CIS 4930/ SCIENTIFICVISUALIZATION

Transcription

1 CIS 4930/ SCIENTIFICVISUALIZATION ISOSURFACING Paul Rosen Assistant Professor University of South Florida slides credits Tricoche and Meyer

2 ADMINISTRATIVE Read (or watch video): Kieffer et al, HOLA: Human-like Orthogonal Network Layout [InfoVis 2015 Best Paper]

3 TODAY visualization for scalar fields pseudocoloring isocurves with marching squares isosurfacing with marching cubes

4 Weiskopf/Machiraju/Möller 19 2D visualization slice images (or multi-planar reformating MPR) Indirect 3D visualization isosurfaces (or surface-shaded display SSD) Direct 3D visualization (direct volume rendering DVR)

5 In Visualization, we Use the Concept of a Transfer Function to set Color as a Function of Scalar Value Scalar values ->[0,1] -> Colors In OpenGL, the mapping of 1D texture

6 USE THE RIGHT TRANSFER FUNCTION COLOR SCALE TO REPRESENT A RANGE OF SCALAR VALUES Gray scale Intensity Interpolation Saturation interpolation Two-color interpolation Rainbow scale Heated object interpolation Blue-White-Red

7 A GALLERY OF COLOR SCALES

8 GREY SCALE.

9 SATURATION SCALE.

10 SPECTRUM SCALE.

11 LIMITED SPECTRUM SCALE.

12 REDUNDANT HUE/LIGHTNESS SCALE.

13 HEATED-OBJECT SCALE.

14 Other examples 35

15 ISOCONTOURS IN 2D

16 PROCESS Get cell Identify grid lines w/cross Find crossings Draw x x Primitives naturally chain together + -

17 SIMPLER TO IMPLEMENT PROCESS check each corner above or below isovalue assign bit 0/1 4-bit string describes a particular case

18 2D SCALAR VISUALIZATION 16 possible marching squares reduce to 5 symmetric cases or 4 topological cases 18

19 x x x x x x x x x x x x

20 what is the isocontour for isovalue = 4? 5x5 grid

21 2D Scalar Visualization 21

22 IN 3D: ISOSURFACES 22

23 Weiskopf/Machiraju/Möller 19 2D visualization slice images (or multi-planar reformating MPR) Indirect 3D visualization isosurfaces (or surface-shaded display SSD) Direct 3D visualization (direct volume rendering DVR)

24 MARCHING CUBES Predominant method used today Efficient and simple Independently reported by Wyvill and McPeeters in 1986, Lorenson and Cline in 1987 Patented in 1987 by Lorenson and Cline 24

25 MARCHING CUBES 3D generalization of isocontours Treat each cube individually No 2D contour curves Allow intersections only on the edges or at vertices Pre-calculate all of the necessary information to construct a surface 25

26 MARCHING CUBES Linear search through cells Trivially parallelizable Row by row, layer by layer No neighborhood information is required 26

27 MARCHING CUBES Consider a single cube Three cases: All vertices above the contour threshold All vertices below Mixed above and below 27

28 MARCHING CUBES Binary label each node (above or below) Examine all possible cases of above or below for each vertex 28

29 MARCHING CUBES Now we have 8 vertices Thus, 2 8 = 256 cases How many unique topological cases? 29

30 CASE REDUCTION Value symmetry 30

31 CASE REDUCTION Rotation symmetry 31

32 CASE REDUCTION Mirror symmetry By inspection, we can reduce 256 cases to only 15 32

33 MARCHING CUBES CASES 33

34 MARCHING CUBES SUMMARY Basic Marching Cubes algorithm: 2. Classify 1. Create a cube each voxel (volume element) 3. Build an index 4. Lookup edge list 5. Interpolate triangle vertices 6. Calculate normals 34

35 STEP 1: CREATE A CUBE Consider a cube defined by eight data values Four values from slice and four from neighbor 35

36 STEP 2: CLASSIFY EACH VOXEL Binary classify each vertex of the cube as to whether it lies Outside the surface voxel value > isosurface value Inside the surface voxel value <= isosurface value 36

37 CLASSIFICATION EXAMPLE 37

38 STEP 3: BUILD AN INDEX Use the binary labeling of each voxel to create an 8- bit index (8 vertices 256 cases) 38

39 STEP 4: LOOKUP EDGE LIST 39

40 STEP 5: INTERPOLATE TRIANGLE VERTICES For each edge Find the vertex location along the edge by using linear interpolation of the voxel values 40

41 STEP 6: COMPUTE NORMALS Calculate the normal at each cube vertex Linearly interpolate the polygon vertex normal Renormalize after interpolation 41

42 EXAMPLES 1 Isosurface 3 Isosurfaces 2 Isosurfaces

43 ENHANCING ISOSURFACING Can add information about additional variables Here, two additional variables control the color 43

44 CHALLENGES what is a good isovalue? ambiguities poorly shaped, nonadaptive triangles gaps between neighboring points looking at every voxel 73

45 MARCHING CUBES SPEEDUP Expensive to search each grid cell Use a MinMax Octree to ignore cells outside the isovalue range 45

46 MINMAX OCTREE BUILDING THE STRUCTURE Create an octree structure for the voxels of the volume In each node store the minimum and maximum isovalues of the children 46

47 MINMAX OCTREE BUILDING THE ISOSURFACE Begin at the root node If min <= isovalue <= max Recurse to the next level of the tree Otherwise Terminate search 47

48 MINMAX OCTREE PERFORMANCE ANALYSIS WORST-CASE PERFORMANCE? O(n log n) or O(nh), where n is the number of voxels and h is the tree height When all voxels cross the isovalue EXPECTED PERFORMANCE? O(k log n) or O(kh), where k is the number of voxels with geometry USUALLY K<<N, MAKING THIS METHOD QUITE EFFICIENT

49 BIGGEST LIMITATION OF ISOSURFACING? 49

50 BIGGEST LIMITATION OF ISOSURFACING? 50

51 Volume Rendering 51

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