
 
compares the $$xcoordinates of $$p and the horizontal projection
of p on h; see (a) in the
figure below. Precondition: h is not horizontal.  

 
This function compares the $$xcoordinates of the horizontal projection
of p on h1 and on h2; see (b) in the figure
below. Precondition: h1 and h2 are not horizontal.  

 
Let $$p be the
intersection
of lines $$l1 and $$l2.
This function compares the $$xcoordinates of $$p and
the horizontal projection of p on h; see (c) in the
figure below. Precondition: l1 and l2 intersect and are not horizontal; h is not horizontal.  

 
Let $$p be the
intersection
of lines $$l1 and $$l2. This
function compares the $$xcoordinates of the horizontal projection of
p on h1 and on h2; see (d) in the figure
below. Precondition: l1 and l2 intersect and are not horizontal; h1 and h2 are not horizontal. 