locations from the discrete topological triangulation. Unfortunately, the combinatorial nature of the triangulation prevents taking derivatives over the space of possible meshings of any given surface. As a result, to date, mesh processing and optimization techniques have been unable to truly take advantage of modular gradient descent components of modern optimization frameworks. In this work, we present a differentiable s

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24

Geuenich, Jan, and Daniel Labardini-Fragoso. "Species with Potential Arising from Surfaces with Orbifold Points of Order 2, Part II: Arbitrary Weights." International Mathematics Research Notices 2020, no. 12 (2018): 3649–752. http://dx.doi.org/10.1093/imrn/rny090.

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Abstract Let ${\boldsymbol{\Sigma }}=(\Sigma ,\mathbb{M},\mathbb{O})$ be either an unpunctured surface with marked points and order-2 orbifold points or a once-punctured closed surface with order-2 orbifold points. For each pair $(\tau ,\omega )$ consisting of a triangulation $\tau $ of ${\boldsymbol{\Sigma }}$ and a function $\omega :\mathbb{O}\rightarrow \{1,4\}$, we define a chain complex $C_\bullet (\tau , \omega )$ with coefficients in $\mathbb{F}_2=\mathbb{Z}/2\mathbb{Z}$. Given ${\boldsymbol{\Sigma }}$ and $\omega $, we define a colored triangulation of ${\boldsymbol{\Sigma }_\omega }=(

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25

FORTUNE, STEVEN. "NUMERICAL STABILITY OF ALGORITHMS FOR 2D DELAUNAY TRIANGULATIONS." International Journal of Computational Geometry & Applications 05, no. 01n02 (1995): 193–213. http://dx.doi.org/10.1142/s0218195995000118.

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We consider the correctness of 2-d Delaunay triangulation algorithms implemented using floating-point arithmetic. The α-pseudocircle through points a, b, c consists of three circular arcs connecting ab, bc, and ac, each arc inside the circumcircle of a, b, c and forming angle α with the circumcircle; a triangulation is α-empty if the α-pseudocircle through the vertices of each triangle is empty. We show that a simple Delaunay triangulation algorithm—the flipping algorithm—can be implemented to produce O(n∈)-empty triangulations, where n is the number of point sites and ∈ is the relative error

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26

Smith, Murray. "Triangulation Revisited." Projections 16, no. 1 (2022): 11–24. http://dx.doi.org/10.3167/proj.2022.160102.

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What is the relationship between detailed critical analysis and the background assumptions made by a given theory of film spectatorship? In this article, I approach this question by looking at Vittorio Gallese and Michele Guerra’s The Empathic Screen in the light of the method of triangulation—the coordination and integration of phenomenological, psychological, and neuroscientific evidence, as set out in my Film, Art, and the Third Culture. In particular, I examine Gallese and Guerra’s arguments concerning the role of camera movement in prompting immersive, embodied simulation, as well as crit

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27

Saudubray, Jérôme. "La triangulation." Humanisme N° 310, no. 1 (2016): 92–95. http://dx.doi.org/10.3917/huma.310.0092.

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28

Beisecker, Dave. "Extending Triangulation." Southwest Philosophy Review 22, no. 2 (2006): 87–90. http://dx.doi.org/10.5840/swphilreview200622232.

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29

Gillies, David. "Aerial Triangulation." Photogrammetric Record 30, no. 149 (2015): 115–18. http://dx.doi.org/10.1111/phor.12095.

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30

Capon, L. B. "Triangulation adjustment." Australian Surveyor 35, no. 1 (1990): 77–86. http://dx.doi.org/10.1080/00050326.1990.10438644.

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31

MURPHY, SHIRLEY A. "Multiple Triangulation." Nursing Research 38, no. 5 (1989): 294???297. http://dx.doi.org/10.1097/00006199-198909000-00014.

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32

Worcester, Robert M., and Roger Mortimore. "Political Triangulation." Journal of Political Marketing 4, no. 2-3 (2005): 45–72. http://dx.doi.org/10.1300/j199v04n02_03.

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33

Mitcbell, Ellen Sullivan. "Multiple triangulation." Advances in Nursing Science 8, no. 3 (1986): 18–26. http://dx.doi.org/10.1097/00012272-198604000-00004.

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34

Denzin, Norman K. "Triangulation 2.0." Journal of Mixed Methods Research 6, no. 2 (2012): 80–88. http://dx.doi.org/10.1177/1558689812437186.

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35

Archibald, Mandy M. "Investigator Triangulation." Journal of Mixed Methods Research 10, no. 3 (2015): 228–50. http://dx.doi.org/10.1177/1558689815570092.

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36

Saks, Michael J. "Methodological triangulation." Nature Human Behaviour 2, no. 11 (2018): 806–7. http://dx.doi.org/10.1038/s41562-018-0458-5.

