Adapted from Min Chen’s Presentation in Dagstuhl Seminar 00211 Enriching Volume Modelling with...

Adapted from Min Chen’s Presentation in

Dagstuhl Seminar 00211

Enriching Volume Modelling with

Scalar Fields

Adapted from Min Chen’s Presentation in

Dagstuhl Seminar 00211

Enriching Volume Modelling with

Scalar Fields

Min Chen, Andrew S Winter,David Rodgman and Steve Treavett

Department of Computer ScienceUniversity of Wales Swansea

[email protected]

Min Chen, Andrew S Winter,David Rodgman and Steve Treavett

Department of Computer ScienceUniversity of Wales Swansea

[email protected]

CONTENTSCONTENTS

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

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

1. THE ROLE OF SCALAR FIELDS1. THE ROLE OF SCALAR FIELDS

“Field” in Surface Graphics (I)“Field” in Surface Graphics (I)

ContinuousSurface Reps.

e.g. F(p) = 0

ContinuousSurface Reps.

e.g. F(p) = 0

DiscreteSurface Reps.

e.g. mesh


e.g. meshProjectionProjection

RayCasting

RayCasting

DiscreteField Reps.

e.g. S.O.E.

DiscreteField Reps.

e.g. S.O.E.

ContinuousField Reps.

e.g. F(p)


e.g. F(p)

“Field” in Surface Graphics (II)“Field” in Surface Graphics (II)

Spatial-Occupancy Enumeration Implicit Surfaces Solid Textures Hypertextures Free Form Deformation Gaseous Phenomena (e.g. clouds) Water

Spatial-Occupancy Enumeration Implicit Surfaces Solid Textures Hypertextures Free Form Deformation Gaseous Phenomena (e.g. clouds) Water

“Fields” in Visualisation (I)“Fields” in Visualisation (I)


e.g. mesh


e.g. meshProjectionProjection

RayCasting

RayCasting

DiscreteField Reps.

e.g. volume

DiscreteField Reps.

e.g. volume


e.g. F(p)


e.g. F(p)

UnderlyingConcept

UnderlyingConcept

“Fields” in Visualisation (II)“Fields” in Visualisation (II)

Ray Casting Pipelinefor Volume RenderingRay Casting Pipelinefor Volume Rendering

“Fields” in Volume Graphics (I)“Fields” in Volume Graphics (I)

ProjectionProjection

RayCasting

RayCasting

DiscreteField Reps.

e.g. volume

DiscreteField Reps.

e.g. volume


e.g. F(p)


e.g. F(p)

“Fields” in Volume Graphics (II)“Fields” in Volume Graphics (II)

Discrete FieldSpecification: MRI and CT Datasets, Image, Video

Continuous FieldSpecification: Cylinders, cuboids (for difference operations)

Discrete FieldSpecification: MRI and CT Datasets, Image, Video

Continuous FieldSpecification: Cylinders, cuboids (for difference operations)

MotivationMotivation

To match surface graphics in most aspects

To supersede surface graphics in some aspects

To feed the techniques back into visualisation

To match surface graphics in most aspects

To supersede surface graphics in some aspects

To feed the techniques back into visualisation

2. MODELLING WITH FIELDS2. MODELLING WITH FIELDS

Scope of Volume Modelling Constructive Volume Geometry Solid, Hyper- and

NPR Textures

Scope of Volume Modelling Constructive Volume Geometry Solid, Hyper- and

NPR Textures

Scope of Volume Modelling (I)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.

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

Scope of Volume Modelling (II)Scope of Volume Modelling (II)

Volume Data Types Scenes, Objects, Attributes Constructive Specification Heterogeneous Object Interior Amorphous Phenomena Software Tools

Volume Data Types Scenes, Objects, Attributes Constructive Specification Heterogeneous Object Interior Amorphous Phenomena Software Tools

Process

Generalisation

Input

Volume Data Types (I)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

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

Volume Data Types (II)Volume Data Types (II)

Non-spatial Fourier Domain Wavelet Domain Compressed Image and Video Light Field

Non-spatial Fourier Domain Wavelet Domain Compressed Image and Video Light Field

Volume Data Types (III)Volume Data Types (III)

High-LevelModels

High-LevelModels

Non-SpatialModels

Non-SpatialModels

DiscreteSpatial Models


ContinuousSpatial ModelsContinuous

Spatial Models

Constructive Volume GeometryConstructive Volume Geometry

scene

object object object......

field O R G B Ge Ka Kd Ks N Dn Rfl Rfr

• Constant• Volume Dataset• Colour-separated image

• Built-in mathematical scalar field• Procedural scalar field• plus various mappings

Txt ...

CVG: Scalar Field (I)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.

