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plotting - VectorScale Explanation


I'm having great difficulty understanding VectorScale. Here are the definitions from the documentation.




With the explicit specification VectorScale -> {unitlen,aratio,sfun} each field vector is constrained to fit in a vector box oriented in the direction of the field, centered at the location of the vector.


The unitlen is given as a fraction of the diagonal of the overall bounding box and is used as a local scale for vector boxes, aratio is the aspect ratio for vector boxes, sfun is a scaling function that determines the width of vector boxes.



I've used it with VectorPlot and have gotten the desired result, but I still just can't understand the above definitions. I've even read some authors saying "don't worry about how this works, but here is how you get a good picture." I just think I need to be a little more ready than that to explain things to my students.


Is it possible to draw a picture, maybe just a few arrows, and show their vector boxes surrounding them? And then explain the numbers used in the VectorScale option and how they relate to the size and shape of the vector boxes?




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