Re: [Algorithms] Projecting a point on a plane

[Ron L. <ro...@do...>]

Aldo Spanghero
>
> I can't remember how to project a point (p2) on a plane (n, p1). I need
this
> to finish the 3D sound system of my engine(this afternoon!) and my math
book
> is in my home!
>
> Someone could, please, help me?
>
> I don't wanna use DirectSound3D, for now.
>
>
> Again, thanks in advance.
>

Why would you need your math book?

Line through p2 perpendicular to plane is described parametrically by
    p2 + t n

This hits plane when the vector from this point to p1 is perpendicular to n
so

   ((p2 + tn) - p1) dot n = 0

Use elementary algebraic properties of dot product to rearrange terms and
solve for t:

    t = (p1 - p2) dot n

In which I also used the fact that n dot n = 1 (unit normal vector).

So the projection is p2 + ((p1 - p2) dot n)n