Saturday, February 5, 2011

The Strain Ellipse and Adobe Illustrator

When you have stretches and orientations for a population of features, you might have a strain ellipse.  Why plot it by hand when you can let Adobe Illustrator do it for you?

Illustrator CS5's Line tool allows you to specify an angle and a length (stretch, in this case).  The line tool uses a slightly different system of orientation than in geology.  360/0 is east, 90 is north, 180 is west, and 270 is south.  So you must keep that in mind when plotting geologic orientations.

First, setup two guides that have an intersection at a convenient location on the artboard; lock your guides.  Use the line tool and snap-click on that intersection.  Define your angle (keeping in mind differences in orientation), and length (stretch).  Do this over and over at the same intersection point until you have exhausted your supply of data.

At this point you may need to copy sets of stretch lines, group them, duplicate, and horizontally or vertically reflect them to get a complete ellipse.  Ensure that their origins snap to your intersection of guides.

Now, use the Ellipse tool and setup a unit circle with radius  S=1 and snap the center of that circle to the intersected guide.  Duplicate the circle and use the shear tool to fit your data; use the scale tool if area cannot be preserved.  If all goes well, you'll end up with Lines of No Finite Extension at the intersection of the unit circle and your ellipse.  Snap drag lines to each intersection to define your fields of lengthening and shortening.

You can then use the incredibly handy Shape builder tool and text tools to clean up your ellipse for others to view.

Remember, to preserve the angular relationships of your resultant strain ellipse when scaling, use the same scaling factor for the horizontal and vertical.  It is really useful to scale so that you can draw (by hand) reasonable tangent lines to your ellipse to find ψ at any geologic orientation.  You could measure this in Illustrator, but I think that it would not be very efficient.

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