Maths & numbers
Plane through three 3D points
Find a unit-normal plane equation from three non-collinear coordinates.
A clear answer. Here’s how.
Uses n=(B−A)×(C−A), normalises n, then sets d=−n·A for n·X+d=0. Requires exactly three finite points within ±1 million and rejects collinear/near-collinear configurations at a relative 10⁻¹² threshold. Reversing point order reverses all equation coefficients without changing the plane. No best-fit plane is inferred from more points.
See a worked example
Worked example
A fixed demonstration, separate from the values you enter above.
- CSV: X,Y,Z
X,Y,Z 0,0,2 1,0,2 0,1,2
Example result
| Coefficient | Value |
|---|---|
| nx | 0 |
| ny | 0 |
| nz | 1 |
| d | -2 |
Unit-normal plane nx·X + ny·Y + nz·Z + d = 0. Normal direction follows (B−A) × (C−A).