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Master's Thesis
 Although a title hasn't been officially set, my thesis is
focusing on visualizing vertical motions using Lagrangian-Eulerian Adection
(LEA). This idea was originally proposed by Bruno Jobard in his paper Lagrangian
Eulerian Advection for Unsteady Flow Visualization.
Vector fields are particularly difficult to visualize in the vertical
directions, mainly because when viewing a dense volume of data, the inner
most regions are lost. To prevent this my research has focused on
visualizing 3D vector
fields on an evolving 2D manifold. Currently the algorithms developed have
been primarily for use with ocean
flow. The vertical velocities in the ocean are 2 to 3 orders of
magnitude smaller than the typical horizontal velocities.
Different Techniques for 3D vector field visualization
- hedge hogs
- animated vectors
- layered LEA textures
- 3D LEA texture
- LEA surfaces
A case study of the research was submitted to IEEE Visualization 2002 this past
month. Below are figures from the paper. The figures below are contrasting
my proposed technique with that proposed by Gerik Scheuermann,
in his paper Visualizing
Planar Vector Fields with Normal Component.
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Three frames from an animation of Eq. (1) from the paper. The height
field is w(x,y,t) (left) and z(x,y,t) (right). Time increases
form top to bottom. The top half of frames are color coded with w,
the bottom half with z.
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Three frames from an animation of the
solution to Eq. (11) from the paper. The height field is w(x,y,t) (left)
and (x,y,t) (right). Time increases from top to bottom.
The half of images are color coded with w, the bottom half with
z.
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{Full domain of the Gulf of Mexico
model, with region of interest shaded.
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Contrasting the different techniques
using the Gulf of Mexico data. Top: height field is
the normal velocity, colored by surface
height (Scheuermann el al.).
Middle and Bottom: height field created using proposed algorithm, middle
colored by normal velocity and bottom colored by surface height.
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Optimizations applied to the extracted
region. Top: the height field uses the 3D vector field for vertical motion
and neglects the variation of v on z. Bottom: the height field
neglects the variation of z for horizontal and vertical motion.
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Animations
| Description |
QuickTime file |
Scheuermann's technique and the
proposed when applied to the horizontal flow defined by Equation 1
of the paper.
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horizontal.qt
(2.2M)
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Scheuermann's technique and the
proposed when applied to the circular flow defined by Equation 11
of the paper.
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circular.qt
(1.9M)
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Scheuermann's technique and the
proposed when applied to actual data from the Gulf of Mexico. The
top is a height field based on vertical velocity and the bottom is
a
height field using the proposed algorithm. Textures are colored
based on surface height
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hf_vs_ncaheight.qt
(2.7M)
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Scheuermann's technique and the
proposed when applied to actual data from the Gulf of Mexico. The
top is a height field based on vertical velocity and the bottom is
a
height field using the proposed algorithm. Textures are colored
based on vertical velocity.
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hf_vs_ncavel.qt
(2.7M)
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Optimization cases when applied to the
Gulf of Mexico data. The top is the original algorithm with no
optimization. The middle used 3D vector field for vertical motion,
but neglects the variation of the horizontal in z. The bottom
neglects variation of z for horizontal and vertical
motion.
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optimizations.qt
(3.8M)
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