Marching cubes: A high resolution 3D surface construction algorithm
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
Guaranteed ray intersections with implicit surfaces
SIGGRAPH '89 Proceedings of the 16th annual conference on Computer graphics and interactive techniques
Solid shape
An implicit surface polygonizer
Graphics gems IV
SIGGRAPH '96 Proceedings of the 23rd 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
Shape transformation using variational implicit functions
Proceedings of the 26th annual conference on Computer graphics and interactive techniques
Modern Differential Geometry of Curves and Surfaces with Mathematica
Modern Differential Geometry of Curves and Surfaces with Mathematica
Robust Creation of Implicit Surfaces from Polygonal Meshes
IEEE Transactions on Visualization and Computer Graphics
Curvature-Dependent Triangulation of Implicit Surfaces
IEEE Computer Graphics and Applications
Smooth meshes for sketch-based freeform modeling
I3D '03 Proceedings of the 2003 symposium on Interactive 3D graphics
Multi-level partition of unity implicits
ACM SIGGRAPH 2003 Papers
Anisotropic polygonal remeshing
ACM SIGGRAPH 2003 Papers
Dynamic Meshes for Accurate Polygonization of Implicit Surfaces with Sharp Features
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
Simplified patterns for extracting the isosurfaces of solid objects
Image and Vision Computing
High-order approximation of implicit surfaces by G1 triangular spline surfaces
Computer-Aided Design
A Convergent Finite Volume Scheme for Diffusion on Evolving Surfaces
SIAM Journal on Numerical Analysis
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We present an algorithm for polygonizing closed implicit surfaces, which produces meshes adapted to the local curvature of the surface. Our method is similar to, but not based on, Marching Triangles, in that we start from a point on the surface and develop a mesh from that point using a surface-tracking approach. However, our approach works by managing fronts, or sets of points on the border of the current polygonization. Fronts can subdivide to form new fronts or merge if they become adjacent. In a marked departure from previous approaches, our meshes approximate the surface through heuristics relying on curvature. Furthermore, our method works completely on-the-fly, resolving cracks as it proceeds, without the need for any post-remeshing step to correct failures. We have tested the algorithm with three different representations of implicit surfaces, variational, analytical and MPU, using non-trivial data sets, yielding results that illustrate the flexibility and scalability of our technique. Performance comparisons with variants of Marching Cubes show that our approach is capable of good accuracy and meshing quality without sacrificing computing resources.