CHAPTER 6 (1)VECTOR VISUALIZATION

OUTLINE• Vector datasets are samplings of vector fields over discrete spatial domains

• Visualizing Vector

• A number of the popular visualization methods for vector datasets

• Vector glyphs• Vector color coding• Displacement plots

• Stream objects

• Texture-based vector visualization

• The simplified representation of vector fields

OUTLINE• Vector Visualization:

• Application: Computational Fluid Dynamics (CFD)

6.1 Mathematical operators to analyze vector fields6.2 Vector glyphs6.3 Scalar Visualization techniques to depict vector fields6.4 Displacement plot technique6.5 Stream objects6.6 Use of textures6.7 Strategies for simplified representation of vector datasets

6.1 DIVERGENCE (发散度 ) AND VORTICITY (旋度 )

• The Divergence of v=(vx,vy,vz) is the scalar quantity

• Vorticity (curl or rotor of v)

v = + +yx zvv v

divx y z

v = ( - , - , - )y yx xz zv vv vv v

roty z z x x y

6.1 DIVERGENCE AND VORTICITY

Fig 6.1. Divergence and curl in 2D. (a) Divergence construction. (b) Source point. (c) Sink point.

(d) Rotor construction. (e) High-vorticity field.

Source point: Positive; Spread

Sink point: Negative; Sucked.

6.1 DIVERGENCE AND VORTICITY

Fig 6.2 (a) Divergence of a 2D vector field (b) Absolute value of vorticity of a 2D vector field

6.1 DIVERGENCE AND VORTICITY

Fig 6.3 Vorticity of a 2D fluid flow field. Note the alternation between vortices with opposite spinning directions. (Courtesy of I. Barosan, Eindhoven University,

Netherlands.)

6.2 VECTOR GLYPHS

• Vector Glyphs• Simplest, fastest, most popular technique for visualizing

vector fields• Associate a vector glyph, or vector icon, with every sample

point of the vector dataset• A sign conveys properties of the represented vector, such as

direction, orientation, and magnitude• Many variations of framework

• Lines (convey direction)• 3D cone (convey direction + orientation)• Arrow (convey direction + orientation)

6.2 VECTOR GLYPHS

• Figure 6.4. Hedgehog visualization of a 2D magnetohydrodynamic velocity field. (Data courtesy of Prof. Martin Rumpf, University of Bonn, Germany.)

6.2 VECTOR GLYPHS

• Figure 6.5. Different glyph types. (a) Cones. (b) Arrows.

6.2 VECTOR GLYPHS6.2.1 VECTOR GLYPH EXAMPLES

• Trade-off

• The power of expression of glyph

• Number of attributes they can encode

• Minimal screen size

• The difference between scalar and vector visualization --- in sampling terms

• Subsampling problem

• Random sampling

6.2 VECTOR GLYPHS6.2.1 VECTOR GLYPH EXAMPLES

• Figure 6.6. Visual interpolation of vector glyphs. (a) Small data variations are easily interpolated. (b) Large data variations create more problems.

6.2 VECTOR GLYPHS6.2.1 VECTOR GLYPH EXAMPLES

• Figure 6.7. (a) Vector glyphs on a dataset regularly subsampled on a rotated sample grid. (b) Subsampling artifacts are alleviated by random sampling. Both visualization

display 1200 glyphs.

6.2 VECTOR GLYPHS6.2.1 VECTOR GLYPH EXAMPLES

• Figure 6.8. Glyph-based visualization of a 3D vector field. (Data courtesy of Prof. Martin Rumpf, University of Bonn, Germany.)

3D glyphOcclusion

problem

Sparse sampling

Draw the glyph transparently

Monochrome: easier to interpret

6.2 VECTOR GLYPHS6.2.1 VECTOR GLYPH EXAMPLES

• Figure 6.9. Glyph-based vector visualization on a 3D velocity isosurface.