Easy Integral Surfaces:
A Fast, Quad-based Stream and Path Surface Algorithm

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Abstract: Despite the clear benefits that stream and path surfaces bring when visualizing 3D vector fields, their use in both industry and for research has not proliferated. This is due, in part, to the complexity of previous construction algorithms. We introduce a novel algorithm for the construction of stream and path surfaces that is fast, simple and does not rely on any complicated data structures or surface parameterization, thus making it suitable for inclusion into any visualization application. We demonstrate the technique on a series of simulation data sets and show that a number of benefits stem naturally from this approach including: easy timelines and timeribbons, easy stream arrows and easy evenly-spaced flow lines. We also introduce a novel interaction tool called a surface painter in order to address the perceptual challenges associated with visualizing 3D flow. The key to our integral surface generation algorithm's simplicity is performing local computations on quad primitives.
Paper Images: (Click on images for higher resolution version)
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(Left) Transparent arrows can be mapped to the stream surface in order to reduce occlusion, while still indicating the downstream direction of the flow field represented by the surface. (Right) Opaque arrows with transparent context reduce occlusion even further. Stream arrows also provide more information about the internal behavior of wide surfaces.

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The stream surface painter shows the evolution of the construction of the stream surface. Starting from the top-left image and commencing clockwise the stream surface painter has been set to render 25%, 50%, 75% and 100% of the stream surface respectively. The stream surface is coloured according to the vector field magnitude.

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We can create a hybrid visualization of surfaces and evenly-spaced flow lines. Color is mapped to velocity magnitude.

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This image shows timeribbons rendered as shaded strips of quads to visualize a smoke plume simulation. Color is mapped to local velocity magnitude.

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When an object boundary is encountered the surface splits. The surface is torn and the separate portions are advanced independently of each other. Color is mapped to velocity magnitude.

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A stream surface depicting the eye of Hurricane Isabel.


This page is maintained by Tony McLoughlin.
In case of comments, questions, suggestions, or collaboration ideas, please send email to: cstony "at" swansea.ac.uk.

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