/**

gridline.pl

Metaphysics > Exposition Description

From quote "first half: describe single walking". 

Draws a line on a grid from one cell to another, describing walking as an example of an exposition.

?- gridline1(0,0,0,3).
*  
*  
*  
*  
true.

?- gridline1(0,0,1,3).
 *  
 *  
*   
*   
true.

?- gridline1(0,0,3,3).
   *  
  *   
 *    
*     
true.

?- gridline1(0,0,3,1).
  **  
**    
true.

?- gridline1(0,0,3,0).
****  
true.

?- gridline1(0,0,3,-1).
**    
  **  
true.

?- gridline1(0,0,3,-3).
*     
 *    
  *   
   *  
true.

?- gridline1(0,0,1,-3).
*   
*   
 *  
 *  
true.

?- gridline1(0,0,0,-3).
*  
*  
*  
*  
true.

?- gridline1(0,0,-1,-3).
 *  
 *  
*   
*   
true.

?- gridline1(0,0,-3,-3).
   *  
  *   
 *    
*     
true.

?- gridline1(0,0,-3,-1).
  **  
**    
true.

?- gridline1(0,0,-3,0).
****  
true.

?- gridline1(0,0,-3,1).
**    
  **  
true.

?- gridline1(0,0,-3,3).
*     
 *    
  *   
   *  
true.

?- gridline1(0,0,-1,3).
*   
*   
 *  
 *  
true.

**/

%% Graphs (X1,Y1) to (X2,Y2)

gridline1(X1,Y1,X2,Y2) :-
	sortbyx(X1,Y1,X2,Y2,XA1,YA1,XA2,YA2),
	equation(XA1,YA1,XA2,YA2,M,C),
	gridline2(XA1,YA1,XA2,YA2,M,C,Grid1),
	writeln(Grid1),
        sort(YA1,YA2,YB1,YB2),
	print(XA1,YB1,XA2,YB2,Grid1,_Grid2),!.

%% Sorts (X1,Y1) and (X2,Y2) by X

sortbyx(X1,Y1,X2,Y2,X1,Y1,X2,Y2) :-
	X2 >= X1.
sortbyx(X1,Y1,X2,Y2,X2,Y2,X1,Y1) :-
        X2 < X1.

%% Finds the rise and run of (X1,Y1) and (X2,Y2)

equation(X1,Y1,X2,Y2,M,C) :-
	DY is Y2-Y1,
	DX is X2-X1,
	equation2(DY,DX,M,Y1,X1,C).

%% Finds the gradient m and y-intercept c of (X1,Y1) and (X2,Y2)

equation2(_DY,0,999999999,_Y1,X1,X1) :-
        !.
equation2(DY,DX,M,Y1,X1,C) :-
	M is DY/DX,
        C is Y1-M*X1.

%% Finds the graph of the line connecting the two points.  It does this by finding the graph flipped in the y=x line if the gradient m is greater than 1 or less than -1, so that the graph is not disjointed

gridline2(X1,_Y1,X2,_Y2,M,C,Grid) :-
	M =< 1, M >= -1,
	gridline3(X1,X2,M,C,[],Grid).
gridline2(X1,Y1,_X2,Y2,M,_C,Grid) :-
	(M > 1; M < -1),
        M2 is 1/M,
	sort(Y1,Y2,YA1,YA2),
        C2 is X1-M2*Y1,
	gridline3(YA1,YA2,M2,C2,[],Grid1),
	flipxy(Grid1,[],Grid).

%% Sorts Y1 and Y2

sort(Y1,Y2,Y1,Y2) :-
	Y1=<Y2, !.
sort(Y1,Y2,Y2,Y1) :-
	Y1>Y2.

%% Plots a point at each x-value of the graph

gridline3(X1,X2,_M,_C,Grid,Grid) :-
	X1 is X2+1.
gridline3(X1,X2,M,C,Grid1,Grid2) :-
	Y is round(M*X1+C),
	Coord = [X1,Y],
	append(Grid1,[Coord],Grid3),
	X3 is X1+1,
	gridline3(X3,X2,M,C,Grid3,Grid2).

%% Flips the graph in the y=x line

flipxy([],Grid,Grid) :- !.
flipxy(Grid1,Grid2,Grid3) :-
	Grid1 = [Coord1 | Coords],
	Coord1 = [X, Y],
	Coord2 = [Y, X],
	append(Grid2,[Coord2],Grid4),
	flipxy(Coords,Grid4,Grid3).

%% Prints the graph from the top row to the bottom row

print(_X1,Y1,_X2,YA1,Grid,Grid) :-
	Y11 is Y1,YA1 < Y11,!.
print(X1,Y1,X2,Y2,Grid1,Grid2) :-
	printline(X1,X2,Y2,Grid1,Grid3),
	writeln(''),
	YA2 is Y2-1,
	print(X1,Y1,X2,YA2,Grid3,Grid2).

%% Prints the current row

printline(XA2,X2,_Y,Grid,Grid) :- 
	XA2 is X2+3, !.
printline(X1,X2,Y,Grid1,Grid2) :-
	member([X1,Y],Grid1),
	delete(Grid1,[X1,Y],Grid3),
	write('*'),
	XA1 is X1+1,
	printline(XA1,X2,Y,Grid3,Grid2).
printline(X1,X2,Y,Grid1,Grid2) :-
        not(member([X1,Y],Grid1)),
        write(' '),
        XA1 is X1+1,
        printline(XA1,X2,Y,Grid1,Grid2).