1. CHAPTER 6 (1) VECTOR VISUALIZATION

2. 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

3. OUTLINE Vector Visualization: Application: Computational Fluid Dynamics (CFD) 6.1 Mathematical operators to analyze vector fields 6.2 Vector glyphs 6.3 Scalar Visualization techniques to depict vector fields 6.4 Displacement plot technique 6.5 Stream objects 6.6 Use of textures 6.7 Strategies for simplified representation of vector datasets

4. 6.1 DIVERGENCE ( 发散度 ) AND VORTICITY ( 旋度 ) The Divergence of v=(v x,v y,v z ) is the scalar quantity Vorticity (curl or rotor of v )

5. 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. 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

7. 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.)

8. 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)

9. 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.)

10. 6.2 VECTOR GLYPHS Figure 6.5. Different glyph types. (a) Cones. (b) Arrows.

11. 6.2 VECTOR GLYPHS 6.2.1 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

12. 6.2 VECTOR GLYPHS 6.2.1 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.

13. 6.2 VECTOR GLYPHS 6.2.1 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.

14. 6.2 VECTOR GLYPHS 6.2.1 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 glyph  Occlusion problem Sparse sampling Draw the glyph transparently Monochrome: easier to interpret

15. 6.2 VECTOR GLYPHS 6.2.1 VECTOR GLYPH EXAMPLES Figure 6.9. Glyph-based vector visualization on a 3D velocity isosurface.