• JO~AO VITOR DE SA HAUCK Departamento de Ci^encia da Computac~ao, Universidade Federal de Juiz de Fora Juiz de Fora, Minas Gerais 36036-900, Brazil
  • RAMON NOGUEIRA DA SILVA Departamento de Ci^encia da Computac~ao, Universidade Federal de Juiz de Fora Juiz de Fora, Minas Gerais 36036-900, Brazil
  • MARCELO BERNARDES VIEIRA Departamento de Ci^encia da Computac~ao, Universidade Federal de Juiz de Fora Juiz de Fora, Minas Gerais 36036-900, Brazil
  • RODRIGO LUIS DE SOUZA DA SILVA Departamento de Ci^encia da Computac~ao, Universidade Federal de Juiz de Fora Juiz de Fora, Minas Gerais 36036-900, Brazil


iterative remeshing, edge length equalization, interval constraining


This paper presents a method for explicitly remesh an arbitrary input surface into a mesh with all edge lengths within a xed interval. The process starts with an arbitrary triangular 2-manifold mesh. The proposed method is iterative and uses stellar operations to achieve the necessary amount of vertices and triangles. It also applies a technique to uniformly distribute the vertices of the model over the surface. At earlier stages of the algorithm, this technique is an approximation of the Laplacian lter. In order to preserve the geometry of the model, some constraints are added to the lter. At later stages, we replace the global uniformization strategy with a nonlinear optimizer, that performs only locally. A projection step is also applied at each iteration, to prevent the geometric distortions caused by the method. We also apply a post processing step to correct the nal edges, if the standard iterations do not converge. Our method results in a very regular mesh, with uniform distribution of vertices. The dual trivalent mesh obtained by this mesh can be useful for several applications. The main contribution of this work is a new approach for edge length equalization, with explicit constraints denition, higher computational performance and lower global geometry losses if compared to previous works.



Download data is not yet available.


C. Rocchini, P. Cignoni, C. Montani, P. Pingi, and R. Scopigno. A low cost 3d scanner based on

structured light. Computer Graphics Forum, 20(3):299{308, 2001.

Marcelo Bernardes Vieira, Luiz Velho, Asla Sa, and Paulo Cezar Carvalho. A camera-projector

system for real-time 3d video. In Computer Vision and Pattern Recognition-Workshops, 2005.

CVPR Workshops. IEEE Computer Society Conference on, pages 96{96. IEEE, 2005.

Renan Dembogurski, Bruno Dembogurski, RodrigoLuis Souza da Silva, and MarceloBernardes

Vieira. Interactive mesh generation with local deformations in multiresolution. In Beniamino

Murgante, Sanjay Misra, Maurizio Carlini, CarmeloM. Torre, Hong-Quang Nguyen, David Taniar,

BernadyO. Apduhan, and Osvaldo Gervasi, editors, Computational Science and Its Applications {

ICCSA 2013, volume 7971 of Lecture Notes in Computer Science, pages 646{661. Springer Berlin

Heidelberg, 2013.

Joachim Schoberl. Netgen an advancing front 2d/3d-mesh generator based on abstract rules.

Computing and Visualization in Science, 1(1):41{52, 1997.

David Bommes, Henrik Zimmer, and Leif Kobbelt. Mixed-integer quadrangulation. ACM Trans.

Graph., 28(3):77:1{77:10, July 2009.

Sumio Iijima et al. Helical microtubules of graphitic carbon. nature, 354(6348):56{58, 1991.

D. C. Rapaport. The Art of Molecular Dynamics Simulation. Cambridge University Press, New

York, NY, USA, 1996.

Yang Liu, Hao Pan, John Snyder, Wenping Wang, and Baining Guo. Computing self-supporting

surfaces by regular triangulation. ACM Trans. Graph., 32(4):92:1{92:10, July 2013.

F Aurenhammer. Power diagrams: properties, algorithms and applications. SIAM J. Comput.,

(1):78{96, February 1987.

Nicolas Ray, Bruno Vallet, Wan-Chiu Li, and Bruno Levy. N-symmetry direction eld design. In

ACM Transactions on Graphics, 2008. Presented at SIGGRAPH.

Jin Huang, MuYang Zhang, WenJie Pei, Wei Hua, and HuJun Bao. Controllable highly regular

triangulation. Science China Information Sciences, 54(6):1172{1183, 2011.

Patrcia Pereira Pampanelli, JP Peanha, Alessandra Matos Campos, Marcelo Bernardes Vieira,

Marcelo Lobosco, and Socrates de Oliveira Dantas. Rectangular hexagonal mesh generation for

parametric modeling. In Computer Graphics and Image Processing (SIBGRAPI), 2009 XXII

Brazilian Symposium on, pages 120{125. IEEE, 2009.

Nico Pietroni, Marco Tarini, and Paolo Cignoni. Almost isometric mesh parameterization through

abstract domains. Visualization and Computer Graphics, IEEE Transactions on, 16(4):621{635,

Mario Botsch and Leif Kobbelt. A remeshing approach to multiresolution modeling. In Proceedings

of the 2004 Eurographics/ACM SIGGRAPH symposium on Geometry processing, pages 185{192.

ACM, 2004.

Vitaly Surazhsky and Craig Gotsman. High quality compatible triangulations. Engineering with

Computers, 20(2):147{156, 2004.

Jo~ao Paulo Pecanha Navarro de Oliveira. Iterative method for edge length equalization. In

International Conference on Computational Science, pages 481{490, Barcelona,Spain, 2013.

Jo~ao Vitor Hauck, Ramon Nogueira da Silva, Marcelo Bernardes Vieira, and Rodrigo Luis de Souza

da Silva. Iterative remeshing for edge length interval constraining. In Computational Science and

Its Applications{ICCSA 2014, pages 300{312. Springer, 2014.

Gabriel Taubin. A signal processing approach to fair surface design. In Proceedings of the 22nd

annual conference on Computer graphics and interactive techniques, SIGGRAPH '95, pages 351{

, New York, NY, USA, 1995. ACM.

Pierre Alliez, Mark Meyer, and Mathieu Desbrun. Interactive geometry remeshing. ACM Trans.

Graph., 21(3):347{354, July 2002.

William H. Press, Saul A. Teukolsky, William T. Vetterling, and Brian P. Flannery. Numerical

Recipes in C (2Nd Ed.): The Art of Scienti c Computing. Cambridge University Press, New York,

NY, USA, 1992.







Most read articles by the same author(s)