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Output-Sensitive 3D Line Integral Convolution

This web page contains additional material accompanying the IEEE Transactions on Visualization and Computer Graphis 2007 paper "Output-Sensitive 3D Line Integral Convolution" by Martin Falk and Daniel Weiskopf.


We propose an output-sensitive visualization method for 3D line integral convolution (LIC) whose rendering speed is largely independent of the data set size and mostly governed by the complexity of the output on the image plane. Our approach of view-dependent visualization tightly links the LIC generation with the volume rendering of the LIC result in order to avoid the computation of unnecessary LIC points: early-ray termination and empty-space leaping techniques are used to skip the computation of the LIC integral in a lazy-evaluation approach; both ray casting and texture slicing can be used as volume-rendering techniques. The input noise is modeled in object space to allow for temporal coherence under object and camera motion. Different noise models are discussed, covering dense representations based on filtered white noise all the way to sparse representations similar to oriented LIC. Aliasing artifacts are avoided by frequency control over the 3D noise and by employing a 3D variant of MIPmapping. A range of illumination models is applied to the LIC streamlines: different codimension-2 lighting models as well as a novel gradient-based illumination model that relies on precomputed gradients and does not require any direct calculation of gradients after the LIC integral is evaluated. We discuss the issue of proper sampling of the LIC and volume-rendering integrals by employing a frequency-space analysis of the noise model and the precomputed gradients. Finally, we demonstrate that our visualization approach lends itself to a fast GPU implementation that supports both steady and unsteady flow. Therefore, this 3D LIC method allows users to interactively explore 3D flow by means of high-quality, view-dependent, and adaptive LIC volume visualization. Applications to flow visualization in combination with feature extraction and focus-and-context visualization are described, a comparison to previous methods is provided, and a detailed performance analysis is included.

Publication Download

A PDF version can be found here.

Source Code

Here you can find a simplified version of our source code. The following techniques mentioned in the paper are not implemented in this version: early-z test and layered empty space skipping. The code was last updated 05/29/2008.

This code is partly based on the Single Pass Volume Renderer from Stegmaier et al.

S. Stegmaier, M. Strengert, T. Klein, and T. Ertl. A Simple and Flexible Volume Rendering Framework for Graphics-Hardware-based Raycasting, Proceedings of Volume Graphics 2005, pp.187-195, 2005.



The following videos and images present the exploration of a vector field with means of 3D LIC. Our noise model supports temporal coherence when moving the camera and also provides constant spatial resolution in the image plane.

Animated rotation showing the resulting 3D LIC of the tornado dataset. Velocity masking was used to emphasize the tornado. [MPEG-1, 1,976 kB] [Hires JPEG image]

Animated rotation of the vortex flow dataset with velocity masking. [MPEG-1, 2,048 kB] [Hires JPEG image]

Film demonstrating constant spatial resolution of the 3D LIC in the image plane (minor "jumping" artifacts are due to the keyframe-based MPEG compression scheme and do not originate from the original rendering). [MPEG1, 1,782 kB] [Hires JPEG image]

Animation demonstrating constant spatial resolution of the 3D LIC in the image plane (minor "jumping" artifacts are due to the keyframe-based MPEG compression scheme and do not originate from the original rendering). [MPEG1, 1,772 kB] [Hires JPEG image]

Unsteady flow visualization of a time-dependent tornado data set. [MPEG1, 2,584 kB] [Hires JPEG image]

Comparison of Illumination Models

3D LIC with no illumination. [Hires JPEG image]

Precomputed noise gradients used for illumination of the 3D LIC. [Hires JPEG image]

Line-based illumination according to illuminated streamlines. [Hires JPEG image]

Another line-based illumination model according to Mallo et al. [Hires JPEG image]

Feature-Based Visualization

Vortex flow data set demonstrating the influence of the transfer function. In the left image, an almost opaque transfer function is used. In the right image, the transfer function was adjusted to reveal the inner flow structure. [Hires JPEG image (opaque)] [Hires JPEG image (transparent)]


Benard flow, displayed by lambda-2 based focus-and-context visualization. Swirling features are emphasized by yellow and red, the context is illustrated by a slightly transparent blue. [Hires JPEG image]

Side view of a data set from a large eddy simulation. The surrounding flow is slightly transparent whereas the turbulences behind the cylinder are almost opaque. [Hires JPEG image]