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37

Castelo, A., L. G. Nonato, M. F. Siqueira, R. Minghim, and G. Tavares. "The triangulation: An adaptive triangulation in any dimension." Computers & Graphics 30, no. 5 (2006): 737–53. http://dx.doi.org/10.1016/j.cag.2006.07.025.

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38

Noël, Raphaële, and Francine Cyr. "Comment penser la fonction du père ? Vers une vision systémique de la fonction de triangulation." Filigrane 19, no. 1 (2010): 91–106. http://dx.doi.org/10.7202/044182ar.

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La conjugalité des parents impose à l’enfant un travail psychique d’aménagement des enjeux d’exclusion et d’inclusion constituant le paradoxe de la triangulation. Nous mettons en évidence un historique des triangulations : celles-ci se définissant comme contenants pour les contenus que sont les fonctions préoedipiennes et oedipiennes du père, ayant elles aussi un historique. Cela nous conduit à plonger dans la mécanique de la triangulation, au plus près de l’interface intrapsychique/interpersonnel : nous développons le concept d’une transitionnalité de la triangulation comme espace de rencontr

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39

Vivek, Ramakrishnan, Yogarajah Nanthagopan, and Sarmatha Piriyatharshan. "Beyond Methods: Theoretical Underpinnings of Triangulation in Qualitative and Multi-Method Studies”." SEEU Review 18, no. 2 (2023): 105–22. http://dx.doi.org/10.2478/seeur-2023-0088.

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Abstract This paper explores the “triangulation approach” in social science research methods. Triangulation is an emerging method specifically in qualitative and multi-method studies. Researchers in the social sciences have increased their use of the triangulation approach recently due to the merits of this approach, especially to conduct in-depth studies through multiple inquiries. Simultaneously, this method has criticism and misconceptions among social researchers in terms of what it is, how it can be used, and the credibility of the findings when used. Therefore, this paper analyses in dep

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40

Cerulli Irelli, Giovanni, and Daniel Labardini-Fragoso. "Quivers with potentials associated to triangulated surfaces, Part III: tagged triangulations and cluster monomials." Compositio Mathematica 148, no. 6 (2012): 1833–66. http://dx.doi.org/10.1112/s0010437x12000528.

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AbstractTo each tagged triangulation of a surface with marked points and non-empty boundary we associate a quiver with potential in such a way that whenever we apply a flip to a tagged triangulation the Jacobian algebra of the quiver with potential (QP) associated to the resulting tagged triangulation is isomorphic to the Jacobian algebra of the QP obtained by mutating the QP of the original one. Furthermore, we show that any two tagged triangulations are related by a sequence of flips compatible with QP-mutation. We also prove that, for each of the QPs constructed, the ideal of the non-comple

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41

Sun, Peng Jiao, Xiao Man Wang, and Bo Huang. "The Design of Weldment Model Based on Improved Delaunay Triangulation Algorithm." Applied Mechanics and Materials 411-414 (September 2013): 1414–18. http://dx.doi.org/10.4028/www.scientific.net/amm.411-414.1414.

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By using Delaunay triangulation algorithm, triangulating with split-merge algorithm and the incremental insertion algorithm, improving the judgment that if the new inserted point meets the Delaunay triangulation "empty circle" criterion in synthesis algorithm, meanwhile, with the corresponding improvement of the LOP optimization algorithm, the design of weldment model in the virtual welding system has achieved good result.

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42

Glen, Marc Elliot. "Colourability and word-representability of near-triangulations." Pure Mathematics and Applications 28, no. 1 (2019): 70–76. http://dx.doi.org/10.1515/puma-2015-0032.

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Abstract A graph G = (V;E) is word-representable if there is a word w over the alphabet V such that x and y alternate in w if and only if the edge (x; y) is in G. It is known [6] that all 3-colourable graphs are word-representable, while among those with a higher chromatic number some are word-representable while others are not. There has been some recent research on the word-representability of polyomino triangulations. Akrobotu et al. [1] showed that a triangulation of a convex polyomino is word-representable if and only if it is 3-colourable; and Glen and Kitaev [5] extended this result to

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43

Zhou Jian-Ming, Shao Ke-Ran, Zhou Ke-Ding, and Zhan Qiong-Hua. "Computing constrained triangulation and Delaunay triangulation: a new algorithm." IEEE Transactions on Magnetics 26, no. 2 (1990): 694–97. http://dx.doi.org/10.1109/20.106412.

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44

Koehl, Patrice, and Henri Orland. "A Physicist’s View on Partial 3D Shape Matching." Algorithms 16, no. 7 (2023): 346. http://dx.doi.org/10.3390/a16070346.

