Thread: Please help me with interseciton of planes

i know how to solve it using inverse matrices...but the answer is in matrix form...and i don't know how to do matrice calculations for you program (prob use for loops)...try googling is about all i can say...if you want the inverse matrix way just let me know

ok lets see, you have x y and z...so i can post some example math equations that you can port over to code.
[algebra]

x+2y-z=10 //note: equations probably don't work out, just an example
2x+4y+z=-1

//you take the coeffecients of the variables into matrix a
1 2 -1
2 4 1
//then take the sums
10
-1
//find the inverse of the first matrix and mulitply it by the second matrix, the resulting matrix will be a set of points for x y an z

[/algebra]

Umm, Waldo what do you mean?

You cannot find the inverse of a non-square matrix!

The intersection of two planes is a line.

*With the three points, you can create two vectors in the plane.
*Use these two vectors to find the normal vector (A,B,C)
*With the normal vector and one of the points, create the equation Ax + By + Cz + D = 0 both both planes.
*Solve the equation system

If there's a result, it should be of the form:

{x = x0 + at
{y = y0 + bt
{z = z0 + ct

Aha, your version works if you add z=t to your matrices.

Plane 1 : x + 2y - z = 10
Plane 2 : 2x + 7y + z = 1

Code:

    ( 1 2 -1 )
A = ( 2 7 1  )
    ( 0 0 1  )

    ( 10 )
B = ( 1  )
    ( t  )

( x )
( y )  =  A^-1 * B
( z )