Plotting Realizations of Spatiotemporal Data

Both (1.) time steps, (2.) processing conditions, and (4.) number of atoms are metadata on a spatial visualization. That is to say that information will be provided as context to the visualization in the form of a title, comment, or other annotation.

In the case of (4.), I have embedded the number of atoms and chains as front-matter.

A typical spatiotemporal visualization will plot the field values or local states at the spatial positions they are sampled at.

The above visualization illustrates the evolution of surface curvature (illustrated by the colormap) sampled at non-uniform positions in space. Each subplot is illustrating the spatial variation of a local state at a place in time under a set of experiment conditions (ie. control parameters, boundary conditions).

Plotting Spatial Datasets

When plotting 3-D datasets, usually the colors annotate local state or field variables these are sampled at positions in space. The spatial sampling is either uniform, voxel data or non-uniform data.

Plotting voxel data and non-uniformally sampled data require two different procedures.

Plotting Voxel Data

Voxel data has a uniformly-gridded spatial domain and each value in a voxel is a numerical or categorical local state or response variable.

3-D Contour Plots in Matlab

  • Vol3d is a great visualization tool on MathLab Central.
  • SliceoMatic serves up interactive visualizations with controls on the slices plotted, isosurfaces, and transparencies.

Plotting Non-uniformly gridded data

This project sits here.

Scatter3 is an example of Matlab function to make interactive 3-D scatter plots where the user can control the size and color of the scatter points. Size and color allow up to 2 local states or responses to be explored at one time.

Plotting Temporal Derivatives of SpatioTemporal Data

Temporal derivatives are different than spatial derivatives. Spatial derivatives can change in time.

Voxel Data Use Case

Assume $A1$ and $A2$ are 3-D arrays sampled at times $t1$ and $t2$, respectively. A simple element-wise numerical derivative can be computed producing $dA$:

$i$ indicates pixel values. $dA$ is a new 3-D array that can be visualized using a 3-D contour plot (see above).

The spatial domain is defined by the index notation in your voxel array. The values in each voxel are numerical or categorical local state or response values.

Non-uniformly Gridded Data Use Case

This is the case for the polymer datasets. There may be a scenario were you grid the voxel data and the Voxel case will apply.

Assume $B1$ and $B2$ are Nx4 arrays sampled at times $t1$ and $t2$, respectively. N is the number spatial positions sampled with the first 3 columns are x,y, and z positions, respectively, with the last column providing numerical or categorical local state or response values.

Requiring each row in $B1$ and $B2$ correspond to the same tracking point. Someone help me say this better please.

$i$ indicates each array index. $dB$ is a new Nx4 where the first 3 columns are changes x,y, and z positions, respectively, with the last column providing change in a numerical local state or response values.

A quiver plot is useful to visualize this type of data. One could discretize the local state space and plot different colored quivers corresponding to the magnitude in the change of the local state and the length of the quivers illustrate the change in position. Categorical fields are likely independent of time.

Plotting Considerations for Multi-Phase Polymer Datasets

This flickr set has example visualizations of these polymer datasets. Each 3-D scatter plot has scatter points with colors overlain that indicate the chain to which each point belongs. In polymer datasets, there is a connectivity of individual atoms. These maybe be important to add to a visualization.