How to find closest point in plane to another point? Matlab solution

If I have a plane

x+y+z=0

and want to find the closest point in this plane to

p=(1,1,1) 

How could I do this in matlab? I understand how to do this mathematically, but can't figure the syntax

Answer 1

[William Rose]

@Sue Swenson,

A plane can be described by

This plane has normal vector .

Suppose is a given external point. Find the point in the plane which is closest to .

The equation which I derived to solve this problem is

We can implement the equation above in Matlab, recalling that prime denotes transpose in Matlab.

In your example, the plane is

x+y+z=0

and therefore and D=0. Also, in your example, the external point is .

The Matlab code to solve this is:

n=[1;1;1];
D=0;
p1=[1;1;1];
p0=p1-((n'*p1-D)/(n'*n))*n;
disp(p0)

     0
     0
     0

Try it.