I have a set of points $A,B,C,D$ in 3-D space:
$$A = (x_a, y_a, z_a)$$
$$B = (x_b, y_b, z_b)$$
$$C = (x_c, y_c, z_c)$$
$$D = (x_d, y_d, z_d)$$
They belong to a 3-D figure, e.g.:
I'm trying to define the entire plane $ABCD$ by a set of functions, based on the points I have:
$ x(y,z)$ defines the x-coordinates on the plane, depending on y and z
$ y(x,z)$ …
$ z(x,y)$ …
I'm finding it a difficult problem. This, I think, is the best way to solve the problem, but maybe there is a better way based on basis vectors (which I also have).
The reason: I'm trying to develop a molecular dynamics software that can handle any periodic system, so I'm trying to find the way to universalize periodic boundary conditions. For example, in a simple cubic system, I would just do (this pseudocode):
move_the_particle();
if (particle[x] < -x_length/2)
particle[x] = particle[x] + x_length
…to check if my particle escaped the box on the left side, and move it over to the right side.
If this is unclear please let me know. I can try to clarify further.
Best Answer
A plane is defined from three points ABC using the following algorithm. How you handle the 4th point is up to you.
See answer to related question for how to interpret the plane equation, in terms of the properties of the plane.