3d flow visualization xiaohong ye email:[email protected]

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3D Flow Visualization Xiaohong Ye Email:[email protected]

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Page 1: 3D Flow Visualization Xiaohong Ye Email:xhye@soe.ucsc.edu

3D Flow Visualization3D Flow Visualization

Xiaohong Ye

Email:[email protected]

Page 2: 3D Flow Visualization Xiaohong Ye Email:xhye@soe.ucsc.edu

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

Purposes and Problems of Flow VisualizationPurposes and Problems of Flow Visualization

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.

Page 3: 3D Flow Visualization Xiaohong Ye Email:xhye@soe.ucsc.edu

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.

Methods for streamline placementMethods for streamline placement

Basic ConceptsBasic ConceptsStreamlineA streamline is an integral curve that is everywheretangent to a given vector field, such as velocity

Page 4: 3D Flow Visualization Xiaohong Ye Email:xhye@soe.ucsc.edu

Critical pointsA 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.

Goal: the visualization does not appear to be cluttered and there are no artifacts introduced in the visualization process

2D Seeding Strategy2D Seeding Strategy

Page 5: 3D Flow Visualization Xiaohong Ye Email:xhye@soe.ucsc.edu

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.

Page 6: 3D Flow Visualization Xiaohong Ye Email:xhye@soe.ucsc.edu

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

Page 7: 3D Flow Visualization Xiaohong Ye Email:xhye@soe.ucsc.edu

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

Flow-guided streamline placement

Page 8: 3D Flow Visualization Xiaohong Ye Email:xhye@soe.ucsc.edu

Different types of critical points in 2DDifferent types of critical points in 2D

Based on the flow features in the data set

Capture flow patterns in the vicinity of critical points

non-iterative and view-independent

Page 9: 3D Flow Visualization Xiaohong Ye Email:xhye@soe.ucsc.edu

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

Page 10: 3D Flow Visualization Xiaohong Ye Email:xhye@soe.ucsc.edu

Project idea: 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.

Page 11: 3D Flow Visualization Xiaohong Ye Email:xhye@soe.ucsc.edu

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

Page 12: 3D Flow Visualization Xiaohong Ye Email:xhye@soe.ucsc.edu

Three dimensional critical points

a) repelling spiral, b) repelling node, c) saddle

d) Attracting spiral, repelling in third dimension, e) attracting node, f) center, repelling in the third dimension

Page 13: 3D Flow Visualization Xiaohong Ye Email:xhye@soe.ucsc.edu

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

Page 14: 3D Flow Visualization Xiaohong Ye Email:xhye@soe.ucsc.edu

2. Intergation Equation:

Several integration schemes can be used a. The simplest is the first order Euler technique x(t+Dt) = x(t) + v (x(t)) Dt

This approximation is too inaccurate

b. I use adaptive fourth-order Runge-Kutta formula

Page 15: 3D Flow Visualization Xiaohong Ye Email:xhye@soe.ucsc.edu

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

Page 16: 3D Flow Visualization Xiaohong Ye Email:xhye@soe.ucsc.edu

3.Rendering3D 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.

Page 17: 3D Flow Visualization Xiaohong Ye Email:xhye@soe.ucsc.edu

References1.A Flow-guided Streamline Seeding Strategy   Vivek Verma, David Kao, Alex Pang IEEE Visualizationhttp://citeseer.nj.nec.com/470972.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/Techreports/1991/rnr-91-017-abstract.html

4. A Multiresolution Streamlines Seeding Planehttp://www.winslam.com/rlaramee/seedingPlane

Page 18: 3D Flow Visualization Xiaohong Ye Email:xhye@soe.ucsc.edu
Page 19: 3D Flow Visualization Xiaohong Ye Email:xhye@soe.ucsc.edu

Questions?