3D Flow Visualization

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3D Flow Visualization

• Xiaohong Ye
• Emailxhye_at_soe.ucsc.edu

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Purposes and Problems of Flow Visualization

• Flow visualization is useful for several
  disciplines including computational fluid
  dynamics, aerodynamics, turbomachinery
  design,meteorology and climate modeling.

• Flow visualization in 3D, as opposed to 2D, is
  more challenging due to perceptual problems such
  as occlusion,lack of directional cues, lack of
  depth cues, and visual complexity.

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Methods for streamline placement

• The challenge of 3D visualizations often
  addressed by selective streamline seeding
  strategies.
• Many of the interesting features of velocity are
  associated with its critical points.

Basic Concepts

• Streamline
• A streamline is an integral curve that is
  everywhere
• tangent to a given vector field, such as
  velocity

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• Critical points
• A critical point, also known as a stationary
  point, is a location in the vector field v where
  v 0.
• Critical points usually are properties
  investigated in the first place. Examing the
  neighborhood of the critical points often tells
  quite important principal characteristics about
  the entire system behavior.

2D Seeding Strategy
Goal the visualization does not appear to be
cluttered and there are no artifacts introduced
in the visualization process
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• Image-guided streamline placement

• Uses a stochastic mechanism to refine the
  placement of the streamlines.
• First an initial set of randomly placed
  streamlines is created.
• Then this set of streamlines is updated using
  three valid operations
• (1) changing the position and/or length of a
  streamline,
• (2) joining streamlines that nearly abut
• (3) creating a new streamline to fill a gap.

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• An energy function to measure the variation of
  energy
• between the current and the updated images
• Modification is only accepted if the variation of
  energy
• is negative.
• The procedure is iterative
• the convergence is very slow

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• Flow-guided streamline placement

• Procedure
• First identify the critical points ,locate the
  position and classify
• Segment flow field into regions, each contain one
  critical point
• each region is seeded with a template
• Additional seed points are randomly distributed
  using a Poisson disk

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• Based on the flow features in the data set
• Capture flow patterns in the vicinity of
  critical points
• non-iterative and view-independent

Different types of critical points in 2D
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Figure. Seed templates for various critical
point. The bold dots represent the seed template
and the dashed lines are the streamlines traced
using the seed from the template. (a) Center,
spiral (b) source, sink (c) saddle
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Project idea

• Extend the flow-guided streamline placement
  on 2D to 3D

• Procedure
• 1. Search the critical points and obtain its
  position in the object space and classify
  them .
• A critical point can be classified according to
  the eigenvalues of the Jacobi matrix of the
  vector with respect to position of the critical
  point.

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• A positive or negative real part of an eigenvalue
  indicates an attracting or repelling nature. The
  nonzero imaginary part of eigenvalues create a
  spiral structure around critical point.
• We can use Fast to compute the critical points
  locations and to classify them

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• Three dimensional critical points
• repelling spiral, b) repelling node, c) saddle
• d) Attracting spiral, repelling in third
  dimension, e) attracting node, f) center,
  repelling in the third dimension

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• 2. Streamline seeding
• We will consider some types of critical
  points, such as saddle, attracting or repelling
  spiral
• In three dimensions, two eigendirections have the
  same sign and span a plane. The third
  eigendirection spans a line. Thus, for example v
  approaches a 3D saddle along a plane and recedes
  along aline

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• 2. Intergation
• Equation
• Several integration schemes can be used
• a. The simplest is the first order Euler
  technique
• x(tDt) x(t) v (x(t)) Dt
• This approximation is too inaccurate
• b. I use adaptive fourth-order Runge-Kutta
  formula

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Formula Use of a variable time step,
depending on the gradients in the velocity field,
is the best solution. This may be done with Dt
a/va, where a is the number of steps per cell,
and v a is the average velocity of the eight
surrounding grid
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• 3.Rendering
• 3D spatial curves are hard to localize without
  further depth cues. Also, only a small number
  of curves can be displayed without confusion.
• Display curves as 3D pipes, allowing occlusion
  and directional light reflection.

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References 1.A Flow-guided Streamline Seeding
Strategy   Vivek Verma, David Kao, Alex Pang
IEEE Visualization http//citeseer.nj.nec.com/4709
72.html 2. Image-Guided Streamline Placement
http//www-lil.univ-littoral.fr/jobard/Research/
Publications/EGW-ViSC97/ViSC97.abstract.html 3.
A Tool for Visualizing the Topology of
Three-Dimensional Vector Fields
http//www.nas.nasa.gov/Research/Reports/Techrepo
rts/1991/rnr-91-017-abstract.html 4. A
Multiresolution Streamlines Seeding
Plane http//www.winslam.com/rlaramee/seedingPlane
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Questions?
Thank you!