2d flow visualization streamline, pathline, hedges, spotnoise 郭翰琦 陈珩
TRANSCRIPT
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
• We use Runge-Kutta 4 to solve the stream integration:
Non-grid points are processed with interpolation
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)
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
• 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