2D Flow Visualizationstreamline, pathline, hedges, spotnoise

郭翰琦 陈珩

Outline

• Introduction• Data Source• Streamline, pathline• Spotnoise• User interactive

Introduction

• Flow Visualization: In fluid dynamics it is critically important to see the patterns produced by flowing fluids, in order to understand them.

Introduction

• Techniques: Point, Line, Surface, Volume, NPR, LIC, etc.

• In 2D FlowVis: geo-based, texture-based, etc.• The techs we have tried: streamlines,

pathlines, hedges, spotnoise.

Data Source

• Using a ‘Navier-Stokes Solver’ in MATLAB, we can get a 2D vector field in a suqare space by assigning boundary conditions.

Square mesh Boundary conditions 2D field

Data Source: interpolation

• After calculation, we get 2D vector data on thousands of triangles.

• Then, through interpolation, we get 128×128 mesh on [0,1]×[0,1] square.

x1,v1

x3,v3x2,v2

Streamline

• Streamlines are a family of curves that are instantaneously tangent to the velocity vector of the flow.

• A streamline is defined as

Streamline

• So, it is a Cauchy problem to integrate a streamline:

Streamline

• We use Runge-Kutta 4 to solve the stream integration:

Non-grid points are processed with interpolation

Streamline

• One streamline:

Seeds are red~ With hedges

Streamlines: seeding strategy

• It is fairy a problem to put the streamlines or select the seeds. Several articles discussed this. (image-guided, even-spaced, etc)

• We used random seeds and man-select seeds.

Random seeds

Streamlines: seeding strategy

• Man-selected seeds may have better effects near the critical points. (also a user-interactive means)

Streamline

• Same seeds with different time-steps:

Pathlines

• Pathlines are the trajectories that individual fluid particles follow.

• Pathlines are defined as

Pathlines

• It is also a Cauchy problem to integrate a pathline. To simplify the calculation, we use Euler method.

Spot Noise

• Texture is characterized by function f

• Spot function allows for local control over texture: maps data value (vector) to spot

Spot Noise

• Elliptical spots for visualizing 2D flows– Long axis proportional to |v|– Small axis proportional to 1/|v|

1 seed 1000 seeds

Spot Noise

• Shortcomings: SLOW…..• It takes 2 minutes to get a spot noise image

with 1000 seeds.• It may get faster using GPU

User interactive• right click to choose one mode• 8 modes: StreamlineHedgePathlinStreamline&HedgeStreamline&PathlineHedge&PathlineStream&Hedge&PathlineSpotnoise

User interactive• create a new line• create a new path

User interactive

• keyboard: Press any key Pass to the next time step

User interactive

• Spotnoise Number - 10, 20, or 50• click and create spots• 10, 20, or 50 each time

User interactive

• different viewpoints in one window• overlay two modes• color coding• 34 colors for streamline and the pathline

User interactive

Thank you

郭翰琦 陈珩2009-01-15