ARTSccelerated ray-tracing system
IEEE Computer Graphics and Applications
Marching cubes: A high resolution 3D surface construction algorithm
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
An introduction to ray tracing
An introduction to ray tracing
Optimal isosurface extraction from irregular volume data
Proceedings of the 1996 symposium on Volume visualization
View dependent isosurface extraction
Proceedings of the conference on Visualization '98
Practical ray tracing of trimmed NURBS surfaces
Journal of Graphics Tools
Nonlinear particle tracking for high-order elements
Journal of Computational Physics
A High Accuracy Volume Renderer for Unstructured Data
IEEE Transactions on Visualization and Computer Graphics
Interactive Ray Tracing for Volume Visualization
IEEE Transactions on Visualization and Computer Graphics
Contouring curved quadratic elements
VISSYM '03 Proceedings of the symposium on Data visualisation 2003
Ray tracing algebraic surfaces
SIGGRAPH '83 Proceedings of the 10th annual conference on Computer graphics and interactive techniques
A 3-dimensional representation for fast rendering of complex scenes
SIGGRAPH '80 Proceedings of the 7th annual conference on Computer graphics and interactive techniques
Parallel Scientific Computing in C++ and MPI
Parallel Scientific Computing in C++ and MPI
Approximation and visualization of scientific data using higher-order elements
Approximation and visualization of scientific data using higher-order elements
Applied Numerical Mathematics
Quick-VDR: Interactive View-Dependent Rendering of Massive Models
VIS '04 Proceedings of the conference on Visualization '04
Rendering Planar Cuts Through Quadratic and Cubic Finite Elements
VIS '04 Proceedings of the conference on Visualization '04
Pixel-Exact Rendering of Spacetime Finite Element Solutions
VIS '04 Proceedings of the conference on Visualization '04
Reconstruction of volume data with quadratic super splines
IEEE Transactions on Visualization and Computer Graphics
Ray casting curved-quadratic elements
VISSYM'04 Proceedings of the Sixth Joint Eurographics - IEEE TCVG conference on Visualization
Methods and Framework for Visualizing Higher-Order Finite Elements
IEEE Transactions on Visualization and Computer Graphics
High-Quality Extraction of Isosurfaces from Regular and Irregular Grids
IEEE Transactions on Visualization and Computer Graphics
Interactive Point-Based Rendering of Higher-Order Tetrahedral Data
IEEE Transactions on Visualization and Computer Graphics
Interactive Isosurface Ray Tracing of Time-Varying Tetrahedral Volumes
IEEE Transactions on Visualization and Computer Graphics
Efficient parallel vectors feature extraction from higher-order data
EuroVis'11 Proceedings of the 13th Eurographics / IEEE - VGTC conference on Visualization
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The purpose of this paper is to present a ray-tracing isosurface rendering algorithm for spectral/hp (high-order finite) element methods in which the visualization error is both quantified and minimized. Determination of the ray-isosurface intersection is accomplished by classic polynomial root-finding applied to a polynomial approximation obtained by projecting the finite element solution over element-partitioned segments along the ray. Combining the smoothness properties of spectral/hp elements with classic orthogonal polynomial approximation theory, we devise an adaptive scheme which allows the polynomial approximation along a ray-segment to be arbitrarily close to the true solution. The resulting images converge toward a pixel-exact image at a rate far faster than sampling the spectral/hp element solution and applying classic low-order visualization techniques such as marching cubes.