Maths & numbers
3D line & plane intersection
Intersect an infinite directed line with a plane or identify parallel cases.
A clear answer. Here’s how.
Normalises the nonzero line direction and plane normal, then solves P+tV against n·X+d=0. Returns the unique point and signed travel in the unit direction. Parallel lines are distinguished from lines lying in the plane using stated small numeric tolerances. The line is infinite; negative travel is allowed and is not treated as a ray intersection.
See a worked example
Worked example
A fixed demonstration, separate from the values you enter above.
- Line origin X
- 1
- Line origin Y
- 2
- Line origin Z
- 5
- Line direction X
- 0
- Line direction Y
- 0
- Line direction Z
- -1
- Plane normal X
- 0
- Plane normal Y
- 0
- Plane normal Z
- 1
- Plane constant d
- 0
Example result
| Coordinate | Value |
|---|---|
| X | 1 |
| Y | 2 |
| Z | 0 |
Intersection with the infinite line. Signed travel along the unit direction: 5.