VIS review:
Lecture 1: introduction
 The use of data visualization
Help understand the data.
High performance computing generates vast quantities of data
 The definition of data visualization
Data derived form the observation to reality and simulation to reality is represented as the
form of the images and animation.
 Application
 Visual programming systems
A sequence of simple processing steps; system provides modules implementing simple steps
in a visualization pipeline; connect modules together.
 Web-based visualization
Client-side: java applet
Server-side: run VIS system and return to client as VRML
Lecture 2: reference model and 1D scalar data
 Reference model:
Observation data
Experimental data
images, animation, sound, text
Simulation data
 The visualization process
Step 1: Data enrichment: interpolating (sparse and accurate), or approximating (sparse but in
error) raw data-effectively creating a model
Step 2: mapping: conversion of data into a geometric representation
Step 3: rendering: assigning visual properties to the geometric object and creating an image.
 General classification scheme
F(x): the independent variable x: x= (x1, x2, … xn)
The dependent variable F: F= (F1, F2, … Fm)
The dimension is n, and the dependent variable can be scalar (m=1) or vector (m>1)
Question: What means Ens/v ?
Lecture 2-8: Visualization techniques
 One-dimensional scalar data
1. Nearest neighbor
2. Linear interpolation
X* is between X1 and X2; t= (X*-X1)/(X2- X1), t ~ [0,1]
So f (X*) = (1-t) f1 + t f2  f (X*) = f1 + t (f2 – f1)
3. Piecewise cubic interpolation
Only be used when the slope continuity is needed
The slopes g1 and g2 may be given,
or if not, then estimated: the slopes of adjacent chords, usually arithmetic mean (average) of
Δ1, Δ2. Δ1= (f2-f1)/(x2-x1)
F(x) = c1(x)*f1 + c2(x)*f2 + d1(x)*g1 + d2(x)*g2, where ci(x), di(x) are cubic Hermite basis
functions.
 Harmonic mean (g2): incline to the smaller number, the equation: 1/g2 = 0.5 (1/Δ1 + 1/
Δ2)
e.g. arithmetic mean: (1+11)/2=6; harmonic mean: 0.5 (1 + 1/11) = 6/11 11/6 = 1+5/6
to control the shape of spline
Question: what means “bounds” in 1D scalar interpolation?
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Two-dimensional scalar data
 Contouring regular grid data
1. Nearest neighbor interpolation
2. Bilinear interpolation
Within a unit square (0, 0) and (1, 1)
(i) f (x,0) = (1-x) f00 + x f10
(ii) f (x, 1) = (1-x) f01 + x f11
(iii) f (x, y) = (1-y) f (x, 0) + y f (x, 1)
Formula: f (x, y) = (1-x)(1-y) f 00 + x (1-y) f 10 + y (1-x) f 01 + xy f 11
Tracking contours
3. Saddle point
Opposite vertices same sign, two +ve, two –ve
Calculate saddle point:
Derivative: fx’ = fy’ = 0, max in one direction, min in other
Where: fx’= σf (x, y)/ σx = - (1-y) f00 + (1-y)f10-y f01 + y f11
∴x = (f00-f01)/D; y = (f00-f10)/D; and D = f00 + f11 - f01 -f10
Saddle value = (f00 f11 - f01 f10)/D
F(x, y) =0
Example:
Say: f 00 = -3; f11 = -5 f01 = 10; f10 = 1
Saddle point= 5/19 (the red point)
F(x, y) =0
4. Greater accurate:
The tangent of the arc
Use shoulder point to get the point that the tangent line passes
 Contouring scattered data
Tessellation:
1. Dirichlet tessellation:
Steps: (assume Q is the new point)
a. Determine polygon containing Q-here P3
b. Construct perpendicular bisector of P3Q and find intersection with D3 –this
becomes point of modified tessellation
c. Determine adjacent polygon –here D2
d. Repeat the above two steps until D3 is reached again, or there is no intersection
e. Remove all vertices and edges interior to the new polygon
2. Delaunay tessellation:
Triangulation formed by joining points whose ‘territories’ share a common boundary in
the tessellation.
