A Quick Guide to Visualization

1. A Quick Guide to Visualization Yingcai Xiao

2. Computation with and without Visual Assistance 67 x 89 = ?

3. Visualized Data Analysis 67 x 89 --------- 603 + 536 --------- 5963

4. Visualization Representing information (data) as computer graphics.

5. Scientific, Engineering and Information Visualization Scientific Visualization: Scientific Data Engineering Visualization: Measurement Data Information Visualization: Abstract Data

6. Scientific Visualization Started from CFD (Computational Fluid Mechanics) in the 80s. Formalized as an research discipline in 1989. (NSF Report on Scientific Visualization).

7. Scientific Data Commonly in the form of a grid: data values are known on the grid nodes.

8. Scientific Visualization: Fundamentals Visualizing data variation through out the volume of interest.

9. Scientific Visualization: Fundamentals Local Trilinear Interpolation

10. Scientific Visualization: Techniques: Color Mapping • Mapping data values to colors with a color map.

11. Scientific Visualization: Techniques: Color Mapping A color map.

12. Scientific Visualization: Techniques: Cut-Away • Revealing data values inside the volume of interest.

13. Scientific Visualization: Techniques: Slicing • Revealing data values on cutting planes.

14. Scientific Visualization: Techniques: Iso-surfacing • Iso-surface: a surface of constant data values.

15. Scientific Visualization: Techniques: Iso-surfacing

16. Scientific Visualization: Techniques: Iso-surfacing

17. Scientific Visualization: Techniques: Iso-Lines • Iso-line: a line of constant data values.

18. Scientific Visualization Data Types

19. Scientific Visualization: Data Types Scalar: one value per data point Vector: 3 values per data point 3 Scalars Tensor: 9 values per data point 9 Scalars 3 Vectors

20. Vector Visualization 3 scalar values, (vx, vy, vz) => direction and length

21. Vector Visualization: Directed Lines 3 scalar values, (vx, vy, vz) => direction and length

22. Vector Visualization: Glyph

23. Vector Visualization: Glyph

24. Vector Visualization: Warping Warping: deformation of geometry according to a vector.

25. Vector Visualization: Displacement Plots Displacement Plots: represent data values as the displacement of a surface in the direction perpendicular to the surface.

26. Vector Visualization: Streamlines Streamlines: outlines of fluid flow

27. Vector Visualization: Streamtubes Stream-tubes: streamline + isosurface + color mapping

28. Tensor Visualization: Tensor Ellipsoid Three eigenvectors: V1 V2 V3

29. Tensor Visualization: Tensor Ellipsoid

30. Scientific Visualization: Mature W. Shroeder, K. Martin, & B. Lorensen The Visualization Toolkit - An Object-oriented Approach to 3D Graphics, 2nd ed. www.kitware.com

31. Engineering Visualization

32. Engineering Visualization Intelligent Monitoring Traffic Assembly Line

33. Intelligent Monitoring • Data capturing • Data analysis • Data representation

34. Intelligent Monitoring • Data capturing • sensors, video cameras, tracking devices • Data analysis • video image processing is a challenge • Data representation • color coding (e.g. GIS – Geographical Information Systems, google map)

35. Intelligent Monitoring video image processing : computer vision : OpenCV http://opencv.willowgarage.com/wiki/ http://sourceforge.net/projects/opencvlibrary/ ITK: http://www.itk.org/

36. Engineering Visualization Measurement Data: Scattered Sparse

37. Scattered Data: sample points distributed unevenly and non-uniformly throughout the volume of interest.

38. Engineering Visualization: Two-Step Approach T. Foley & A. D. Lane Visualization of Irregular Multivariate Data Proceedings of the First IEEE Conference on Visualization, San Francisco, CA, 1990

39. __________ ____________ __ ___ _______ Modeling Rendering Scattered Data Intermediate Grid Rendered Volume Interpolation Grid-based

40. Interpolation Methods G. M. Nielson Scattered Data Modeling IEEE Computer Graphics & Applications, 13(1), 1993

41. Interpolation Methods (Nielson, 1993) Global: all sample points are used to interpolated a grid value.Exact: the interpolation function can exactly reproduce the data values on the sample points.

42. Global Exact Interpolation Functions(Foley & Lane, 1990; Nielson, 1993) n sample points: (xi,yi,zi,vi) for i = 1,2,..nTo define an interpolation function: e.g., thin-plate spline, di is the distance between sample point i and the point to be interpolated p(x,y,z).di = ((x-xi)2+(y-yi )2+(z-zi )2)1/2bi,c1,c2,c3,c4 are n+4 constants to be solved by enforcing the following conditions:f (xi,yi,zi) = vi for i = 1,2,..n

43. Global Exact Interpolation Functions(Foley & Lane, 1990; Nielson, 1993) Thin-plate spline Volume Spline Multiquadric Shepard

44. Two-step Approach: Problems Yingcai Xiao, John Ziebarth, Chuck Woodbury, Eric Bayer, Bruce Rundell, Jeroen Zijp “The Challenges of Visualizing and Modeling Environmental Data” IEEE Visualization 96, Conference Proceeding, San Francisco, California, October 1996

45. Scattered Data: sample points distributed unevenly and non-uniformly throughout the volume of interest.

46. Thin-plate Spline

47. Volume Spline

48. Shepard method

49. Deficiencies of the Interpolation-based Two-step Approach • Misinterpretation (negative concentration) • Ambiguity in selecting interpolation methods • Inconsistent interpolations in modeling and rendering • Visualizing secondary data instead of the original data • No error estimation • Unable to add known information • Not efficient

50. Information Visualization • Data abstract • Not interpolatable • Domain dependent http://en.wikipedia.org/wiki/Information_visualization For examples: Database Visualization (RbDbVis.ppt) Visual Analytics (IA: Intelligence Amplification)