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A new algorithm is presented to compute nonrigid, possibly partial comparisons of shapes defined by unstructured triangulations of their surfaces. The algorithm takes as input a pair of surfaces with each surface given by a distinct and unrelated triangulation. Its goal is to define a possibly partial correspondence between the vertices of the two triangulations, with a cost associated with this correspondence that can serve as a measure of the similarity of the two shapes. To find this correspondence, the vertices in each triangulation are characterized by a signature vector of features. We t

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Bueno, Lucas Moutinho, and Jorge Stolfi. "4-Colored Triangulation of 3-Maps." International Journal of Computational Geometry & Applications 27, no. 04 (2017): 297–325. http://dx.doi.org/10.1142/s0218195917500091.

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We describe an algorithm to triangulate a general 3-dimensional-map on an arbitrary space in such way that the resulting 3-dimensional triangulation is vertex-colorable with four colors. (Four-colorable triangulations can be efficiently represented and manipulated by the GEM data structure of Montagner and Stolfi.) The standard solution to this problem is the barycentric subdivision (BCS) of the map. Our algorithm yields a 4-colored triangulation that is provably smaller than the BCS, and in practice is often a small fraction of its size. When the input map is a shellable triangulation of a 3-

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46

Krtolica, Predrag V., Predrag S. Stanimirović, Sead H. Mašović, Islam A. Elshaarawy, and Alena Stupina. "Convex Polygon Triangulation Based on Symmetry." Symmetry 15, no. 8 (2023): 1526. http://dx.doi.org/10.3390/sym15081526.

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A polygon with n nodes can be divided into two subpolygons by an internal diagonal through node n. Splitting the polygon along diagonal δi,n and diagonal δn−i,n, i∈{2,…,⌊n/2⌋} results in mirror images. Obviously, there are ⌊n/2⌋−1 pairs of these reflectively symmetrical images. The influence of the observed symmetry on polygon triangulation is studied. The central result of this research is the construction of an efficient algorithm used for generating convex polygon triangulations in minimal time and without generating repeat triangulations. The proposed algorithm uses the diagonal values of

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47

BERN, MARSHALL, and DAVID EPPSTEIN. "POLYNOMIAL-SIZE NONOBTUSE TRIANGULATION OF POLYGONS." International Journal of Computational Geometry & Applications 02, no. 03 (1992): 241–55. http://dx.doi.org/10.1142/s0218195992000159.

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We describe methods for triangulating polygonal regions of the plane so that no triangle has a large angle. Our main result is that a polygon with n sides can be triangulated with O(n2) nonobtuse triangles. We also show that any triangulation (without Steiner points) of a simple polygon has a refinement with O(n4) nonobtuse triangles. Finally we show that a triangulation whose dual is a path has a refinement with only O(n2) nonobtuse triangles.

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48

Hanke, Sabine, Thomas Ottmann, and Sven Schuierer. "The Edge-Flipping Distance of Triangulations." JUCS - Journal of Universal Computer Science 2, no. (8) (1996): 570–79. https://doi.org/10.3217/jucs-002-08-0570.

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An edge-flipping operation in a triangulation T of a set of points in the plane is a local restructuring that changes T into a triangulation that differs from T in exactly one edge. The edge-flipping distance between two triangulations of the same set of points is the minimum number of edge-flipping operations needed to convert one into the other. In the context of computing the rotation distance of binary trees Sleator, Tarjan, and Thurston show an upper bound of 2n - 10 on the maximum edge-flipping distance between triangulations of convex polygons with n nodes, n > 12. Using volumetric a

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49

Gaifullin, Alexander Aleksandrovich. "On possible symmetry groups of 27-vertex triangulations of manifolds like the octonionic projective plane." Sbornik: Mathematics 215, no. 7 (2024): 869–910. http://dx.doi.org/10.4213/sm10017e.

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In 1987 Brehm and Kühnel showed that any triangulation of a $d$-manifold (without boundary) that is not homeomorphic to a sphere has at least $3d/2+3$ vertices. Moreover, triangulations with exactly $3d/2+3$ vertices can exist only for ‘manifolds like projective planes’, which can have dimension $2$, $4$, $8$ or $16$ only. There is a $6$-vertex triangulation of the real projective plane $\mathbb{RP}^2$, a $9$-vertex triangulation of the complex projective plane $\mathbb{CP}^2$ and $15$-vertex triangulations of the quaternionic projective plane $\mathbb{HP}^2$. Recently the author constructed

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Silva, Luis F., Luiz F. Scheidegger, Tiago Etiene, João L. D. Comba, Luis G. Nonato, and Cláudio T. Silva. "A Weighted Delaunay Triangulation Framework for Merging Triangulations in a Connectivity Oblivious Fashion." Computer Graphics Forum 33, no. 6 (2014): 18–30. http://dx.doi.org/10.1111/cgf.12274.

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