The Visualization Handbook

Overview of Visualization

Classification of Algorithms

Algorithms to transform data can be classified by structure, which means the effect the transformation has on topology, or type, the type of data the algorithm takes as input.

Structural transformations can be classified by how they affect topology, geometry, or attributes of the dataset.

• topology -- the relationship of discreet data samples to each other which are not affected by geometric transformations, for example volume data vs. a finite element mesh
• geometry -- the specification of the topology in space, including point coordinates and interpolation functions
• attributes -- the data points themselves

Given these three classifications of datasets, transformations can be put into one of four categories: Geometric transformations, which only affect geometry but not topology (rotation / scaling), topological transformations, which affect topology but not geometry (this is rare), attribute transformations, which only affect the attribute data, and combined transformations, compositing two or more of the other three categories.

Classification based on the type of input data is also common, under which the possible categories are scalar algorithms, vector algorithms, tensor algorithms, and modeling algorithms. Modeling algorithms refer to those algorithms that generate some sort of indirect representation, such as surface normals, glyphs, or texture data.

Algorithm Notes

• Generality Vs. Efficiency -- In developing algorithms, choices must be made regarding what data types to support. The more data types supported the more general the algorithm, but usually at the cost of performance.
• Algorithms as Filters -- In most visualization packages, algorithms are used as filters to change data into a useful format for visualization. Data objects and filter objects are connected together to produce a desired effect.

Scalar Algorithms

Color Mapping

Color mapping is a very basic way of visualizing scalar data. Scalar values are mapped onto a color lookup table, and a color is assigned to each point. More generally, the color table can be called a transfer function, which maps a scalar value to a color specification.

• Greyscale color tables often provide better structural detail
• A good color table can enhance important features, but it is easy to exaggerate unimportant details

Contouring

Contouring can be an extension of color mapping, where a certain scalar value is identified with a solid line, separating the data into two or more distinct regions. In 3D, contours are called isosurfaces, and can be represented by polygonal meshes.