:blink: Kawecki knows about the dark age of CG and all it's horrors!
Yeah I had totally forgotten about these old green or amber colored "graphic" displays. On the other hand I would say the start of vector graphics in relation with computers was with the eraly VG programs and later the Corel stuff that made them somewhat popular.

The holy vector that is used by electronic and CG apps comes from math. A vector is always a vector here, no matter which application or circuit element. There are also vectors in biology but that's a different topic.
The vector itself is nothing more than the expression of how informations are associated.
For example if you move your hand from left to right with 1 m/s, that's an vector applied to your hand. Basically traditional painters were the first who made vector graphics.

As described by the surface integral of vector fields it is possible to express a spheroid the surface is parametrized using a system of curvilinear coordinates.
**For Poser there are only 3 vectors ready for plug&play use. P-Node, N-Node and displacement.
I know, it's horrible boring for like 99.99% to read, but these P and N nodes get used much to seldom.

Description:
A P-vector is a tensor that get it's properties from the linear combinations of the exterior product of tangent vectors of P.**
Would be a lot easier if I could write formulas here or do some sketch, but this crappy editor won't let me be creative.
A tensor is an array that expresses an geometrical entity relative to an set of vectors. Like (1,5,4).
A tensor is of course much more than this, but not for Poser.
Linear combination is just a fancy word...
Let's assume you have scalars (a) and vectors (v). The linear combination would then be:
a1v1+a2v2+...a[n]v[n]. Nothing difficult. a1v1 means a1 MUL v1.

All this happens in an vector space V over the field K - to list the common used letters as we need them now for the exterior product... :lol:

Dunno where to start.
Let's say that the exterior algebra is a case of unital associative algebra - in case one wants to go deeper into this topic that is a point to start.
Unital (for engineers and some CS folks it's sometimes "unitary") means that the algebra must contain an multiplicative unit. This is also called "identity element" and has the property 1=1x=x1=x for all x of the algebra.
The exterior product is the multiplication of the exterior algebra and thus it is alternating on  vector space V and further a bilinear operator.

The P-vector is a concept where "P" comes from p-form. It is related to dual space vectors.

The N-vector... Is easier.
N is a (surface) normal. A surface normal is a 3-dimensional vector (x,y,z) that is perpendicular to an surface and based on it or on the tangent plane to an point p if the surface is not flat.
Dunno about the spelling of perpendicular... I mean 90° to the tangen plane or the surface.
The normals have no specified direction by default.  It can be 90°  to both sides or inward and outward.

Displacement needs not much explanation I think.
It's again a vector and the distance is not specified.
Displacement is if you move from A to B in n seconds. You can go whatever way you want as long as you are at B after n seconds. There is no information about the path in this vector.

There could be different descriptions about these topics of vector math. I have only written them down as I remember them from everyday use. No guarantee for nothing...

But after all it's like Casette said. Having fun with the figure is important. Not as important as learning math but it comes second to it and before anything else.

And I have not even written a word about NURBS yet...