On Mesh-Free Valley Surface Extraction with Application to Low Frequency Sound Simulation

Crease surfaces describe extremal structures of 3D scalar fields. We present a new region-growing-based approach to the meshless extraction of adaptive nonmanifold valley and ridge surfaces that overcomes limitations of previous approaches by decoupling point seeding and triangulation of the surface...

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Bibliographic Details
Published in:IEEE transactions on visualization and computer graphics 2012-02, Vol.18 (2), p.270-282
Main Authors: Obermaier, H., Mohring, J., Deines, E., Hering-Bertram, M., Hagen, H.
Format: Article
Language:English
Subjects:
Acoustics
adaptive surface
complex-valued scalar field
Computer simulation
crease
Curvature
Data visualization
Extraction
Linear approximation
Low frequencies
Mathematical analysis
meshing
Meshless methods
Polynomials
ridge
Surface reconstruction
Surface treatment
Valley
Valleys
Visualization
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Summary:Crease surfaces describe extremal structures of 3D scalar fields. We present a new region-growing-based approach to the meshless extraction of adaptive nonmanifold valley and ridge surfaces that overcomes limitations of previous approaches by decoupling point seeding and triangulation of the surface. Our method is capable of extracting valley surface skeletons as connected minimum structures. As our algorithm is inherently mesh-free and curvature adaptive, it is suitable for surface construction in fields with an arbitrary neighborhood structure. As an application for insightful visualization with valley surfaces, we choose a low frequency acoustics simulation. We use our valley surface construction approach to visualize the resulting complex-valued scalar pressure field for arbitrary frequencies to identify regions of sound cancellation. This provides an expressive visualization of the topology of wave node and antinode structures in simulated acoustics.
ISSN:1077-2626
1941-0506
DOI:10.1109/TVCG.2011.98