Plotting

Nearly everything in texture analysis lives in three dimensions or more, while a page has two. In that broad sense, every figure in MTEX is a projection, and every projection gives up some information. Reading a plot starts with knowing what it preserves and what it hides.

The practical side is easier than that sounds. Apply plot to almost any MTEX variable and it chooses a sensible representation. This works for directions, Miller indices, orientations, pole figures, ODFs, maps, grains, and tensors. This chapter addresses the decisions that follow: plot type, projection, screen alignment, colour, composition, and export.

One pole figure, two projections

A spherical projection maps directions on a sphere to points in a plane. The example below draws the same pole density in two projections. Both panels use the same colour range, so their colours remain comparable.

plottingConvention.default('y↑→x');

cs = crystalSymmetry('432');
odf = unimodalODF(...
  orientation.byEuler(30*degree,50*degree,10*degree,cs),...
  'halfwidth',15*degree);
h = Miller(1,0,0,cs);

newMtexFigure('layout',[1,2])

% equal area: areas are preserved, so densities can be compared by eye
plotPDF(odf,h,'contourf','projection','earea')
mtexTitle('equal area')

nextAxis

% stereographic, also called equal angle: angles are preserved, areas are not
plotPDF(odf,h,'contourf','projection','stereo')
mtexTitle('stereographic')

setColorRange('equal')
mtexColorbar

The panels show the same function, yet the peak has a different size and position on the page. Neither picture is wrong. Only the equal-area panel lets you judge how much material a peak represents from its plotted area. Stereographic areas become increasingly misleading towards the rim. Equal area is therefore the MTEX default and the usual texture convention.

Colour is a choice, not a measurement

A colour bar exposes a numerical colour mapping, while an orientation map can hide that a mapping was chosen. Turning a three-parameter orientation into a colour requires a colour key. Different keys give visibly different maps of identical data. Orientation colours alone do not provide a quantitative orientation value.

The related trap is comparison. Two maps or pole figures with independently chosen colour ranges cannot be compared by eye. The same colour can mean a different number in each plot. Whenever figures belong in one comparison, fix a common range explicitly. The call to setColorRange('equal') above applies one range to both projection panels.

Figures are built up, not produced whole

MTEX figures are assembled one layer at a time. Draw one object, hold the axes, draw the next object on top, and release the axes. Boundaries over a map, crystal directions over an inverse pole figure, and a fitted fibre over its data all follow the same pattern.

plot(ebsd,ebsd.orientations)
hold on
plot(grains.boundary)
hold off

Plot order matters because each new layer can cover the previous layer. Transparency shows how alpha values reveal both layers when an opaque overlay would hide the background.

MTEX manages layout, colour bars, and annotations across all axes in a figure. A pole-figure command that produces seven subplots therefore still arranges them as one figure.

Follow the chapter workflow

Start with Plot Types. It compares scatter plots, contour lines, filled contours, smooth shading, and line plots. Raw measurements usually need a scatter or smooth plot, while a density usually needs contours.

Next, Axes Alignment decides which specimen direction points where on the page. This session-wide setting affects every figure. Check it first when a plot is mirrored or rotated unexpectedly.

Combined Plots and Multiplot show more than one object. The first overlays objects in one axes, while the second places related axes side by side. Annotations then adds colour bars, labels, and marked directions.

Export writes the finished figure. Vector formats keep text and lines sharp. A map of a million pixels is usually better exported as an image, and the page explains where that boundary lies.

Spherical Projections develops the comparison above. It covers equal-area, equal-angle, equal-distance, plain, and three-dimensional views. Legends identifies phases and marker series.

Color Maps develops colour coding and consistent ranges. Contour Plots then shows how to choose, overlay, and label contour levels. Finally, Transparency uses alpha values for overlapping markers, superposed maps, boundaries, and three-dimensional surfaces.

Plot the object you are analysing

The chapter for each object explains what its plots mean. Continue with EBSD, Grains, ODF, or Pole Figures when that is the object being analysed. IPF Maps develops the orientation colour keys introduced above.

References

Next

Continue with Plot Types to choose marks that match sampled data, continuous functions, and the comparison you need to make.