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).
1 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)