Its nice property is to avoid long-skinny triangles
‘Empty circle’ property of the Delaunay tessellation: every circle not cover more than
three point.
 Other 2D techniques
1. Interpolation in a triangle
Linear rather than bilinear, can construct linear interpolation f (x, y) = a + bx + cy
2. An alternative for contouring on rectangular grids
Average = (f00 + f11 + f01 + f10)/4 is the value of the geometry center
3. Smooth contouring with bicubic interpolation: too complex
/* 2D  3D */
4. Surface views:
5. Image plots
6. Cross sections:
Fix y, and look at f in terms of just x; and then repeat for different y. simplify the Es2
problem
Question: What is ‘Tracking contours’?
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Three-dimensional scalar data (Volume visualization)
 Surface extraction:
1. Slicing: 3D --> 2D
2. Isosurface: a surface of constant value
 Direct volume rendering:
The volume is modelled as a semi-transparent ‘jelly’, where the colour and opacity of the
jelly varies and reflects the scalar value at any point.
 Isosurface
 Data enrichment
1. Nearest neighbor interpolation
2. Trilinear interpolation
Formula: f (x, y, z) = (1-z) f xy0 + z f xy1
3D --> 28 arrays --> 15 topologically distinct configurations
 Marching cubes algorithm
Step 1: classify the eight vertices relative to the Isosurface value (encode), if the vertex
of cell has greater or less than Isosurface value
Step 2: look up table, which identifies the 15 canonical configuration which means the
basic surface topology
Step 3: inverse linear interpolation along the identified edges will locate the intersection
points
Step 4: the canonical configuration will determine how the pieces of the Isosurface are
created (0, 1, 2, 3 or 4 triangles)
Step 5: pass triangles to renderer for display
 Ambiguities
1. Ambiguities on faces
Similar to 2D ambiguities, be resolved by the saddle point on the face:
Which sub-case is chosen depends on the value of the saddle point on the face
2. Interior ambiguities:
Decided by value at body saddle point: saddle point: fx = fy = fz =0
3. Marching tetrahedral: too much triangles are created--> slowing down the rendering
time
 Isosurface rendering
Generate a triangular mesh surface
In visualization it is enough just to consider diffuse reflection
- This gives a dull effect
- Light is scattered evenly and gives the colour of the surface
Rendering of Isosurface
Key is the estimation of vertex normals for Gouraud shading
1. One possibility is to construct the entire surface, then assign vertex normals as
average of normals of surrounding triangles
2. Surface normal is equal to the gradient vector of f (preferred)
 Volume rendering
A different mapping technique for 3D scalar data, compared to isosufacing.
The volume render pipeline:
Segmentation --> gradient computation --> interpolation --> classification --> shading
--> compositing
 Segmentation: done before the actual rendering to label all the voxel.
 Gradient computation: to find the boundaries between the different materials depended
on the how quickly the data changes.
The boundaries between materials are of key importance
(I)
Calculate αas above
(II)
Scale by gradient of function to highlight boundaries
α* = α|grad f |, grad f = (df/dx, df/dy, df/dz)
Gradient is a 3D vector, f = [x, y, z] the direction indicates the orientation of a structure,
and the magnitude |grad f| tells how quickly data changes.
 Data classification:
1. Opacity transfer function:
Histogram of CT numbersX-ray absorptionsassign materialopacity classification
Constructing the Gel-CT data
Binary segmented data
2. Colour transfer function:
If the classification is done at the vertices, there is a choice:
1. Gouraud-type
2. Phong-type
 Interpolation:
1. Classify-interpolate: classification as pre-processing, smoothing effect obscure
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detail, classification is independent to the viewpoint
The danger of this method: opacity-weighted color interpolation
2. Interpolate-classify: classification within the inner loop of ray casting, get fine detail
Compositing:
Ray casting:
Composite the samples along a ray:
1. Back to front
2. Front to back: advantage is: if the accumulated opacity reaches 1.0, the process will
be stopped. (early ray termination)
The speed up method: maximum intensity projection (MIP)
To the performance rather than accuracy
Texture-based:
Draw from back-to-front
Select slices perpendicular to this direction
Simpler solution-2D texture mapping
- View volume as set of slices parallel to coordinate planes
The speed up method:
1. Shear warp rendering: project front-to-back to get intermediate “sheared object
space”, then warp image
2. Splatting: Fuzzy balls around each voxel
Question:
The third step of marching cubes algorithm?
