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
Visualization of higher order singularities in vector fields
VIS '97 Proceedings of the 8th conference on Visualization '97
VIS '97 Proceedings of the 8th conference on Visualization '97
A novel approach to vortex core region detection
VISSYM '02 Proceedings of the symposium on Data Visualisation 2002
Visualizing Vector Field Topology in Fluid Flows
IEEE Computer Graphics and Applications
Visualizing Critical Points of Arbitrary Poincaré-Index
Dagstuhl '97, Scientific Visualization
Discrete multiscale vector field decomposition
ACM SIGGRAPH 2003 Papers
Tracking of Vector Field Singularities in Unstructured 3D Time-Dependent Datasets
VIS '04 Proceedings of the conference on Visualization '04
Gaigen 2:: a geometric algebra implementation generator
Proceedings of the 5th international conference on Generative programming and component engineering
Nested OpenMP for efficient computation of 3D critical points in multi-block CFD datasets
Proceedings of the 2006 ACM/IEEE conference on Supercomputing
Geometric Algebra for Computer Science: An Object-Oriented Approach to Geometry
Geometric Algebra for Computer Science: An Object-Oriented Approach to Geometry
3D winding number: theory and application to medical imaging
Journal of Biomedical Imaging - Special issue on modern mathematics in biomedical imaging
Boundary aligned smooth 3D cross-frame field
Proceedings of the 2011 SIGGRAPH Asia Conference
Feature detection and tracking in optical flow on non-flat manifolds
Pattern Recognition Letters
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Critical points of a vector field are key to their characterization. Not only their positions but also their indexes are crucial for understanding vector fields. Considerable work exists in 2D, but less is available for 3D or higher dimensions. Geometric Algebra is a derivative of Clifford Algebra that not only enables a succinct definition of the index of a critical point in higher dimension; it also provides insight and computational pathways for calculating the index. We describe the problems in terms of Geometric Algebra and present an octree based solution using the algebra for finding critical points and their index in a 3D vector field.