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

CVG: Scalar Fields (II)CVG: Scalar Fields (II)

O: sphereR: noiseG: constantB: constant

O: torusR: datasetG: constantB: dataset

O: hyperbolic paraboloid R, G, B: constantGeo: hyperbolic paraboloid + noise

Scalar Fields (III)Scalar Fields (III)

O: implicit function R, G, B: linear functionsGeo: implicit function

O: implicit function R, G, B: linear functionsGeo: hyperbolic paraboloid

CVG: Data RepresentationCVG: Data Representation

(o1, o2)(o1, o2)

o1o1 o2o2

composite volume objectcomposite volume object

convex volume object




1

CVG: 4 Colour Channel ModelCVG: 4 Colour Channel Model

operations on scalarsoperations on scalars

operations on scalar

fields

operations on scalar

fields

operations on spatial

objects

operations on spatial

objects

(o1, o2) = ((o1, o2) = ( MAX(O1, O2),SELECT(O1, R1, O2, R2),SELECT O1, G1, O2, G2),SELECT(O1, B1, O2, B2) )

MAX(O1, O2),SELECT(O1, R1, O2, R2),SELECT O1, G1, O2, G2),SELECT(O1, B1, O2, B2) )

max(s1, s2) = max(s1, s2) = s1 s1 s2

s2 s1 < s2

s1 s1 s2

s2 s1 < s2{{

select(s1, t1, s2, t2) = select(s1, t1, s2, t2) = t1 s1 s2

t2 s1 < s2

t1 s1 s2

t2 s1 < s2{{

............

CVG: Operation (I)CVG: Operation (I)

o1=(O1, R1, G1, B1)o1=(O1, R1, G1, B1)

o2=(O2, R2, G2, B2)o2=(O2, R2, G2, B2)

(o1, o2)(o1, o2)

CVG: Operation (II)CVG: Operation (II)

(o1, o2)(o1, o2)

(o1, o2)(o1, o2)

(o1, o2)(o1, o2)

(o2, o1)(o2, o1)

CVG: Interior & Real DomainCVG: Interior & Real Domain

CVG: Solid and Fuzzy Objects CVG: Solid and Fuzzy Objects

CVG: Image and Texture (I)CVG: Image and Texture (I)

CVG: Image and Texture (II)CVG: Image and Texture (II)

CVG: Non-Photorealistic RenderingCVG: Non-Photorealistic Rendering

Solid, Hyper- and NPR TexturesSolid, 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

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

Solid Texture and HypertextureSolid Texture and Hypertexture

NPR Texture (I)NPR Texture (I)

NPR Texture (II)NPR Texture (II)

NPR Texture (III)NPR Texture (III)

NPR Texture (IV)NPR Texture (IV)

NPR Texture (V)NPR Texture (V)

NPR Texture (VI)NPR Texture (VI)

2+D NPR Rendering (I)2+D NPR Rendering (I)

2+D NPR Rendering (II)2+D NPR Rendering (II)

2+D NPR Rendering (III)2+D NPR Rendering (III)

3. RENDERING FIELDS3. RENDERING FIELDS

Direct Rendering of Fields Discrete Sampling Rendering Effects

Direct Rendering of Fields Discrete Sampling Rendering Effects

Rendering ComplexityRendering ComplexityComplexity Level

of Direct Rendering

Single Regular VolumeSingle Regular Volume

Tetrahedral MeshTetrahedral Mesh

Predefined Scalar Fields

Predefined Scalar Fields

Arbitrary Explicit FieldsArbitrary Explicit Fields

Parametric FieldsParametric Fields

Constructive RepsConstructive Reps

Non-spatial DomainNon-spatial Domain

Ray MarchingRay Marching

Issues in Discrete SamplingIssues 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.

Relationships among density, opacity and sampling distance;

Rendering amorphous phenomena with reflection, refraction and shadows;

Mathematical fields suit software better than hardware.

Direct Surface RenderingDirect Surface Rendering

Multiple IsosurfacesMultiple Isosurfaces

Direct Volume RenderingDirect Volume Rendering

Volume vs. SurfaceVolume vs. Surface

Consistent Sampling (I)Consistent Sampling (I)

accumulated colour

density

sampled colours

sampled opacities

sampling distance

dueuuC

duuuuCtC

tu

tu

dvv

tu

tusum

uv

tv

1

1

1)()(

Volume Rendering Integral

Consistent Sampling (II)Consistent Sampling (II)

oo 0.10.1

Consistent Sampling (III)Consistent Sampling (III)

0.5:0.5 0.1:0.5

0.005:0.50.01:0.50.05:0.5

1.0:0.5

2

ShadowShadow

ReflectionReflection

Refraction (I)Refraction (I)

Surface Ray Tracer (POV-Ray)

Volume Ray Tracer(vlib)

Refraction (II)Refraction (II)

With normals estimated from raw

data

With spherical normals

4. SUMMARY4. SUMMARY

Volume Data TypesVolume Data Types

High-LevelModels

High-LevelModels

Non-SpatialModels

Non-SpatialModels



ContinuousSpatial ModelsContinuous

Spatial Models

Scalar Fields

Vlib: Volume Graphics APIVlib: Volume Graphics API

http://www.vg.swan.ac.uk/vlib/

THANKS/DANKTHANKS/DANK

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Adapted from Min Chen’s Presentation in Dagstuhl Seminar 00211 Enriching Volume Modelling with...

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