Semi-automatic generation of transfer functions for direct volume rendering
VVS '98 Proceedings of the 1998 IEEE symposium on Volume visualization
Opacity-weighted color interpolation, for volume sampling
VVS '98 Proceedings of the 1998 IEEE symposium on Volume visualization
Multiresolution techniques for interactive texture-based volume visualization
VIS '99 Proceedings of the conference on Visualization '99: celebrating ten years
VVS '00 Proceedings of the 2000 IEEE symposium on Volume visualization
Hardware-accelerated volume and isosurface rendering based on cell-projection
Proceedings of the conference on Visualization '00
High-quality pre-integrated volume rendering using hardware-accelerated pixel shading
Proceedings of the ACM SIGGRAPH/EUROGRAPHICS workshop on Graphics hardware
Principles of Digital Image Synthesis
Principles of Digital Image Synthesis
A two-step approach for interactive pre-integrated volume rendering of unstructured grids
VVS '02 Proceedings of the 2002 IEEE symposium on Volume visualization and graphics
Proceedings of the conference on Visualization '01
A High Accuracy Volume Renderer for Unstructured Data
IEEE Transactions on Visualization and Computer Graphics
Fast Ray-Tracing of Rectilinear Volume Data Using Distance Transforms
IEEE Transactions on Visualization and Computer Graphics
Smart hardware-accelerated volume rendering
VISSYM '03 Proceedings of the symposium on Data visualisation 2003
Integrating pre-integration into the shear-warp algorithm
VG '03 Proceedings of the 2003 Eurographics/IEEE TVCG Workshop on Volume graphics
Physically Based Rendering: From Theory to Implementation
Physically Based Rendering: From Theory to Implementation
Acceleration Techniques for GPU-based Volume Rendering
Proceedings of the 14th IEEE Visualization 2003 (VIS'03)
Empty Space Skipping and Occlusion Clipping for Texture-based Volume Rendering
Proceedings of the 14th IEEE Visualization 2003 (VIS'03)
Gaussian Transfer Functions for Multi-Field Volume Visualization
Proceedings of the 14th IEEE Visualization 2003 (VIS'03)
Unitary equivalence: a new twist on signal processing
IEEE Transactions on Signal Processing
Reproducing kernel structure and sampling on time-warped spaces with application to warped wavelets
IEEE Transactions on Information Theory
High-quality lighting and efficient pre-integration for volume rendering
VISSYM'04 Proceedings of the Sixth Joint Eurographics - IEEE TCVG conference on Visualization
Improving the quality of multi-resolution volume rendering
EUROVIS'06 Proceedings of the Eighth Joint Eurographics / IEEE VGTC conference on Visualization
Conjoint Analysis to Measure the Perceived Quality in Volume Rendering
IEEE Transactions on Visualization and Computer Graphics
Adaptive GPU ray casting based on spectral analysis
MIAR'10 Proceedings of the 5th international conference on Medical imaging and augmented reality
Procedural Texture Synthesis for Zoom-Independent Visualization of Multivariate Data
Computer Graphics Forum
Estimation and modeling of actual numerical errors in volume rendering
EuroVis'10 Proceedings of the 12th Eurographics / IEEE - VGTC conference on Visualization
Filtering color mapped textures and surfaces
Proceedings of the ACM SIGGRAPH Symposium on Interactive 3D Graphics and Games
Instant convolution shadows for volumetric detail mapping
ACM Transactions on Graphics (TOG)
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In this paper we investigate the effects of function composition in the form g(f(x)) = h(x) by means of a spectral analysis of h. We decompose the spectral description of h(x) into a scalar product of the spectral description of g(x) and a term that solely depends on f(x) and that is independent of g(x). We then use the method of stationary phase to derive the essential maximum frequency of g(f(x)) bounding the main portion of the energy of its spectrum. This limit is the product of the maximum frequency of g(x) and the maximum derivative of f(x). This leads to a proper sampling of the composition h of the two functions g and f. We apply our theoretical results to a fundamental open problem in volume rendering---the proper sampling of the rendering integral after the application of a transfer function. In particular, we demonstrate how the sampling criterion can be incorporated in adaptive ray integration, visualization with multi-dimensional transfer functions, and pre-integrated volume rendering.