Scalar Representation of 2D Steady Vector Fields
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866916089200377856 |
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| author | Theisel, Holger Motejat, Michael Zimmermann, Janos Rössl, Christian |
| author_facet | Theisel, Holger Motejat, Michael Zimmermann, Janos Rössl, Christian |
| contents | We introduce a representation of a 2D steady vector field ${\mathbf v}$ by two scalar fields $a$, $b$, such that the isolines of $a$ correspond to stream lines of ${\mathbf v}$, and $b$ increases with constant speed under integration of ${\mathbf v}$. This way, we get a direct encoding of stream lines, i.e., a numerical integration of ${\mathbf v}$ can be replaced by a local isoline extraction of $a$. To guarantee a solution in every case, gradient-preserving cuts are introduced such that the scalar fields are allowed to be discontinuous in the values but continuous in the gradient. Along with a piecewise linear discretization and a proper placement of the cuts, the fields $a$ and $b$ can be computed. We show several evaluations on non-trivial vector fields. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_06576 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Scalar Representation of 2D Steady Vector Fields Theisel, Holger Motejat, Michael Zimmermann, Janos Rössl, Christian Graphics We introduce a representation of a 2D steady vector field ${\mathbf v}$ by two scalar fields $a$, $b$, such that the isolines of $a$ correspond to stream lines of ${\mathbf v}$, and $b$ increases with constant speed under integration of ${\mathbf v}$. This way, we get a direct encoding of stream lines, i.e., a numerical integration of ${\mathbf v}$ can be replaced by a local isoline extraction of $a$. To guarantee a solution in every case, gradient-preserving cuts are introduced such that the scalar fields are allowed to be discontinuous in the values but continuous in the gradient. Along with a piecewise linear discretization and a proper placement of the cuts, the fields $a$ and $b$ can be computed. We show several evaluations on non-trivial vector fields. |
| title | Scalar Representation of 2D Steady Vector Fields |
| topic | Graphics |
| url | https://arxiv.org/abs/2401.06576 |