Min Chen, Andrew S Winter, David Rodgman and Steve Treavett Department of Computer Science

1. Adapted from Min Chen’s Presentation inDagstuhl Seminar 00211Enriching Volume Modelling withScalar Fields Min Chen, Andrew S Winter,David Rodgman and Steve Treavett Department of Computer Science University of Wales Swansea m.chen@swansea.ac.uk

2. CONTENTS 1. The Role of Scalar Fields • Motivation 2. Volume Modelling with Scalar Fields • Scope of Volume Modelling • Constructive Volume Geometry • Solid, Hyper- and NPR Textures 3. Direct Rendering of Scalar Fields • Rendering Issues • Rendering Effects

3. 1. THE ROLE OF SCALAR FIELDS

4. Continuous Field Reps. e.g. F(p) Discrete Field Reps. e.g. S.O.E. “Field” in Surface Graphics (I) Continuous Surface Reps. e.g. F(p) = 0 RayCasting Discrete Surface Reps. e.g. mesh Projection

5. “Field” in Surface Graphics (II) • Spatial-Occupancy Enumeration • Implicit Surfaces • Solid Textures • Hypertextures • Free Form Deformation • Gaseous Phenomena (e.g. clouds) • Water

6. Continuous Field Reps. e.g. F(p) Underlying Concept “Fields” in Visualisation (I) Discrete Field Reps. e.g. volume RayCasting Discrete Surface Reps. e.g. mesh Projection

7. “Fields” in Visualisation (II) Ray Casting Pipeline for Volume Rendering

8. “Fields” in Volume Graphics (I) Continuous Field Reps. e.g. F(p) RayCasting Discrete Field Reps. e.g. volume Projection

9. “Fields” in Volume Graphics (II) Discrete FieldSpecification: MRI and CT Datasets, Image, Video Continuous Field Specification: Cylinders, cuboids (for difference operations)

10. Motivation • To match surface graphics in most aspects • To supersede surface graphics in some aspects • To feed the techniques back into visualisation

11. 2. MODELLING WITH FIELDS • Scope of Volume Modelling • Constructive Volume Geometry • Solid, Hyper- andNPR Textures

12. Scope of Volume Modelling (I) • the process of modelling volume data; • a generalisation in dimension to surface modelling; • the means to provide the input to the volume rendering integral. Gregory M. Nielson (1999)Arizona State University

13. Scope of Volume Modelling (II) Generalisation • Volume Data Types • Scenes, Objects, Attributes • Constructive Specification • Heterogeneous Object Interior • Amorphous Phenomena • Software Tools Process Input

14. Volume Data Types (I) • Spatial, Continuous Specification • Explicit Field Function: F(x, y, z)(Mathematical and Procedural) • Parametric Field Function: F(t1,t2,...) • Spatial, Discrete Specification • Discrete Point Set • Regular Dataset (e.g. CT dataset) • Irregular Dataset (e.g. tetrahedral mesh, free-hand ultrasound) • Image and Video

15. Volume Data Types (II) • Non-spatial • Fourier Domain • Wavelet Domain • Compressed Image and Video • Light Field

16. Volume Data Types (III) High-LevelModels DiscreteSpatial Models Non-SpatialModels ContinuousSpatial Models

17. Constant • Volume Dataset • Colour-separated image • Built-in mathematical scalar field • Procedural scalar field • plus various mappings Constructive Volume Geometry scene object object ...... object field O R G B Ge Ka Kd Ks N Dn Rfl Rfr Txt ...

18. CVG: Scalar Field (I) A spatial object is a tuple o = (O, A1, A2, …, Ak) of scalar fields defined in E3, including an opacity field O: E3 [0,1] specifying the visibility of every point in E3 and possibly other attribute fields, A1, A2, …, Ak: E3 [0,1], k>0. O: hyperbolic paraboloidR: cylindrical field G: cylindrical field B: cylindrical field

19. CVG: Scalar Fields (II) O: torusR: datasetG: constantB: dataset O: hyperbolic paraboloid R, G, B: constantGeo: hyperbolic paraboloid + noise O: sphereR: noiseG: constantB: constant

20. Scalar Fields (III) O: implicit function R, G, B: linear functionsGeo: implicit function O: implicit function R, G, B: linear functionsGeo: hyperbolic paraboloid

21. (o1, o2) CVG: Data Representation composite volume object o1 o2 convex volume object convex volume object 1

22. { s1 s1 s2s2 s1 < s2 max(s1, s2) = { t1 s1 s2t2 s1 < s2 select(s1, t1, s2, t2) = CVG: 4 Colour Channel Model (o1, o2) = ( MAX(O1, O2),SELECT(O1, R1, O2, R2),SELECT O1, G1, O2, G2),SELECT(O1, B1, O2, B2) ) operations on spatial objects operations on scalar fields ...... operations on scalars

23. (o1, o2) o1=(O1, R1, G1, B1) o2=(O2, R2, G2, B2) CVG: Operation (I)

24. (o1, o2) (o1, o2) CVG: Operation (II) (o1, o2) (o2, o1)

25. CVG: Interior & Real Domain

26. CVG: Solid and Fuzzy Objects

27. CVG: Image and Texture (I)

28. CVG: Image and Texture (II)

29. CVG: Non-Photorealistic Rendering

30. Solid, Hyper- and NPR Textures • Solid Texture: • Defining R(p), G(p), B(p) with Fields • Defining Geo(p) with Fields • Hypertexture: • Defining Distance Fields Dist(p) • Defining R(Dist(p)), G(...), B(...) • Non-Photorealistic Texture: • Defining O(p), R(p), G(p), B(p) Defining a NPR mapping

31. Solid Texture and Hypertexture

32. NPR Texture (I)

33. NPR Texture (II)

34. NPR Texture (III)

35. NPR Texture (IV)

36. NPR Texture (V)

37. NPR Texture (VI)

38. 2+D NPR Rendering (I)

39. 2+D NPR Rendering (II)

40. 2+D NPR Rendering (III)

41. 3. RENDERING FIELDS • Direct Rendering of Fields • Discrete Sampling • Rendering Effects

42. Rendering Complexity Complexity Level of Direct Rendering Predefined Scalar Fields Single Regular Volume Tetrahedral Mesh Arbitrary Explicit Fields Constructive Reps Non-spatial Domain Parametric Fields

43. Ray Marching

44. Issues in Discrete Sampling • Relationships among density, opacity and sampling distance; • Rendering amorphous phenomena with reflection, refraction and shadows; • Mathematical fields suit software better than hardware.

45. Direct Surface Rendering

46. Multiple Isosurfaces

47. Direct Volume Rendering

48. Volume vs. Surface

49. density sampled opacities sampling distance sampled colours Volume Rendering Integral Consistent Sampling (I) accumulated colour

50.   Consistent Sampling (II)