Calculating new coordinates in 3D after moving an object

Good evening.

I have a question on how to calculate an objects coordinated after altering its position.

Example:

A triangle with coordinates;

P1 : -4, -4, 4 (x, y, z)
P2 : -3, -4, 4
P3 : -3, -4, 5


Let's say I want to rotate the line P2-P3 about 14 degrees around the axis P1-P2.

How can I find out the new coordinates of P3?

It would be a simple task using trigonometry if it it was only a 2D space, but 3D is puzzling me a little.
Someone hinted me that "Quaternion" would be the solution, but I tried to understand but didn't. Embarrassingly that area is a little over my understanding of mathematics.


Another question is if the object would be more complex, such as a Dodecahedron.

I assume I first must find the a central point around which the rotation should be done, but since all points are moving...
How can I find out the new coordinates of each and every one?


Any pointers to online resources or direct help are much appreciated.

Thank you.
.

Relevant Pages

  • Re: Mathematical "Proof"
    ... I would like to know if you can use patterns as the "proof". ... A proof in mathematics is an exact logical form. ... uses abstract relation of all triangle. ... NOT NOTATION. ...
    (sci.math)
  • Re: Mathematical "Proof"
    ... I would like to know if you can use patterns as the "proof". ... A proof in mathematics is an exact logical form. ... uses abstract relation of all triangle. ... NOT NOTATION. ...
    (sci.math)
  • Re: What has fractal theory achieved?
    ... do this with nonexistence, because by definition it ... of the hypoteneuse of a 5-sided triangle. ... "existence," or that mathematical existence implies ... get mathematics ...
    (sci.math)
  • Re: Calculating new coordinates in 3D after moving an object
    ... coordinated after altering its position. ... A triangle with coordinates; ... Let's say I want to rotate the line P2-P3 about 14 ... understanding of mathematics. ...
    (sci.math)
  • Re: Cantor Confusion
    ... That's WM's Equilateral Infinite Triangle, i.e., the list with line n ... Then it must be an equilateral /right/ triangle if rows are horizontal ... I use the language of mathematics. ...
    (sci.math)