Change Plot3D, etc., axes orientation and position?

Question

On paper or a blackboard, mathematicians (as opposed to engineers, physicists, etc.) typically draw 3D plots is with:

1. axes origin is at (0, 0, 0) and axes are drawn emanating from there;
2. the positive y-axis points due east, the positive z-axis points due north, and the positive x-axis pointing southwest (as if pointing forward, out of the paper); and
3. the positive ends of these axes have arrowheads (just plain 2D arrowheads, not conical or similar quasi-3D objects.

In other words, the way that's shown in this image from https://en.wikipedia.org/wiki/Three-dimensional_space#/media/File:Coord_planes_color.svg:

What is the best way to arrange this for Plot3D and the family of related functions (ParametricPlot3D, SphericalPlot3D, etc.)?

I'm aware of using options Boxed -> False, AxesOrigin -> {0,0,0}, Axes -> True, which accomplishes (1). But how best accomplish (2) and (3)?

More specifically:

• For (3), is there some better way than the awkward method of using Show to combine the Plot3D with a Graphics3D consisting of three commands such as Arrow[{{0,0,0}, {1,0,0}}]?
• For (2), is there some better way than effecting a geometric transformation on each geometric object created?

Answer 1

I know this question is old, but I stumbled across it and thought I'd post this in case it helps someone in the future. I use something like this:

ViewPoint -> RotationTransform[Pi/2, {0, 0, 1}][{1, -2, 0.85}]