Computer Graphics & Multimedia (AD-503 (B)) Unit 4 Notes

How unit 4 is examined

This unit covers scientific and information visualization (scalar, volume, vector, time-varying, high-dimensional and non-spatial data), evaluation, and basic animation; no topic has been asked recently, so learn definitions and key points.

Visualization of 2D/3D scalar fields: color mapping, ISO surfaces

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Definition. A scalar field assigns one number $f(x,y)$ or $f(x,y,z)$ to every point, such as temperature or pressure; ==color mapping paints each scalar value with a colour and an isosurface joins all points where $f = c$ for a chosen constant $c$.==

Key points.

A colour map (transfer table) converts each scalar value into an RGB colour, for example blue for low and red for high values.
A rainbow map shows detail well, but a perceptually uniform single-hue map is safer because equal data steps look like equal colour steps.
In 2D the isosurface becomes an isoline (contour), as on a weather map.
In 3D an isosurface is extracted with Marching Cubes, which checks each cell's corners against $c$ and places triangles where the value crosses it.

Direct volume data rendering: ray-casting, transfer functions, segmentation

Definition. Direct volume rendering displays a 3D grid of voxels directly, without extracting surfaces, by accumulating colour and opacity along viewing rays.

Key points.

In ray-casting one ray is sent from each pixel through the volume, and samples along it are composited front to back.
A transfer function maps each voxel value to colour and opacity, so it decides which tissues or materials are visible.
Compositing uses $C = C + (1-\alpha)\,\alpha_i C_i$ and stops early once the accumulated opacity is near 1.
Segmentation labels voxels into regions (organs, bone) by thresholding or region growing, so each region can get its own transfer function.

Visualization of Vector fields and flow data

Definition. A vector field assigns a vector (magnitude and direction) to each point, as in wind or fluid velocity, and flow visualization shows how the field moves.

Key points.

Arrow (hedgehog) glyphs show direction and magnitude at sample points but clutter dense fields.
A streamline is a curve tangent to the velocity at every point, found by integrating $\dfrac{d\mathbf{x}}{dt} = \mathbf{v}(\mathbf{x})$ with Euler or Runge-Kutta steps.
For steady flow, streamlines, pathlines and streaklines coincide; for unsteady flow they differ.
Line Integral Convolution (LIC) textures and colour-coded speed give a dense picture of the whole field.

Time-varying data

Definition. Time-varying data is a dataset whose values change over time, so each time step is a separate scalar, vector or volume field.

Key points.

It can be shown as an animation that plays the time steps in order, which is intuitive but relies on memory to compare frames.
Small multiples or a space-time view lay several time steps side by side for direct comparison.
Data volume is huge, so compression, caching and feature tracking (following a vortex or front across steps) are used.
Interaction with a time slider and a fixed colour map across all frames keeps the comparison honest.

High-dimensional data: dimension reduction, parallel coordinates

Definition. High-dimensional data has many attributes per record, more than a 2D or 3D screen can show directly.

Key points.

Dimension reduction projects the data to 2D or 3D while keeping structure, using PCA (linear, keeps maximum variance), MDS or t-SNE.
In parallel coordinates each attribute is a vertical axis and each record is a polyline crossing all axes.
Clusters appear as bundles of similar lines, and correlation appears as parallel or crossing lines between neighbouring axes.
Scatter-plot matrices and glyphs are alternatives, but parallel coordinates scale better with many attributes.

Non-spatial data: multi-variate, tree/graph structured, text; perceptual and cognitive foundations

Definition. Non-spatial data has no natural position in space, such as tables, hierarchies, networks and documents, so the layout must be chosen by the designer.

Key points.

Multi-variate tables use bar charts, scatter plots, heat maps and glyphs.
Trees are drawn as node-link diagrams, treemaps (nested rectangles sized by value) or sunburst charts.
Graphs use force-directed layouts, where edges act as springs and nodes repel, or matrix views for dense graphs.
Text uses word clouds, keyword-in-context and topic maps.
Perceptual foundations: position is judged most accurately, then length, angle, area and colour, and pre-attentive features (colour, size, orientation) are noticed instantly.

Evaluation of visualization methods, Applications of visualization

Definition. Evaluation checks whether a visualization is effective, meaning accurate, efficient and useful for its users' tasks.

Key points.

Methods include user studies measuring task time and error, expert heuristic review, and questionnaires on satisfaction.
Criteria are expressiveness (shows all and only the data), effectiveness, and scalability with data size.
Applications include medical imaging (CT and MRI), weather and climate, computational fluid dynamics, geology and oil exploration, and business dashboards.
Other applications are finance, network monitoring, bioinformatics and education.

Basic Animation Techniques like traditional, key framing

Definition. Animation creates the illusion of motion by showing a sequence of still images quickly, usually 24 or more frames per second.

Key points.

Traditional animation has artists draw every frame by hand on transparent cels, with senior artists drawing keyframes and assistants drawing in-betweens.
In computer keyframing the animator specifies key poses at chosen times and the computer interpolates the frames between them.
Interpolation is usually linear, $p(t) = (1-t)\,p_0 + t\,p_1$, or a spline for smooth motion.
Keyframing gives control with far less work than drawing every frame.

Last-minute revision

A scalar field has one value per point; an isosurface is the set where $f = c$; the 2D form is an isoline.
Marching Cubes extracts isosurfaces cell by cell.
Direct volume rendering casts rays through voxels and composites colour and opacity using a transfer function.
Segmentation splits a volume into labelled regions.
A streamline is tangent to the velocity field and is found by integrating $d\mathbf{x}/dt = \mathbf{v}$.
Time-varying data is shown by animation, small multiples and feature tracking.
PCA is linear dimension reduction; parallel coordinates draw each record as a polyline across attribute axes.
Trees: node-link, treemap; graphs: force-directed layout.
Position is the most accurately judged visual channel.
Keyframing: the animator sets key poses and the computer creates in-betweens.

Memory hooks

ISO = "I Set One value": one constant, one surface.
Ray-casting: "Ray, Colour, Opacity, Add" from front to back.
Streamline = the path a leaf takes on a steady stream.
PCA = "Pack Countless Attributes" into two.
Keyframe = the artist's pose, in-between = the computer's job.

Coverage checklist

Visualization of 2D/3D scalar fields: color mapping, ISO surfaces (no past questions)
Direct volume data rendering: ray-casting, transfer functions, segmentation (no past questions)
Visualization of Vector fields and flow data (no past questions)
Time-varying data (no past questions)
High-dimensional data: dimension reduction, parallel coordinates (no past questions)
Non-spatial data: multi-variate, tree/graph structured, text Perceptual and cognitive foundations (no past questions)
Evaluation of visualization methods, Applications of visualization (no past questions)
Basic Animation Techniques like traditional, key framing (no past questions)

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Computer Graphics & Multimedia (AD-503 (B)) - Unit 4 Short Notes

How unit 4 is examined

Visualization of 2D/3D scalar fields: color mapping, ISO surfaces

Direct volume data rendering: ray-casting, transfer functions, segmentation

Visualization of Vector fields and flow data

Time-varying data

High-dimensional data: dimension reduction, parallel coordinates

Non-spatial data: multi-variate, tree/graph structured, text; perceptual and cognitive foundations

Evaluation of visualization methods, Applications of visualization

Basic Animation Techniques like traditional, key framing

Last-minute revision

Memory hooks

Coverage checklist