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Topic · Computer Graphics and Computer-Aided Design

Computational Geometry and Mesh Generation

Computational Geometry and Mesh Generation is a research topic within Computer Graphics and Computer-Aided Design. Science Explorer counts 25k research works in it since 1950. 10.1% of them reached the world's top 10% most cited for their field and year.

This cluster of papers focuses on advances in mesh generation algorithms, including Delaunay triangulations, Voronoi diagrams, and centroidal Voronoi tessellations. It also covers topics such as geometric optimization, quality meshing, computational geometry, hexahedral meshing, and approximation algorithms.

  • Mesh Generation
  • Delaunay Triangulations
  • Voronoi Diagrams
  • Geometric Optimization
  • Centroidal Voronoi Tessellations
  • Quality Meshing
  • Computational Geometry
  • Hexahedral Meshing
  • Approximation Algorithms
  • Planar Graph Embedding
Research works
25k
fractional, since 1950
In the world top 10%
2.5k
per year above
Top-10% rate
10.1%
share of its works in the world top 10%
Growth, 2018-21 → 2022-25
+9%
the tick is no change
Largest producer
China
27% of the 10 largest, 2022-now
Computational Geometry and Mesh Generation

Which countries lead Computational Geometry and Mesh Generation research?

By volume, China and the United States publish the most (546 and 542 works in 2022-now).

By volume, 2022-now

  1. 1 China 546 works
  2. 2 United States 542 works
  3. 3 Germany 213 works
  4. 4 France 148 works
  5. 5 India 125 works
  6. 6 Japan 107 works
  7. 7 Russia 94 works
  8. 8 United Kingdom 91 works
  9. 9 Canada 88 works
  10. 10 Italy 76 works

How concentrated that is

The same countries as shares of everything the list above accounts for. A node where two countries do two thirds of the work and one spread evenly across twelve read alike as a ranking and not at all alike here.

China: 26.9%United States: 26.7%Germany: 10.5%France: 7.3%6 others listed: 28.6%27%largest
China546 · 26.9%United States542 · 26.7%Germany213 · 10.5%France148 · 7.3%6 others listed581 · 28.6%

Shares of the rows listed above, not of the whole node.

Which institutions lead Computational Geometry and Mesh Generation research?

By volume in 2022-now, Centre National de la Recherche Scientifique publishes the most Computational Geometry and Mesh Generation research, followed by Russian Academy of Sciences and Chinese Academy of Sciences.

By volume, 2022-now

  1. 1 Centre National de la Recherche ScientifiqueFrance 63 works
  2. 2 Russian Academy of SciencesRussia 25 works
  3. 3 Chinese Academy of SciencesChina 21 works
  4. 4 Zhejiang UniversityChina 19 works
  5. 5 Carnegie Mellon UniversityUnited States 18 works
  6. 6 Helmholtz Association of German Research CentresGermany 16 works
  7. 7 University of Science and Technology of ChinaChina 16 works
  8. 8 Massachusetts Institute of TechnologyUnited States 15 works
  9. 9 ETH ZurichSwitzerland 15 works
  10. 10 Dalian University of TechnologyChina 14 works

Who are the leading researchers in Computational Geometry and Mesh Generation?

The most-cited researchers publishing on Computational Geometry and Mesh Generation include Steven L. Salzberg, Andrew Zisserman and Li Fei-Fei.

  1. 1 Steven L. Salzberg United States 372k citations
  2. 2 Andrew Zisserman United Kingdom 255k citations
  3. 3 Li Fei-Fei United States 225k citations
  4. 4 Kai You Wang China 224k citations
  5. 5 Luc Van Gool Switzerland 177k citations

Ranked by citations received across their whole record, among researchers with at least three works on this topic.

What are the most cited papers in Computational Geometry and Mesh Generation?

The most cited paper in Computational Geometry and Mesh Generation is "UMAP: Uniform Manifold Approximation and Projection" (Leland McInnes, John Healy, Nathaniel Saul et al., 2018), with 10,200 citations. Next come "Gmsh: A 3‐D finite element mesh generator with built‐in pre‐ and post‐processing facilities" (7,914) and "The quickhull algorithm for convex hulls" (5,441).

