Perpendicular on a line segment from a given point

Question

I want to calculate a point on a given line that is perpendicular from a given point.

I have a line segment AB and have a point C outside line segment. I want to ca

Answer 1

A point on line AB can be parametrized by:

M(x)=A+x*(B-A), for x real.

You want D=M(x) such that DC and AB are orthogonal:

dot(B-A,C-M(x))=0.

That is: dot(B-A,C-A-x*(B-A))=0, or dot(B-A,C-A)=x*dot(B-A,B-A), giving:

x=dot(B-A,C-A)/dot(B-A,B-A) which is defined unless A=B.