The projection vector of a vector to a plane

The projection vector of a vector to a plane

Find the projection vector of a vector projected onto a plane , Here's the picture

Known item ： vector sq, Plane normal vector n
set sth. up o Is a point q The vertical point to the plane
Then the vector oq Perpendicular to the plane
Then the vector so That is to say sq Projection on a plane .
so = sq + qo
so = sq + n*(sq·n* -1)

In the above reasoning, for qo The step-by-step transformation is like this
because qo Parallel to the n, And n It's the unit vector
|qo| = |sq·n|
When sq When facing the front of the plane sq·n >= 0,qo And n In the opposite direction
When sq When facing the negative side of the plane sq·n <= 0, qo And n In the same direction
therefore qo = n*(sq·n -1)