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
Guaranteed ray intersections with implicit surfaces
SIGGRAPH '89 Proceedings of the 16th annual conference on Computer graphics and interactive techniques
Topological considerations in isosurface generation extended abstract
VVS '90 Proceedings of the 1990 workshop on Volume visualization
Interval analysis for computer graphics
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
Polygonization of non-manifold implicit surfaces
SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
SIGGRAPH '96 Proceedings of the 23rd annual conference on Computer graphics and interactive techniques
Octree-based decimation of marching cubes surfaces
Proceedings of the 7th conference on Visualization '96
Guaranteeing the topology of an implicit surface polygonization for interactive modeling
Proceedings of the 24th annual conference on Computer graphics and interactive techniques
Feature sensitive surface extraction from volume data
Proceedings of the 28th annual conference on Computer graphics and interactive techniques
Topology-reducing surface simplification using a discrete solid representation
ACM Transactions on Graphics (TOG)
Dual contouring of hermite data
Proceedings of the 29th annual conference on Computer graphics and interactive techniques
Adaptive Polygonalization of Implicitly Defined Surfaces
IEEE Computer Graphics and Applications
Spherical parametrization and remeshing
ACM SIGGRAPH 2003 Papers
Multi-level partition of unity implicits
ACM SIGGRAPH 2003 Papers
Isotopic implicit surface meshing
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
ACM SIGGRAPH 2004 Papers
ACM SIGGRAPH 2004 Papers
Shrinkwrap: An efficient adaptive algorithm for triangulating an iso-surface
The Visual Computer: International Journal of Computer Graphics - Special section on implicit surfaces
Topology preserving surface extraction using adaptive subdivision
Proceedings of the 2004 Eurographics/ACM SIGGRAPH symposium on Geometry processing
Isotopic approximation of implicit curves and surfaces
Proceedings of the 2004 Eurographics/ACM SIGGRAPH symposium on Geometry processing
Provably good moving least squares
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Provably good sampling and meshing of surfaces
Graphical Models - Solid modeling theory and applications
Reliable implicit surface polygonization using visibility mapping
SGP '06 Proceedings of the fourth Eurographics symposium on Geometry processing
Reliable implicit surface polygonization using visibility mapping
SGP '06 Proceedings of the fourth Eurographics symposium on Geometry processing
Unconstrained isosurface extraction on arbitrary octrees
SGP '07 Proceedings of the fifth Eurographics symposium on Geometry processing
Digital geometry processing with topological guarantees
DGCI'08 Proceedings of the 14th IAPR international conference on Discrete geometry for computer imagery
Fast and accurate evaluation of regularized Boolean operations on triangulated solids
Computer-Aided Design
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We present a new algorithm to compute a topologically and geometrically accurate triangulation of an implicit surface. Our approach uses spatial subdivision techniques to decompose a manifold implicit surface into star-shaped patches and computes a visibilty map for each patch. Based on these maps, we compute a homeomorphic and watertight triangulation as well as a parameterization of the implicit surface. Our algorithm is general and makes no assumption about the smoothness of the implicit surface. It can be easily implemented using linear programming, interval arithmetic, and ray shooting techniques. We highlight its application to many complex implicit models and boundary evaluation of CSG primitives.