What means “If the classification is done at the vertices, there is a choice”?
What means the advantages of ray-casting, binary classification, binary decision?
Lecture 9: what makes a good visualization?
The principle includes:
1. Easy to understand—get message across
2. Different things shown
 Time
 Direction/pass time of troops
 Temp
 No. Of soldiers
3. Enable comparison
4. Show causality
5. Display multivariate data
6. Integrate multimedia
7. Show scale explicitly: Good labelling/scale information
8. Preserve quality, relevance, and integrity of the data
Lecture 9-11: visualizing flow:
 Experimental techniques:
The distinction between steady and unsteady (time-dependent) flow
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Experimental techniques (Particle tracing):
1. Time lines: perpendicular to the direction of velocity
Line connecting particles that have been released at the same time
2. Streak line: a line joining the positions, at an instance in time, of all particles that have
been previously released from a seed location. It can be simulated by releasing particles
continuously from the seed locations at each time step.
3. Path line:
The trajectory of a single particle released from one fixed location, seed location.
4. Streamline: a filed line tangent to the velocity field at an instance in time
5. Fixing tufts: the flow past a fixing point
Computer flow visualization:
Scalar techniques:
1. Speed =sqrt (vx2 + vy2 + vz2)
2. Arrows:
Particle traces (particle advection)
Trajectories traced by fluid particles over time
 Steps:
Find cell containing initial position
Determine velocity at current position (interpolation)
Calculate new position (integration)
Find the cell containing new position (point location)
The trace is (x(t), y(t), z(t))
Vx = dx/dt; Vy = dy/dt; Vz = dz/dt;
Ordinary Differential Equations (ODEs): X(0), Y(0), Z(0)
Seed point: initial position (x0, y0, z0)
Simplest method, Euler’s method: dx/dt = (x(t+Δt)-x(t))/Δt=Vx (Ρ(t)), whereΡ(t)=(x, y, z)
∴x(t+Δt) = x(t) +Δt.Vx(Ρ(t)), similarly for y(t) and z(t)  (x1, y1, z1)
The velocity of new position (x1, y1, z1) is calculated by interpolation (bilinear)
 Improving the integrating:
If the Vx* is the velocity of original distinct, average the Vx and Vx* is the better velocity of
distinct, new Vx*.
This is just the 2nd order – the 4th order method is more accurate
Another source of error: interpolation to calculate the velocity of current position
 Rake of seed: points, line, circle even an area.
Streamline
Streamline is everywhere tangential to the flow
To reader streamlines,
- Stream ribbons: as a thin flat ribbon
- Tube:
Stream surface
 Basic approach
Surface has parameters s (streamline) and t (timeline): where: (s, t), 0<s<1; 0<t<N
1. Regularly spaced seed points at t = t0: (si, 0), I=0, 1, …K; si = i/K
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2. Compute each streamline to create points on time lines:
(si, 0), (si, 1),…(si, N), I=0, 1, …K
3. This forms polygonal mesh which can be rendered- but need to allow for dynamic
behavior
 Tiling the surface:
1. Regular tiling (simplest):
2. Greedy tiling: on a highly sheared flow
 Diverging flow
1. Current quadrilateral has width greater than twice its height
2. Near an obstacle
 Converging flow
Two abutting quadrilaterals on adjacent ribbons- if 6 points nearly coplanar and height
greater than combined width
Stream flow visualization:
Streamline and stream surface: better for flow direction
Particle traces: better for flow speed
Unsteady flow visualization
Velocity depends on time
Different types of grid
Curvilinear grids:
Texture-based methods: visualize flow as a texturing effect
 Spot noise:
Aligning the shape of the spot with the direction of flow to give a good visualization effect
In direction of flow, scale to (1+ |v|), |v| = the velocity magnitude
At 90 degrees to flow, scale to 1/(1+|v|)
 Line integral convolution (LIC)
Essence of method is:
- Consider a white noise texture: T(x,y)
- For each pixel, set its intensity as a function (e.g. average) of values of T
along a short streamline segment through the pixel
- This has effect of correlating the resulting pixel values along streamlines,
so a sense of the flow direction is obtained.
