Adapted from Min Chen’s Presentation in Dagstuhl Seminar Enriching Volume Modelling with Scalar Fields Min Chen, Andrew S Winter, David Rodgman and Steve Treavett Department of Computer Science University of Wales Swansea Min Chen, Andrew S Winter, David Rodgman and Steve Treavett Department of Computer Science University of Wales Swansea

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

1. THE ROLE OF SCALAR FIELDS

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

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

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

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

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

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

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

2. MODELLING WITH FIELDS n Scope of Volume Modelling n Constructive Volume Geometry n Solid, Hyper- and NPR Textures n Scope of Volume Modelling n Constructive Volume Geometry n Solid, Hyper- and NPR Textures

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

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

Volume Data Types (I) n Spatial, Continuous Specification l Explicit Field Function: F(x, y, z) (Mathematical and Procedural) l Parametric Field Function: F(t 1,t 2,...) n Spatial, Discrete Specification l Discrete Point Set l Regular Dataset (e.g. CT dataset) l Irregular Dataset (e.g. tetrahedral mesh, free-hand ultrasound) l Image and Video n Spatial, Continuous Specification l Explicit Field Function: F(x, y, z) (Mathematical and Procedural) l Parametric Field Function: F(t 1,t 2,...) n Spatial, Discrete Specification l Discrete Point Set l Regular Dataset (e.g. CT dataset) l Irregular Dataset (e.g. tetrahedral mesh, free-hand ultrasound) l Image and Video

Volume Data Types (II) n Non-spatial l Fourier Domain l Wavelet Domain l Compressed Image and Video l Light Field n Non-spatial l Fourier Domain l Wavelet Domain l Compressed Image and Video l Light Field

Volume Data Types (III) High-Level Models Non-Spatial Models Discrete Spatial Models Continuous Spatial Models

Constructive Volume Geometry scene object field ORGBGeKaKdKsNDnRflRfr Constant Volume Dataset Colour-separated image Built-in mathematical scalar field Procedural scalar field plus various mappings Txt...

CVG: Scalar Field (I) A spatial object is a tuple o = (O, A 1, A 2, …, A k ) of scalar fields defined in E 3, including an opacity field O: E 3  [0,1] specifying the visibility of every point in E 3 and possibly other attribute fields, A 1, A 2, …, A k : E 3  [0,1], k>0. O: hyperbolic paraboloid R: cylindrical field G: cylindrical field B: cylindrical field

CVG: Scalar Fields (II) O: sphere R: noise G: constant B: constant O: torus R: dataset G: constant B: dataset O: hyperbolic paraboloid R, G, B: constant Geo: hyperbolic paraboloid + noise

Scalar Fields (III) O: implicit function R, G, B: linear functions Geo: implicit function O: implicit function R, G, B: linear functions Geo: hyperbolic paraboloid

CVG: Data Representation ( o 1, o 2 ) o1o1 o1o1 o2o2 o2o2 composite volume object convex volume object 1

CVG: 4 Colour Channel Model operations on scalars operations on scalar fields operations on spatial objects ( o 1, o 2 ) = ( MAX (O 1, O 2 ), SELECT (O 1, R 1, O 2, R 2 ), SELECT O 1, G 1, O 2, G 2 ), SELECT (O 1, B 1, O 2, B 2 ) ) max(s 1, s 2 ) = s 1 s 1  s 2 s 2 s 1 < s 2 { { select(s 1, t 1, s 2, t 2 ) = t 1 s 1  s 2 t 2 s 1 < s 2 { {......

CVG: Operation (I) o 1 =(O 1, R 1, G 1, B 1 ) o 2 =(O 2, R 2, G 2, B 2 ) ( o 1, o 2 )

CVG: Operation (II) ( o 1, o 2 ) ( o 2, o 1 )

CVG: Interior & Real Domain

CVG: Solid and Fuzzy Objects

CVG: Image and Texture (I)

CVG: Image and Texture (II)

CVG: Non-Photorealistic Rendering

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

Solid Texture and Hypertexture

NPR Texture (I)

NPR Texture (II)

NPR Texture (III)

NPR Texture (IV)

NPR Texture (V)

NPR Texture (VI)

2 + D NPR Rendering (I)

2 + D NPR Rendering (II)

2 + D NPR Rendering (III)

3. RENDERING FIELDS n Direct Rendering of Fields n Discrete Sampling n Rendering Effects n Direct Rendering of Fields n Discrete Sampling n Rendering Effects

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

Ray Marching

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

Direct Surface Rendering

Multiple Isosurfaces

Direct Volume Rendering

Volume vs. Surface

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

Consistent Sampling (II)    

Consistent Sampling (III) 0.5:0.50.1: : : : :0.5 2

Shadow

Reflection

Refraction (I) Surface Ray Tracer (POV-Ray) Volume Ray Tracer (vlib)

Refraction (II) With normals estimated from raw data With spherical normals

4. SUMMARY

Volume Data Types High-Level Models Non-Spatial Models Discrete Spatial Models Continuous Spatial Models Scalar Fields

Vlib: Volume Graphics API

THANKS/DANK