Customizing arrowheads in VectorPlot3D[ ]?

Questions
1

  1. Please explain or point me to documentation about how Graphics3D and Directive work with plotting software like VectorPlot3D. For example, I want smaller arrowheads in the attached notebook so I can see what’s happening. I’m still looking and experimenting but haven’t found documentation that helps, and experimentation has been unsuccessful.

  2. Is there graphic that creates a 3D vector field with a single arow vector that can be moved around either by entering coordinates or with a manipulator or both?

  3. I suspect there are more elegant ways to define the attached notebook. Suggestions would be appreciated.

Math 4145 HW 4 Prob 2 vector field.nb (124 KB)

2

You may have a look at my old package CurvesGraphics6 . Much of it has been gradually superseded by built-in functionality, but not everything yet. PhasePlot may help for your problem.

3

Wow, Gianluca! Thanks. I just did some preliminary testing with it. It looks sensational. One of your examples is exactly what I want to do. And some of the others are inspirational. It seems to work okay with the current version of Mathematica.

I have no experience with packages. I’m really new at Mathematica. I appreciate the instructions in the first page of your notebook. I’m still trying to devise a best practice for controlling kernels and managing notebooks.