Line of intersection between two planes

Question

How can I find the line of intersection between two planes?

I know the mathematics idea, and I did the cross product between the the planes normal vectors

b

Answer 1

The cross product of the line is the direction of the intersection line. Now you need a point in the intersection.

You can do this by taking a point on the cross product, then subtracting Normal of plane A * distance to plane A and Normal of plane B * distance to plane b. Cleaner:

p = Point on cross product

intersection point = ([p] - ([Normal of plane A] * [distance from p to plane A]) - ([Normal of plane B] * [distance from p to plane B]))

Edit:

You have two planes with two normals:

N1 and N2

The cross product is the direction of the Intersection Line:

C = N1 x N2

The class above has a function to calculate the distance between a point and a plane. Use it to get the distance of some point p on C to both planes:

p = C //p = 1 times C to get a point on C
d1 = plane1.getDistance(p)
d2 = plane2.getDistance(p)

Intersection line:

resultPoint1 = (p - (d1 * N1) - (d2 * N2))
resultPoint2 = resultPoint1 + C