An extended triangulation to the Marching Cubes 33 algorithm

Lis Custodio, Sinesio Pesco, Claudio Silva

Research output: Contribution to journalArticle

Abstract

The Marching Cubes algorithm is arguably the most popular isosurface extraction algorithm. Since its inception, two problems have lingered, namely, triangle quality and topology correctness. Although there is an extensive literature to solve them, topology correctness is achieved in detriment of triangle quality and vice versa. In this paper, we present an extended version of the Marching Cubes 33 algorithm (a variation of the Marching Cubes algorithm which guarantees topological correctness), called Extended Marching Cubes 33. In the proposed algorithm, the grid vertex are labeled with “+,” “ −,” and “=,” according to the relationship between its scalar field value and the isovalue. The inclusion of the “=” grid vertex label naturally avoids degenerate triangles. As an application of our method, we use the proposed triangulation to improve the quality of the triangles in the generated mesh while preserving its topology as much as possible.

Original languageEnglish (US)
Article number6
JournalJournal of the Brazilian Computer Society
Volume25
Issue number1
DOIs
StatePublished - Dec 1 2019

Fingerprint

Triangulation
Topology
Labels

Keywords

  • Extended lookup table
  • Isosurface extraction
  • Marching Cubes 33
  • Mesh quality

ASJC Scopus subject areas

  • Computer Science(all)

Cite this

An extended triangulation to the Marching Cubes 33 algorithm. / Custodio, Lis; Pesco, Sinesio; Silva, Claudio.

In: Journal of the Brazilian Computer Society, Vol. 25, No. 1, 6, 01.12.2019.

Research output: Contribution to journalArticle

@article{61af50957db4469bbff5af71ed0acbc5,
title = "An extended triangulation to the Marching Cubes 33 algorithm",
abstract = "The Marching Cubes algorithm is arguably the most popular isosurface extraction algorithm. Since its inception, two problems have lingered, namely, triangle quality and topology correctness. Although there is an extensive literature to solve them, topology correctness is achieved in detriment of triangle quality and vice versa. In this paper, we present an extended version of the Marching Cubes 33 algorithm (a variation of the Marching Cubes algorithm which guarantees topological correctness), called Extended Marching Cubes 33. In the proposed algorithm, the grid vertex are labeled with “+,” “ −,” and “=,” according to the relationship between its scalar field value and the isovalue. The inclusion of the “=” grid vertex label naturally avoids degenerate triangles. As an application of our method, we use the proposed triangulation to improve the quality of the triangles in the generated mesh while preserving its topology as much as possible.",
keywords = "Extended lookup table, Isosurface extraction, Marching Cubes 33, Mesh quality",
author = "Lis Custodio and Sinesio Pesco and Claudio Silva",
year = "2019",
month = "12",
day = "1",
doi = "10.1186/s13173-019-0086-6",
language = "English (US)",
volume = "25",
journal = "Journal of the Brazilian Computer Society",
issn = "0104-6500",
publisher = "Sociedade Brasileira de Computacao",
number = "1",

}

TY - JOUR

T1 - An extended triangulation to the Marching Cubes 33 algorithm

AU - Custodio, Lis

AU - Pesco, Sinesio

AU - Silva, Claudio

PY - 2019/12/1

Y1 - 2019/12/1

N2 - The Marching Cubes algorithm is arguably the most popular isosurface extraction algorithm. Since its inception, two problems have lingered, namely, triangle quality and topology correctness. Although there is an extensive literature to solve them, topology correctness is achieved in detriment of triangle quality and vice versa. In this paper, we present an extended version of the Marching Cubes 33 algorithm (a variation of the Marching Cubes algorithm which guarantees topological correctness), called Extended Marching Cubes 33. In the proposed algorithm, the grid vertex are labeled with “+,” “ −,” and “=,” according to the relationship between its scalar field value and the isovalue. The inclusion of the “=” grid vertex label naturally avoids degenerate triangles. As an application of our method, we use the proposed triangulation to improve the quality of the triangles in the generated mesh while preserving its topology as much as possible.

AB - The Marching Cubes algorithm is arguably the most popular isosurface extraction algorithm. Since its inception, two problems have lingered, namely, triangle quality and topology correctness. Although there is an extensive literature to solve them, topology correctness is achieved in detriment of triangle quality and vice versa. In this paper, we present an extended version of the Marching Cubes 33 algorithm (a variation of the Marching Cubes algorithm which guarantees topological correctness), called Extended Marching Cubes 33. In the proposed algorithm, the grid vertex are labeled with “+,” “ −,” and “=,” according to the relationship between its scalar field value and the isovalue. The inclusion of the “=” grid vertex label naturally avoids degenerate triangles. As an application of our method, we use the proposed triangulation to improve the quality of the triangles in the generated mesh while preserving its topology as much as possible.

KW - Extended lookup table

KW - Isosurface extraction

KW - Marching Cubes 33

KW - Mesh quality

UR - http://www.scopus.com/inward/record.url?scp=85067554169&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85067554169&partnerID=8YFLogxK

U2 - 10.1186/s13173-019-0086-6

DO - 10.1186/s13173-019-0086-6

M3 - Article

AN - SCOPUS:85067554169

VL - 25

JO - Journal of the Brazilian Computer Society

JF - Journal of the Brazilian Computer Society

SN - 0104-6500

IS - 1

M1 - 6

ER -