Computational geometry: an introduction
Computational geometry: an introduction
The Science of Fractal Images
Efficient antialiased rendering of 3-D linear fractals
Proceedings of the 18th annual conference on Computer graphics and interactive techniques
Hierarchical splatting: a progressive refinement algorithm for volume rendering
Proceedings of the 18th annual conference on Computer graphics and interactive techniques
Numerical recipes in C (2nd ed.): the art of scientific computing
Numerical recipes in C (2nd ed.): the art of scientific computing
Fractal image compression: theory and application
Fractal image compression: theory and application
Accelerated volume rendering and tomographic reconstruction using texture mapping hardware
VVS '94 Proceedings of the 1994 symposium on Volume visualization
Visualizing the behavior of higher dimensional dynamical systems
VIS '97 Proceedings of the 8th conference on Visualization '97
HWWS '00 Proceedings of the ACM SIGGRAPH/EUROGRAPHICS workshop on Graphics hardware
A rendering algorithm for visualizing 3D scalar fields
SIGGRAPH '88 Proceedings of the 15th annual conference on Computer graphics and interactive techniques
Harnessing chaos for image synthesis
SIGGRAPH '88 Proceedings of the 15th annual conference on Computer graphics and interactive techniques
IEEE Transactions on Visualization and Computer Graphics
Line Art Illustrations of Parametric and Implicit Forms
IEEE Transactions on Visualization and Computer Graphics
Accelerating Volume Reconstruction With 3D Texture Hardware
Accelerating Volume Reconstruction With 3D Texture Hardware
Acceleration Techniques for GPU-based Volume Rendering
Proceedings of the 14th IEEE Visualization 2003 (VIS'03)
SuperFractals
A simple and flexible volume rendering framework for graphics-hardware-based raycasting
VG'05 Proceedings of the Fourth Eurographics / IEEE VGTC conference on Volume Graphics
| Hi-index | 0.00 |
In this paper we tackle the problem of approximation and visualization of invariant measures arising from Iterated Function Systems with Probabilities (IFSP) and Recurrent Iterated Function Systems (RIFS) on R3. The measures are generated during the evolution of a stochastic dynamical system, which is a random process commonly known as the chaos game. From the dynamical system viewpoint, an invariant measure gives a temporal information on the long-term behavior of the chaos game related to a given IFSP or RIFS. The non-negative number that the measure takes on for a given subset of space says how often the dynamical system visits that subset during the temporal evolution of the system as time tends to infinity. In order to approximate the measures, we propose a method of measure instancing that can be considered an analogue of object instancing for IFS attractors. Although the IFSP and RIFS invariant measures are generated by the long-term behavior of stochastic dynamical systems, measure instancing makes it possible to compute the value that the measure takes on for a given subset of space in a deterministic way at any accuracy required. To visualize the data obtained with the algorithm, we use direct volume rendering. To incorporate the global structure of invariant measures along with their local properties in an image, a modification of a shading model based on varying density emitters is used. We adapt the model to match the fractal measure context. Then we show how to implement the model on commodity graphics hardware using an approach that combines GPU-based direct volume raycasting and 3D texture slicing used in the object-aligned manner. By means of the presented techniques, visual exploration of 3D IFSP and RIFS measures can be carried out efficiently at interactive frame rates.