Original LIC  oriental LIC to indicate the orientation, by using a sparse texture and a
weighting of samples along streamline
Vector field topology
To visualize the significant features of a flow field
Critical points:
1. Velocity magnitude is zero;
2. Point of repulsion, attraction or a saddle point
3. Streamlines from critical points divide space into regions of similar behavior
Charactering a critical point
Say u: Vx; V: Vy
Eigenvalues of Jacobian matrix: a1 + ib1, a2 + ib2
- Repulsion a1, a2 position
- Attraction a1, a2 negative
- Saddle
a1, a2 opposite signs
- Center
a1, a2 zero
Imaginary part
- No rotation b1, b2 zero
- Rotation
b1, b2 non-zero
Attachments are the start point, and detachment points are end points
* The flow field topology is produced by:
a. identifying the critical points
b. Drawing streamlines from detachment or attachment points and
saddle points… to repulsors and attractors
c. Drawing streamlines to/from critical points that exit boundary
Question:
1. What means numerical techniques for integrating the ODEs?
2. The relation between streak line, streamline and particle trace, same each other?
3. How to select the next point, when tiling the stream surface?
4. What means ‘height’ and ‘width’ in the converging flow?
5. What means Jacobian matrix?
6. What means the ‘curvilinear grids’?
Lecture 12 & 14: VRML and via Web
Web browser has become the universal user interface
1. Presentation of data-publishing visualization
2. Analysis of data- performing visualization
 Publishing visualization (lecture 12)
 VRML
 Coordinate system
 Hierarchical structure: VRML scene graph
 Instance: can be used multiple times
 Anchors: link
 Textures
 Lights
 Viewing
 Making world come active
Sensors and events
1. Sensor is a type of node that generates data within the world
2. Data generated within a node is called an event, which are routed from one node to
another to program behavior
3. Sensor can active an animation by routing event to an animation engine
Sensor: time sensor, proximity sensor-collision detection
 Performing visualization (lecture 14)
 Two distinct application:
1. For the scientist, to gain a visualization of their own data
2. For the general public, to gain a visualization of data published by someone else
 Players:
 User
 Visualization service provider
 Data provider: either the user themselves, or an independent agency, or the visualization
service provider
 Architectures:
 Client-side software and compute
The visualization software is installed on client. User enters data source on form; data
transferred to users with a MIME type that invokes a particular helper application.
1. Data as MIME-type:
Data is of a unique type
Data is downloaded to a Web browser as MIME-type, whereupon the software is
invoked.
2. Script as MIME-type:
More general application
To download over the web not just the data, but also a script to define how the data
should be processed.
 Server-side software and compute
Server provides both software and processing power
User enters data sources, and style of visualization on form  service runs visualization
software and returns picture to use.
The limitation of server-side on form: restrictive interface server-side on Java applet
(group several key into one which is used by client)
How to create a Java applet to control the visualization software:
#1: Take a dataflow network (map)  combine modules with key interface widgets into
a ‘group’ save the resulting map
#2: ibulder:
Input saved map  constructs a Java applet, which replicate the group interface,
plus an HTML wrapper  complier applet  outputs web page with embedded applet
How to use:
User downloads page  enters parameters  submitted to IRIS Explorer map running
on server  VRML returned to browser
 Server software and client compute
User downloads a Java applet from the visualization service; security restriction affect data
input (applet only reads from its own file store (a file on the host which the applet was
loaded)); Data is from two sources: local data, data at a URL. Software is transferred across
the web to the client, rather than being pre-installed.
