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Visualization

The Ohio State UniversityThe Ohio State University

CSE 694L Roger Crawfis

3/26/2005 R. Crawfis, Ohio State Univ. 2

Introduction

Getting acquainted - teamsCurrent studies or majorHometownA interesting data problem


Outline

Scientific VisualizationData Topologies and Data Sources1D and 2D Visualization AlgorithmsOverview of 3D Visualization techniques

Iso-contour surfacesVolume Rendering

Transfer functions and segmentation (2D)Flow Visualization Algorithms (2D)


Outline (con’t)

Volume RenderingOptical ModelsAlgorithmsTransfer Functions

Global Vector Field VisualizationVirtual Environments

The CAVEData or Information Visualization

Overview of perceptual issuesBrushingFocus + contextSuccesses


What is Visualization?

Understanding of dataInsight into informationPresentation and sharing of insights.


Data Sources

Computational ScienceData Acquisition / ImagingHistorical ObservationSurvey, Census, etc.


Data Topologies - Structured

Cartesianx j+1 = xi + ∆

Regular or Uniformx j+1 = xi + ∆x

Rectilinear or Perimeterx j+1 = x(i)


Data Topologies - Structured

Curvilinearx j+1 = x(i,j)y j+1 = y(i,j)

Curves may intersect in i or jCurves may not cross in i or j

i=0

i=3

i=0j=1


Data Topologies - Unstructured

Unstructured or cell data or finite-element data

Tetrahedral



Hexahedral


Finite-element zoo



New Data Topologies

Improved data topologies offer huge potential for savings in computational scienceHierarchical models are becoming more common


New Data Topologies

HierarchicalMulti-Block CurvilinearN-sided Polyhedron where n>6Multi-Grid or Adaptive Mesh Refinement


Working with data

Reconstruction is criticalUseful Image Processing operations

HistogramData mappersRegion of interest selectionEdge detectionNoise removal or blurring

1D and 2D Visualization Techniques

CSE 694L


1D Visualization

y = f(x)Line ChartsCurve FittingSmoothing or Approximation

Sin(x)

-1.5

-1

-0.5

0

0.5

1

1.5

x

y


1D Visualization

Non-cartesioncoordinate systems

Sin(x)

-1

-0.5

0

0.5

1


Basic 2D Visualizations

Scalar Data on a Regular GridSurface plots(2 D graphics)


2D Visualizations

Contour Lines - f(x,y) = constant


2D Visualizations

Psuedo Coloring


2D Computer Graphics

Image formats and pixel limitationsColor Tables

grey-scalehot to coldperceptual


Transfer Functions

Besides the basics, most tools allow you to define your own color mappings.


2D Visualization

Vector FieldsHedgehogsStreamlines


1D Visualization

Vector?


2D Contouring

Continuous f(x,y)Use steepest decent to find zero crossing (root) of the function f(x,y)-cFollow contour from this seed point until we reach a boundary or loop back.Direction close to ∇f ⊗ zProblems?


2D Contouring

Discrete DataAssume the Mean Value ThereomAssume monoticity?

1D Analogy5 Points

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

3

3.5


2D Contouring

Given a quadrilateral f(x,y) = 0.5

0.0

0.0 0.0

1.0 0.0

0.0 0.0

1.0

>0.5

<0.5

Three-dimensional Visualization Techniques

CSE 694L


Visualization Algorithms

2D Slice planes in 3D


2D Slice Planes

Orthogonal to a coordinate axisUniform Grids => image

ArbitrarySpecify the normal and a pointProduces a 2D unstructured grid


2D Slice Planes

Mesh with colors at vertices128x128x128 volume can produce over 50,000 triangles.

Mesh with 2D texture coordinatesVery slow if no hardware supportMore precise transitions

Mesh with 3D texture coordinates


2D Flip book of slices

Rather than view the 2D slice in 3D, rapidly play a sequence of orthogonal slice planes in a movie loop.Sometimes difficult to build a complete mental model.


3D Visualizations

Point plotsAnimation can bring out the surface or pattern (MacSpin)Depth Cueing aids in the depth perception.


3D Visualizations

Spheres or cubes dispersed throughout the volume

color-codedoptional shape-controlled.


3D Visualization

Iso-contour surfaces


3D Visualization

Can add information about an additional variableHere, two additional variables control the color.


3D Visualization

Volume Rendering


3D Visualization


Material Classification

Drebin, Carpenter and HanrahanMaterial Probabilities

LevoyContour surfaces

MRI dataSkin versus Brain

Using Texture mapping


Transfer Functions

Maps raw voxel value into presentable entities: color, intensity, opacity...

Raw-data ⇒ material (R, G, B, α, Ka, Kd, Ks,...).Material ⇒ shaded material.

High gradient in the data values detects a surface and is used as a measure of its orientation.


3D Visualization

Volume Rendering can mimic contouring.Use a transfer function with an impulse at the contour level.

Getting acquainted - teams Current studies or major ...crawfis.3/cis694L/... · 3D...

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