Contour tracing by piecewise linear approximations
ACM Transactions on Graphics (TOG)
Numerical continuation methods: an introduction
Numerical continuation methods: an introduction
A dimensionality paradigm for surface interrogations
Computer Aided Geometric Design
Some techniques for visualizing surfaces in four-dimensional space
Computer-Aided Design - Beyond solid modelling
Visualization of four-dimensional space and its applications
Visualization of four-dimensional space and its applications
Using particles to sample and control implicit surfaces
SIGGRAPH '94 Proceedings of the 21st annual conference on Computer graphics and interactive techniques
Complex-valued contour meshing
Proceedings of the 7th conference on Visualization '96
SIGGRAPH '85 Proceedings of the 12th annual conference on Computer graphics and interactive techniques
Point Based Rendering of Implicit 4-Dimensional Surfaces
CGIV '07 Proceedings of the Computer Graphics, Imaging and Visualisation
Introduction to Interval Analysis
Introduction to Interval Analysis
Implicit Curves and Surfaces: Mathematics, Data Structures and Algorithms
Implicit Curves and Surfaces: Mathematics, Data Structures and Algorithms
Extended papers from NPAR 2010: Shape and tone depiction for implicit surfaces
Computers and Graphics
Beam Casting Implicit Surfaces on the GPU with Interval Arithmetic
SIBGRAPI '11 Proceedings of the 2011 24th SIBGRAPI Conference on Graphics, Patterns and Images
Automatic generation of riemann surface meshes
GMP'10 Proceedings of the 6th international conference on Advances in Geometric Modeling and Processing
EuroVis'09 Proceedings of the 11th Eurographics / IEEE - VGTC conference on Visualization
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We present a point-based algorithm for rendering implicit surfaces in R^4. Our algorithm combines a new method for approximating an implicit surface with points which uses interval arithmetic for topological robustness with a new 4D illumination model that together with a color transfer function enhances the visualization of a two-dimensional surface in four-dimensional space.