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
Interactive techniques for implicit modeling
I3D '90 Proceedings of the 1990 symposium on Interactive 3D graphics
Using plane vector fields to obtain all the intersection curves of two general surfaces
Theory and practice of geometric modeling
Generating textures on arbitrary surfaces using reaction-diffusion
Proceedings of the 18th annual conference on Computer graphics and interactive techniques
Generative modeling for computer graphics and CAD: symbolic shape design using interval analysis
Generative modeling for computer graphics and CAD: symbolic shape design using interval analysis
A physically based approach to 2–D shape blending
SIGGRAPH '92 Proceedings of the 19th 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
Illumination from curved reflectors
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
Physically-based methods for polygonization of implicit surfaces
Proceedings of the conference on Graphics interface '92
Using particles to sample and control implicit surfaces
SIGGRAPH '94 Proceedings of the 21st annual conference on Computer graphics and interactive techniques
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)
Visualizing Vector Field Topology in Fluid Flows
IEEE Computer Graphics and Applications
Generic Sign Systems in Medical Imaging
IEEE Computer Graphics and Applications
Surface Coding Based on Morse Theory
IEEE Computer Graphics and Applications
An Evaluation of Implicit Surface Tilers
IEEE Computer Graphics and Applications
Generation and display of geometric fractals in 3-D
SIGGRAPH '82 Proceedings of the 9th annual conference on Computer graphics and interactive techniques
Polygonizing implicit surfaces with guaranteed topology
Polygonizing implicit surfaces with guaranteed topology
The topology of symmetric, second-order tensor fields
VIS '94 Proceedings of the conference on Visualization '94
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Morse theory shows how the topology of an implicit surface is affected by its function's critical points, whereas catastrophe theory shows how these critical points behave as the function's parameters change. Interval analysis finds the critical points, and they can also be tracked efficiently during parameter changes. Changes in the function value at these critical points cause changes in the topology. Techniques for modifying the polygonization to accommodate such changes in topology are given. These techniques are robust enough to guarantee the topology of an implicit surface polygonization, and are efficient enough to maintain this guarantee during interactive modeling. The impact of this work is a topologically-guaranteed polygonization technique, and the ability to directly and accurately manipulate polygonized implicit surfaces in real time.