- Visualization is the graphical presentation of information, with the goal of providing the viewer with a qualitative understanding of the information contents.
- Information may be data, processes, relations, or concepts.
- Graphical presentation may entail manipulation of graphical entities (points, lines, shapes, images, text) and attributes (color, size, position, shape).
- Understanding may involve detection, measurement, and comparison, and is enhanced via interactive techniques and providing the information from multiple views and with multiple techniques.

- Numeric, symbolic (or mix)
- Scalar, vector, or complex structure
- Various units
- Discrete or continuous
- Spatial, quantity, category, temporal, relational, structural
- Accurate or approximate
- Dense or sparce
- Ordered or non-ordered
- Disjoint or overlapping
- Binary, enumerated, multilevel
- Independent or dependent
- Multidimensional
- Single or multiple sets
- May have similarity or distance metric
- May have intuitive graphical representation (e.g. temperature with color)
- Has semantics which may be crucial in graphical consideration

f(x, y) -> (t, p)

f1(x, y) -> t, f2(x, y) -> p

f3(x, y, t) -> 0 or 1, f4(x, y, p) -> 0 or 1

f5(x, y, t, p) -> 0 or 1

The key is that the mapping must go to a single value (or vector), e.g. f(x, t) -> 0 or more values of elements with position x and temp t, therefore losing information (e.g. hidden surfaces in projection). This is OK for statistics (e.g. histogram).

- Entity: point, line, polyline, glyph, surface, solid, image, text
- Attribute: color/intensity, location, style, size, relative position/motion

- Different viewers perceive different graphical/spatial/color in different degrees
- Context varies our sensitivity
- According to one researcher (Cleveland), in increasing inaccuracy
- Position along a common scale
- Position along identical, non-aligned scales
- Length
- Angle/slope
- Area
- Volume
- Hue/saturation/intensity (informally derived)

- Weber's law - detection is proportional to percent change, not scale
- Stevens' law - perceived scale is proportional to a power of the actual scale. power is .9 - 1.1 for length, .6 - .9 for area, .5 - .8 for volume

- Effective: the viewer gets it (ease of interpretation)
- Accurate: sufficient for correct quantitative evaluation. Lie factor = size of visual effect/size of data effect
- Efficient: minimize data-ink ratio and chart-junk, show data, maximize data-ink ratio, brase non-data-ink, brase redundant data-ink
- Aesthetics: must not offend viewer's senses (e.g. moire patterns)
- Adaptable: can adjust to serve multiple needs

- Examine cardinality of dimension with detectible variations in graphics (see below for evaluation under human perception)
- Use scaling and offset to fit in range
- Use derived values (residuals, logs) to emphasize changes
- Use projections, other combinations, to compress information, get statistics
- Use random jiggling to separate overlaps
- Use multiple views to handle hidden relations, high dimensions
- Use effective grids, keys and labels to aid understanding

- Dynamically adjust mapping
- Tour data by varying views
- Labeling to get original data
- Deleting to eliminate clutter
- Brushing/Highlighting to see correspondence in multiple views
- Zooming to focus attention
- Panning to explore neighborhoods

- Charts: bar or pie
- Graphs: good for structure, relationships
- Plots: 1- to n-dimensional
- Maps: one of most effective
- Images: use color/intensity instead of distance (surfaces)
- 3-D surfaces and solids
- isosurfaces/slices
- translucency
- stereopsis
- animation