Marching cubes: A high resolution 3D surface construction algorithm
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
Efficient algorithms for 3D scan-conversion of parametric curves, surfaces, and volumes
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
What every computer scientist should know about floating-point arithmetic
ACM Computing Surveys (CSUR)
Volumetric shape description of range data using “Blobby Model”
Proceedings of the 18th annual conference on Computer graphics and interactive techniques
Interval analysis for computer graphics
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
Interval arithmetic recursive subdivision for implicit functions and constructive solid geometry
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
Defining and rendering of textured objects through the use of exponential functions
CVGIP: Graphical Models and Image Processing
Distance approximations for rasterizing implicit curves
ACM Transactions on Graphics (TOG)
Parallel 3-D filling with octrees
Journal of Parallel and Distributed Computing
Polygonization of non-manifold implicit surfaces
SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
A Generalization of Algebraic Surface Drawing
ACM Transactions on Graphics (TOG)
Alias-Free Voxelization of Geometric Objects
IEEE Transactions on Visualization and Computer Graphics
Rasterizing Algebraic Curves and Surfaces
IEEE Computer Graphics and Applications
IEEE Computer Graphics and Applications
Computer
Methods and Applications of Interval Analysis (SIAM Studies in Applied and Numerical Mathematics) (Siam Studies in Applied Mathematics, 2.)
Efficient volume measurement using voxelization
SCCG '03 Proceedings of the 19th spring conference on Computer graphics
Arbitrary 3d resolution discrete ray tracing of implicit surfaces
DGCI'05 Proceedings of the 12th international conference on Discrete Geometry for Computer Imagery
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Voxelization is the transformation of geometric surfaces into voxels. Up to date this process has been done essentially using incremental algorithms. Incremental algorithms have the reputation of being efficient but they lack an important property: robustness. The voxelized representation should envelop its continuous model. However, without robust methods this cannot be guaranteed. This article describes novel techniques of robust voxelization and visualization of implicit surfaces. First of all our recursive subdivision voxelization algorithm is reviewed. This algorithm was initially inspired by Duff's image space subdivision method. Then, we explain the algorithm to voxelize implicit surfaces defined in spherical or cylindrical coordinates. Next, we show a new technique to produce infinite replications of implicit objects and their voxelization method. Afterward, we comment on the parallelization of our voxelization procedure. Finally we present our voxel visualization algorithm based on point display. Our voxelization algorithms can be used with any data structure, thanks to the fact that a voxel is only stored once the last subdivision level is reached. We emphasize the use of the octree, though, because it is a convenient way to store the discrete model hierarchically. In a hierarchy the discrete model refinement is simple and possible from any previous voxelized scene thanks to the fact that the voxelization algorithms are robust.