Most cited papers
#PaperReleasedCitations
1 UMAP: Uniform Manifold Approximation and Projection Leland McInnes, John Healy, Nathaniel Saul et al. · The Journal of Open Source Software Open access 2 Sep 2018 10,200
2 Gmsh: A 3‐D finite element mesh generator with built‐in pre‐ and post‐processing facilities Christophe Geuzaine, Jean‐François Remacle · International Journal for Numerical Methods in Engineering Open access 7 May 2009 7,914
3 The quickhull algorithm for convex hulls C. Bradford Barber, David Dobkin, Hannu T. Huhdanpaa · ACM Transactions on Mathematical Software Open access Dec 1996 5,441
4 A new polynomial-time algorithm for linear programming Narendra K. Karmarkar · COMBINATORICA Dec 1984 4,858
5 An analysis of approximations for maximizing submodular set functions—I George L. Nemhauser, Laurence A. Wolsey, Marshall L. Fisher · Mathematical Programming Dec 1978 4,553
All 98 most cited papers, with filters and sorting

Where is Computational Geometry and Mesh Generation research done?

The largest centres of Computational Geometry and Mesh Generation research in 2022-now are Beijing (China), Moscow (Russia), Paris (France) and Shanghai (China).

Largest cities, 2022-now

  1. 1 BeijingChina 94 works
  2. 2 MoscowRussia 45 works
  3. 3 ParisFrance 39 works
  4. 4 ShanghaiChina 37 works
  5. 5 TokyoJapan 36 works
  6. 6 HangzhouChina 35 works
  7. 7 BudapestHungary 30 works
  8. 8 WuhanChina 28 works
  9. 9 NanjingChina 28 works
  10. 10 PragueCzechia 26 works
See Computational Geometry and Mesh Generation on the map

Where is the best place to study Computational Geometry and Mesh Generation?

Among universities, judged by research, University of Science and Technology of China, Carnegie Mellon University and Zhejiang University score highest, combining excellence, specialisation, size, growth and international reach. Research strength is one signal when choosing where to study; it does not measure teaching.

0%10%20%30%mean 16.63%fractional works in this field (log) →share of work in the world top 10% →University of Scienc…Carnegie Mellon Univ…Zhejiang UniversityETH Zurich
above the meannear itbelow it

One dot per university in the first ten of the table below, at the default weights. The upper left is the interesting corner: small places doing unusually strong work.

Excellenceshare of its work in the world top 10%, 2022-now and all time averaged
40%
Specialisationhow much of its work is in this field, counted up to 10× the world share
10%
Sizeits output in this field, on a log scale
30%
Growthoutput growth, counted from -20% to +20%
10%
Internationalshare of its work with a co-author abroad
10%
Each slider sets a weight; the share it gets of the score is beside it.
#UniversityScoreTop 10%SpecialisationWorksGrowth
1University of Science and Technology of ChinaChina 79.025.7%5.3×16 +27.8%
2Carnegie Mellon UniversityUnited States 78.825.7%17.7×18 -28.2%
3Zhejiang UniversityChina 74.522.7%2.8×19 +57.7%
4ETH ZurichSwitzerland 72.815.4%8.5×15 +40.9%
5Massachusetts Institute of TechnologyUnited States 69.315.8%8.8×15 +2.1%
6Technical University of MunichGermany 65.413.2%6.0×13 +21.6%
7RWTH Aachen UniversityGermany 58.223.5%4.8×9 -7.8%
8Graz University of TechnologyAustria 54.810.3%23.8×11 +39.9%
9Dalian University of TechnologyChina 54.611.3%6.0×14 +69.6%
10Charles UniversityCzechia 53.82.7%11.9×14 +45.8%

Universities only. The score blends excellence (40%), size (30%), specialisation (10%), growth (10%), international reach (10%), 2022-now; growth compares 2018-21 with 2022-25 and counts up to +20%, since a jump from a small base is mostly noise.

Every institution in Computational Geometry and Mesh Generation, country by country

Is Computational Geometry and Mesh Generation research growing?

Output in 2022-2025 was 9% higher than in 2018-2021, peaking in 2009. The fastest-growing topics are Computational Geometry and Mesh Generation.

still counting19801990200020102020
grewheldshrank

The same series as a ribbon: one cell per year, darker for more. The line above answers how much; this answers when.

Its share of all research

Growing output can still be a shrinking share: all of science grows. This is Computational Geometry and Mesh Generation as a percentage of every work published that year, 0.013% in 2024.

still counting0.020%0.040%0.060%Computational Geometry and Mesh Generation0.013% in 202519801990200020102020

Fractional works of Computational Geometry and Mesh Generation over all fractional works that year. How the balance of science has shifted.

How much of it reaches the world top 10%

Year by year.

still counting5%10%15%Computational Geometry and Mesh Generation9.9% in 2025200020102020

Of each year's works in it, the share that reached the world's 10% most cited for their field and year. A field is the world for its own topics, so there is no other line to hold it against.

Which topics inside it are moving

Growth and decline on one axis around a shared zero. Two lists side by side hide the thing that matters: whether the growth dwarfs the decline, or the other way round.

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