Hello... I have some knowledge of 2d math, as well as a little os 3d vectors, but I just have some problems mixing things up... Right now, i am trying to get a line equation from two points [x, y, z], but i''m not getting anywere. Could someone tell me the notation of lines in 3d? ex. in 2d you write them as: ax + by + c = 0 but you have some cool formulae like (y - y_0) = m * (x - x_0) and things like that, so anything in general you can provide me would be helpfull. Also, other things like how you write a plane ( a plane, not a triangle, like a line is to a line segment), any basic 3d formula, etc would be nice. I know it sounds a bit lazy from my part, but I''m not asking for very complex things (and I did a little STFWed, getting lots of tutorials for matrices transformations too complex for me). thanks.

As far as I know, there is no equation for a line or a line segment in 3-space unless you limit a bunch of variables. The analog in 3D to the 2D line is the plane, which has the form

Ax + By + Cz + D = 0

In order to find any plane, you need 3 points, just like in 2D you need 2 points for a line. I forget the exact method of finding the equation from those three points, but for that you can just look in a multi-variable calculus book (I know, not much help). But the only thing I''ve ever needed an equation for a plane is in a math class, but I could be underestimating it.

Elijah

There are multiple forms of the line equation in 3D. You could check out Ask Dr. Math...

If you want one single equation, AFAIK, there is only one form:

P = P0 + t * (P1 - P0) , where t is between 0 and 1

P, P0 and P1 are all vectors (points, actually). t is a scalar.

It states that P is a point on the line segment if and only if it is somewhere between P1 and P0.

If you don't know vector math, it's a little bit hard to follow. Essentially, it breaks down into the following three equations:
x = x0 + t * (x1 - x0)
y = y0 + t * (y1 - y0)
z = z0 + t * (z1 - z0)

Try it out in 2D to understand better, and good luck!

Cédric

EDIT: If you intend on working in 3D, you should read a tutorial on vectors. It will be very useful.

REEDIT: There is also the so-called symetrical form, which can be considered one equation.

[edited by - cedricl on August 6, 2002 12:29:19 AM]

[edited by - cedricl on August 6, 2002 12:47:42 AM]