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キーワード:
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要旨:
We present an implicit method for globally computing all four classic types of
integral surfaces -- stream, path, streak, and time surfaces in 3D
time-dependent vector fields. Our novel formulation is based on the
representation of a time surface as implicit isosurface of a 3D scalar function
advected by the flow field. The evolution of a time surface is then given as an
isovolume in 4D space-time spanned by a series of advected scalar functions.
Based on this, the other three integral surfaces are described as the
intersection of two isovolumes derived from different scalar functions. Our
method uses a dense flow integration to compute integral surfaces globally in
the entire domain. This allows to change the seeding structure efficiently by
simply defining new isovalues. We propose two rendering methods that exploit
the implicit nature of our integral surfaces: 4D raycasting, and projection
into a 3D volume. Furthermore, we present a marching cubes inspired surface
extraction method to convert the implicit surface representation to an explicit
triangle mesh. In contrast to previous approaches for implicit stream surfaces,
our method allows for multiple voxel intersections, covers all regions of the
flow field, and provides full control over the seeding line within the entire
domain.