 Collaborative web-based visualization
Data --> filter --> Map --> Render --> image
Selective share using: master and slave
The visualization is fixed by the parameters entered in the form, so adding an audit facility to
store the form parameters, then a collaborator can pick up from the point reached.
The tree is used to collaborative visualization over the web. The threads represent different
exploration path, every user in the same group sees current tree
- Clicking on the node retrieves a stored form
- New form setting can be stored as new nodes on tree
Lecture 13: high dimensional visualization
Scalar visualization:
- 1D – graphs
- 2D – contouring, surface views
- 3D – isosurfaceing, volume rendering
- 4D – animation a 3D technique or ??
Question: what means hyper slice?
Lecture 13: overview of major systems
 The major systems: AVS, IRIS explorer, IBM Open Visualization Data Explorer, and pV3
The major toolkit: Visualization Toolkit
 IRIS explorer:
 Create own modules, mbuilder tool creates a wrapper around own code
 Computation steering:
Control simulate  visualize  render
 Scripting-Skm
Be driven by GUI, command line interface, which can be grouped as a “script”
Be run in batch mode or by another application
 Distributed computing
Remove the intensive computation or share the result
1. Computation remotely: install explorer on remote machine using ‘Hosts’ or ‘New Host’
menu  give access to librarian for explorer  select module or map as required
2. Render remotely: not require explorer to be installed
Lecture 15: Visualization of very large datasets
Key is to sort cells in advance, according to value, in order to reduce the number of cells which
should be calculated—presorting
 Active cell:
To tell if the Isosurface with threshold T passes through this cell, we must compare minimum
and maximum to T.
 Span space:
Define a 2D space, minimum as x-axis and maximum as y-axis  plot cell as a point in the
space
 2D lattice subdivision of the span space
Cover span space with a 2D lattice, sort cells into ‘buckets’, to identity quickly the active
cells.
The elements are allowed to be of unequal size; the method suitable to use on distributed
system.
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A kd tree: an extension of a binary tree
Slicing:
If the slice is axially aligned
If cell has arbitrary orientation
If data is unstructured
 For axially aligned planes, construct tree using appropriate x/y/z coordinate, similar to
kd tree, to
For arbitrary orientation, apply suitable rotation then construct tree using appropriate
x/y/z coordinate.
Question:
How to use the kd tree?
What means “range based methods form Isosurface” ?
Lecture 16: information Visualization
 Application:
1. Data mining
2. Hierarchies of information
3. Networks of information
 The character of information
1. Typically multivariate, with very large number of variables
2. Not necessarily numeric information
 Geometric Techniques:
 Scatter plot—Ens0
At pairs in 2D scatter plots
Use of a ‘brushing’ can highlight subsets of data
 Parallel coordinate—Ens0
Create k equidistant vertical axes, each corresponding to a variable
Each data item corresponds to a line drawn through point on each axis corresponding to
value of the variable
 Daisy charts
Variables and their values placed around circle
Lines connect the value for one data item
 Iconic techniques
Chernoff faces: encode a variety of variable
 Pixel-based techniques—aim at very large data sets
 Circle segment technique-- Ens1
Each segment represents one variable
 Hierarchical techniques
Visualize data using a hierarchical subdivision of the display area
 Tree maps:
Hierarchical partition of the screen into regions depending on attribute values
 Hyperbolic trees
Popular method of displaying hierarchical structure such as link of web sites
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Graph-based techniques
Suitable for visualization of network type data
- Trade flows
- Communication networks
- Software engineering
 SeeNet:
To understand e-mail traffic
Ignore geography
 Document retrieval
Question:
What means document retrieval?
Terminology:
Underlying
Independent variable
Dependent variable
Say: 假定
Slope
Polynomial
I.e.
Hyperbola
Multivariate
X against Y
Y versus X