<p>You can determine <code>x</code> by calculating line-plane intersection. Your line starts at <code>P</code> and has direction <code>D=[1, 0, 0]</code>, and plane <code>T=[V, N]</code>. This can be done as follows:
$$x=\frac{(V-P)\cdot N}{N\cdot D}$$
<code>x</code> is the distance from <code>P</code> along <code>D</code> to the intersection point with <code>T</code> (assuming both <code>D</code> and <code>N</code> are unit vectors)</p>

CC BY-SA 3.0
2016-12-07T16:38:40.270Z
2016-12-07T16:38:40.270Z
JarkkoL
<p>I have a point $P = (0, y, z)$. I need to determine the $x$ coordinate of its projection $P'$ onto a plane $T$ along the $x$ axis unit vector $\vec{X} = (1, 0, 0)$. The plane $T$ is defined by a point $V$ that lies on $T$ and its normal $\vec{N}$ (see the attached picture).</p>

<p><a href="https://i.sstatic.net/NIbgq.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/NIbgq.png" alt="Projection onto plane along a vector."></a></p>

<computational-geometry>
How to project a 3D point onto a plane along another (axis) vector?
niksbenik
# How to project a 3D point onto a plane along another (axis) vector?

(Asked by: username_0 on 2016-12-06)

I have a point $P = (0, y, z)$. I need to determine the $x$ coordinate of its projection $P'$ onto a plane $T$ along the $x$ axis unit vector $\vec{X} = (1, 0, 0)$. The plane $T$ is defined by a point $V$ that lies on $T$ and its normal $\vec{N}$ (see the attached picture).

[![Projection onto plane along a vector.](https://i.sstatic.net/NIbgq.png)](https://i.sstatic.net/NIbgq.png)

**Tags:** computational-geometry


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## 1 answers

### Answer by username_1 on 2016-12-07. Score: 6 | Accepted answer

You can determine `x` by calculating line-plane intersection. Your line starts at `P` and has direction `D=[1, 0, 0]`, and plane `T=[V, N]`. This can be done as follows:
$$x=\frac{(V-P)\cdot N}{N\cdot D}$$
`x` is the distance from `P` along `D` to the intersection point with `T` (assuming both `D` and `N` are unit vectors)


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