SciVis Overview

Understanding Data Organization
(Grids, Lattices and Meshes)

These definitions provide a useful conceptual framework for discussing data organization. Be aware that some visualization packages have their own terminology or even creatively misuse the standard terminology.

Input data can be described by the following components:

Grid

The set of coordinates at which data values can be located. The points can be uniformly or non-uniformly spaced.

Topology

The geometrical relationship between successive locations in the grid. This is usually expressed as a dimension.

Mesh or Lattice

A mesh (or alternatively,"lattice") is defined by its Grid and Topology. A mesh can be thought of as the domain of the data. Here is an example of a mesh description: "uniform 2-dimensional lattice in the plane". It is shown below. In most contexts, lattice is equivalent to Mesh, but can also mean Mesh+Data. (This term is also used generically in Numerical Algorithms Group Explorer to refer to data structures.)

Data

The actual values located at the points in the grid. The "range".

Mapping Computational Space to Coordinate Space:

There are two kinds of spaces that describe your data organization, computational space and coordinate space. Computational space is the parameter space used to calculate or collect the data. Coordinate space can be thought of as a mapping to "physical space". Coordinate and computational space do not have to have the same dimensionality, as some of the examples below will show.

Examples:

Uniform 2D Lattice in the Plane:

Uniform distance between any coordinates along an axis, and is the same for all axes.

A 2D Perimeter Lattice in the Plane:

Coordinates still lie on intersections of orthogonal grid-lines, but there distance between any two grid-lines along an axis varies.

A 2D Curvilinear Lattice in the Plane:

Also known as Curvilinear or Non-uniform. Points can exist anywhere in space.

Here are some examples that sometimes confuse people:

A 1D Curvilinear Lattice in 3-space:

The grid is the set of points in R^3 space, but is parameterized by only one value, say t. Although each coordinate in the grid lives in R^3, the next coordinate is obtained by some f(t+1). Consider this example, a pilot flies through a storm cloud collecting water density data at distinct time intervals. She records the density at her current location. Her location at time t defines the points in the grid, and each successive point in the grid can be obtained by f(t+dt), not by incrementing x,y, and z.

A 2D Vector field

Each point in this 2D field has a 2D vector associated with it (the data) instead of a scalar.