Computational geometry: an introduction
Computational geometry: an introduction
Marching cubes: A high resolution 3D surface construction algorithm
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
Polygonization of implicit surfaces
Computer Aided Geometric Design
Interactive techniques for implicit modeling
I3D '90 Proceedings of the 1990 symposium on Interactive 3D graphics
Proceedings of the 18th annual conference on Computer graphics and interactive techniques
Surface modeling with oriented particle systems
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
An implicit surface polygonizer
Graphics gems IV
Using particles to sample and control implicit surfaces
SIGGRAPH '94 Proceedings of the 21st annual conference on Computer graphics and interactive techniques
A unified approach for hierarchical adaptive tesselation of surfaces
ACM Transactions on Graphics (TOG)
A Generalization of Algebraic Surface Drawing
ACM Transactions on Graphics (TOG)
Introduction to Implicit Surfaces
Introduction to Implicit Surfaces
Adaptive Polygonalization of Implicitly Defined Surfaces
IEEE Computer Graphics and Applications
An Evaluation of Implicit Surface Tilers
IEEE Computer Graphics and Applications
Curvature-Dependent Triangulation of Implicit Surfaces
IEEE Computer Graphics and Applications
SMI '01 Proceedings of the International Conference on Shape Modeling & Applications
Implicit Surfaces that Interpolate
SMI '01 Proceedings of the International Conference on Shape Modeling & Applications
Reconstructing multi-scale variational partition of unity implicit surfaces with attributes
Graphical Models - Special issue on SMI 2004
A hierarchical sampling approach for polygonizing variational implicit surfaces
Computers and Graphics
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In this paper, we present a novel method to triangulate variational implicit surfaces. The core of the algorithm is an incremental Delaunay tetrahedralization of the constraint points defining the surface; it can be refined over time by adding new points around the surface as needed. Each tetrahedron that crosses the surface can then be triangulated to locally approximate the surface. This method allows getting several meshes of the same shape at different resolutions, which can be updated dynamically when adding new constraint points. This level-of-detail property makes variational surfaces more appealing for applications such as interactive modeling.