Data Visualization (DSC 530/CIS )

Transcription

1 Data Visualization (DSC 530/CIS 60-01) Scalar Visualization Dr. David Koop

2 Online JavaScript Resources Good coverage of data wrangling using JavaScript

3 Fields in Visualization Scalar Fields Vector Fields Tensor Fields (Order-0 Tensor Fields) (Order-1 Tensor Fields) (Order-+) Each point in space has an associated... s 0 4 v v 1 v Scalar Vector Tensor 3 5 3

4 Grids Remember we have continuous data and want to sample it in order to understand the entire domain Possible schemes? 4

5 Grids Remember we have continuous data and want to sample it in order to understand the entire domain Possible schemes? uniform rectilinear structured unstructured [ Weiskopf/Machiraju/Möller] Geometry: the spatial positions of the data (points) Topology: how the points are connected (cells) Type of grid determines how much data needs to be stored for both geometry and topology 4

6 Nearest Neighbor Interpolation Value at.? 5

7 Linear Interpolation Value at.? 6

8 Visualizing Volume (3D) Data D visualization slice images (or multi-planar reformating MPR) Indirect 3D visualization isosurfaces (or surface-shaded display SSD) Direct 3D visualization (direct volume rendering DVR) [ Weiskopf/Machiraju/Möller] 7

9 Assignment 4 Filtering, Aggregation, and Brushing

10 Final Projects Creativity of designs improved Think about the task and how well your visualization supports it Disappointed with some prototypes (minimal implementation) Do your own work! Presentations on Monday, May 7 from 3pm-6pm Turn in code and a report describing how your visualization works, design decisions, and how it helps one answer the questions posed 9

11 Isolines (D) Isoline: a line that has the same scalar value at all locations Example: Topographical Map [USGS via Wikipedia] 10

12 Isosurfaces (3D) Isosurface: a surface that has the same scalar value at all locations Often use multiple isosurfaces to show different levels [J. Kniss, 00] 11

13 Generating Isolines [R. Wenger, 013] 1

14 Generating Isolines [R. Wenger, 013] 13

15 Generating Isolines [R. Wenger, 013] 14

16 Generating Isolines [R. Wenger, 013] 15

17 Marching Squares [R. Wenger, 013] 16

18 Ambiguous Configurations There are some cases for which we cannot tell which way to draw the isolines 16 I II 16 I 16 II [R. Wenger, 013] 17

19 Ambiguous Configurations Either works for marching squares, this isn't the case for 3D 1 [R. Wenger, 013]

20 3D: Marching Cubes Same idea, more cases [Lorensen and Cline, 197] # Positive Vertices 4A 4B 4C 4D 4E Zero Five 0 5A 5B 5C One Six 1 6A 6B 6C Two Seven A B C 7 Three Eight 3A 3B 3C Four 4A 4B 4C 4D 4E 4F [R. Wenger, 013] 19

21 Incompatible Choices If we have ambiguous cases where we choose differently for each cell, the surfaces will not match up correctly there are holes Fix with the asymptotic decider [Nielson and Hamann,1991] [R. Wenger, 013] 0

22 Marching Cubes Algorithm For each cell: - Classify each vertex as inside or outside (>=, <) 0 or 1 - Take the eight vertex classifications as a bit string - Use the bit string as a lookup into a table to get edges - Interpolate to get actual edge locations - Compute gradients - Resolve ambiguities Render a bunch of triangles: easy for graphics cards 1

23 Multiple Isosurfaces Topographical maps have multiple isolines to show elevation trends Problem in 3D? Occlusion Solution? Transparent surfaces Issues: - Think about color in order to make each surface visible - Compositing: how do colors "add up" with multiple surfaces - How to determine good isovalues? Next: - Direct Volume Rendering [J. Kniss, 00]

24 Visualizing Volume (3D) Data D visualization slice images (or multi-planar reformating MPR) Indirect 3D visualization isosurfaces (or surface-shaded display SSD) Direct 3D visualization (direct volume rendering DVR) [ Weiskopf/Machiraju/Möller] 3

25 Volume Rendering vs. Isosurfacing (a) Direct volume rendered (b) Isosurface rendered [Kindlmann, 199] 4

26 (Direct) Volume Rendering Isosurfacing: compute a surface (triangles) and use standard computer graphics to render the triangles Volume rendering: compute the pixels shown directly from the volume information Why? - No need to figure out precise isosurface boundaries - Can work better for data with noise or uncertainty - Greater control over appearance based on values 5

27 Object order approach Volume Ray Casting Image Plane Data Set Eye [Levine] 6

28 Volume Ray Casting Image Plane Data Set Eye [Levine] 7

29 How? Approximate volume rendering integral: light absorption & emission Sample at regular intervals along each ray Trilinear interpolation: linear interpolation along each axes (x,y,z) Use trilinear interpolation Not the only possibility, also "object order" techniques like splatting or texture-based and combinations like shear-warp

30 Compositing Need one pixel from all of the values along the ray Q: How do we "add up" all of those values along the ray? A: Compositing! Different types of compositing - First: like isosurfacing, first intersection at a certain intensity - Max intensity: choose highest val - Average: mean intensity (density, like x-rays) - Accumulate: each voxel has some contribution intensity max intensity accumulate average first depth [Levine and Weiskopf/Machiraju/Möller] 9

31 Types of Compositing max intensity intensity accumulate average first depth [Levine and Weiskopf/Machiraju/Möller] 30

32 Types of Compositing max intensity intensity accumulate average first depth [Levine and Weiskopf/Machiraju/Möller] 31

33 Types of Compositing max intensity Synth intensity accumulate average first depth [Levine and Weiskopf/Machiraju/Möller] 3

34 Types of Compositing max intensity intensity accumulate average first depth [Levine and Weiskopf/Machiraju/Möller] 33

35 Accumulation If we're not just calculating a single number (max, average) or a position (first), how do we determine the accumulation? Assume each value has an associated color (c) and opacity (α) Over operator (back-to-front): - c = αf cf + (1-αf) αb cb - α = αf + (1-αf) αb Order is important! Blue Last Blue First 34

36 Transfer Functions Where do the colors and opacities come from? Idea is that each voxel emits/absorbs light based on its scalar value but users get to choose how that happens x-axis: color region definitions, y-axis: opacity α RGB Simp value [Kindlmann] 35

37 Transfer Function Design Transfer function design is non-trivial! Lots of tools to help visualization designers to create good transfer functions Histograms, more attributes than just value like gradient magnitude 36

38 Multidimensional Transfer Functions [J. Kniss] 37

39 Multidimensional Transfer Functions [J. Kniss] 3

40 Fields in Visualization Scalar Fields Vector Fields Tensor Fields (Order-0 Tensor Fields) (Order-1 Tensor Fields) (Order-+) Each point in space has an associated... s 0 4 v v 1 v Scalar Vector Tensor

41 Examples of Vector Fields Wind [earth.nullschool.net, 014] 40

42 Examples of Vector Fields Wind [earth.nullschool.net, 014] 40

43 Examples of Vector Fields Computational Fluid Dynamics [newmerical] 41

44 Examples of Vector Fields Earthquake Ground Surface Movement [H. Yu et. al., SC004] 4

45 Examples of Vector Fields Gradient Vector Fields 43

46 Examples of Vector Fields Wildfire Modeling [E. Anderson] 44