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Exercise

Given a two-dimensional grid, as shown below, using array coordinates, and given
the real coordinate pairs (A1,B1) and A2,B2) of two points P1 and P2 in the region,
we want to record in an array the set of squares through which the straight line
segments from P1 and P2 passes.


























The input:				The desired character array.
A1=1.3, B1=2.5,				Image[2,3]=`*'
A2=5.4, B2=6.6				Image[2,4]=`*', etc.

A procedure to do this task can be used in a program to print crude line
drawings using a standard line (character) printer or a character-based
terminal screen.

The line through P1 and P2 passes through a particular square if it goes above
at least one of the four corners, and below at least one.
























As the illustration above shows, when B1<B2, the point (A,B) falls 
above the line if A>A1+(B-B1)(A2-A1)/(B2-B1), and below the line if 
A<A1+(B-B1)(A2-A1)/(B2-B1).

Here is a proposed Pascal program to put the line segment into a page image
and print it.

(Declarations)

PROCEDURE ABOVE(VERT,HORIZ:REAL):BOOLEAN;
	BEGIN
	ABOVE:=VERT>A1+(HORIZ-B1)*(A2-A1)/(B2-B1)
	END;

PROCEDURE BELOW(VERT,HORIZ:REAL):BOOLEAN;
	BEGIN
	BELOW:=VERT<A1+(HORIZ-B1)*(A2-A1)/(B2-B1)
	END;

READ(A1,B1,A2,B2);
FOR R:=1 TO 132 DO
	FOR C:=1 TO 60 DO
		IF (ABOVE(R-1,C-1) OR ABOVE(R-1,C))
			AND (BELOW(R,C-1) OR BELOW(R,C))
		THEN IMAGE[R,C]:=`*'
		ELSE IMAGE[R,C]:=` ';
WRITEPAGE(IMAGE) 


Unfortunately, the program is incorrect, in at least two ways.  It fails if

	A1= 5, B1=17, A2= 5, B2=43, and also if
   	A1=17, B1= 5, A2=43, B2= 5.

Your task: find all errors and report them. Correct them.  Test the corrected
program, and submit with it, in legible and coherent English, a persuasive
argument that it now works on any values of A1,B1,A2,B2.