Marching cubes: A high resolution 3D surface construction algorithm
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
Guaranteed-quality mesh generation for curved surfaces
SCG '93 Proceedings of the ninth annual symposium on Computational geometry
Triangulating topological spaces
SCG '94 Proceedings of the tenth annual symposium on Computational geometry
Surface simplification using quadric error metrics
Proceedings of the 24th annual conference on Computer graphics and interactive techniques
Guaranteeing the topology of an implicit surface polygonization for interactive modeling
Proceedings of the 24th annual conference on Computer graphics and interactive techniques
Out-of-core simplification of large polygonal models
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Feature sensitive surface extraction from volume data
Proceedings of the 28th annual conference on Computer graphics and interactive techniques
Reconstruction and representation of 3D objects with radial basis functions
Proceedings of the 28th annual conference on Computer graphics and interactive techniques
Dual/Primal mesh optimization for polygonized implicit surfaces
Proceedings of the seventh ACM symposium on Solid modeling and applications
Dual contouring of hermite data
Proceedings of the 29th annual conference on Computer graphics and interactive techniques
Parameterized Families of Polynomials for Bounded Algebraic Curve and Surface Fitting
IEEE Transactions on Pattern Analysis and Machine Intelligence
Constrained Elastic Surface Nets: Generating Smooth Surfaces from Binary Segmented Data
MICCAI '98 Proceedings of the First International Conference on Medical Image Computing and Computer-Assisted Intervention
Discretization of functionally based heterogeneous objects
SM '03 Proceedings of the eighth ACM symposium on Solid modeling and applications
SMI '03 Proceedings of the Shape Modeling International 2003
Multi-level partition of unity implicits
ACM SIGGRAPH 2003 Papers
Sampling and meshing a surface with guaranteed topology and geometry
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
Isotopic implicit surface meshing
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Provably good sampling and meshing of surfaces
Graphical Models - Solid modeling theory and applications
High-Quality Extraction of Isosurfaces from Regular and Irregular Grids
IEEE Transactions on Visualization and Computer Graphics
SGP '07 Proceedings of the fifth Eurographics symposium on Geometry processing
Reconstruction of Cellular Biological Structures from Optical Microscopy Data
IEEE Transactions on Visualization and Computer Graphics
Delpsc: a delaunay mesher for piecewise smooth complexes
Proceedings of the twenty-fourth annual symposium on Computational geometry
Delaunay meshing of isosurfaces
The Visual Computer: International Journal of Computer Graphics
Least squares quantization in PCM
IEEE Transactions on Information Theory
IEEE Transactions on Image Processing
Optimized surface discretization of functionally defined multi-material objects
Advances in Engineering Software
Real-time isosurface rendering of smooth fields
Journal of Visualization
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In this paper, we propose a new algorithm to mesh implicit surfaces which produces meshes both with a good triangle aspect ratio as well as a good approximation quality. The number of vertices of the output mesh is defined by the end-user. For this goal, we perform a two-stage processing: an initialization step followed by an iterative optimization step. The initialization step consists in capturing the surface topology and allocating the vertex budget. The optimization algorithm is based on a variational vertices relaxation and triangulation update. In addition a gradation parameter can be defined to adapt the mesh sampling to the curvature of the implicit surface. We demonstrate the efficiency of the approach on synthetic models as well as real-world acquired data, and provide comparisons with previous approaches.