I'm new to Prolog and my task requires finding all equilateral triangles which are built from DB points. As a result, I'm getting identical points of the triangles. I do not understand what the problem is. Help me pls!
:- dynamic
point/3.
%?Point_Sign, ?Abscissa, ?Ordinate
db_filling:-
point(_,_,_),!.
db_filling:-
assert(point(a,1,1)),
assert(point(b,1,2)),
assert(point(c,1,3)),
assert(point(d,2,2)),
assert(point(e,3,3)),
assert(point(f,-1,1)),
assert(point(g,-2,1)),
assert(point(h,-2,2)),
assert(point(i,-3,3)),
assert(point(j,-3,-1)),
assert(point(k,-3,-2)),
assert(point(l,-3,-3)),
assert(point(n,-1,-1)),
assert(point(m,-3,0)),
assert(point(o,3,0)),
assert(point(p,0,3)).
% +List
points_main(Xs):-
db_filling,
findall(Xs1,equilateral_triangles(Xs1),Xs).
% +Points
equilateral_triangles([P1,P2,P3]):-
point(P1,X1,Y1),
point(P2,X2,Y2),
point(P3,X3,Y3),
L1 is sqrt((X2 - X1)^2 + (Y2 - Y1)^2),
L2 is sqrt((X3 - X2)^2 + (Y3 - Y2)^2),
L3 is sqrt((X1 - X3)^2 + (Y1 - Y3)^2),
L1 = L2,
L2 = L3.
Result:
?- points_main(Res).
Res = [[a, a, a], [b, b, b], [c, c, c], [d, d, d], [e, e, e], [f, f, f], [g, g|...], [h|...], [...|...]|...].
You have a couple of fundamental issues here.
From memory, the two-dimensional coordinates of an equilateral triangle cannot all be integers. You must have at least one irrational number. Computers are not good at representing irrational numbers.
So, you're also confusing real maths with computer maths. You can't simply get the sqrt and check for equality.
To illustrate I produced these three points:
point(j1,0,0).
point(j2,1,0).
point(j3,0.5,0.866025403784439). % 1/2 & sqrt(3)/2
That's an equilateral triangle.
When I run that with your code, the lengths that get produced are like this:
[1.0,1.0000000000000004,1.0000000000000004]
They are all effectively 1.0, but of course 1.0000000000000004 is not 1.0. So, even this doesn't comeback as a equal.
So you are really forced to check the confidence as an epsilon to say two numbers are equal.
Here's what I did to do that:
points_main(Xs):-
findall(Xs1,equilateral_triangles(Xs1),Xs).
equilateral_triangles([P1,P2,P3]):-
point(P1,X1,Y1),
point(P2,X2,Y2),
P1 \= P2,
point(P3,X3,Y3),
P1 \= P3,
P2 \= P3,
L12 is sqrt((X2 - X1)^2 + (Y2 - Y1)^2),
L23 is sqrt((X3 - X2)^2 + (Y3 - Y2)^2),
L31 is sqrt((X1 - X3)^2 + (Y1 - Y3)^2),
D1223 is abs(L12 - L23),
D1223<0.00000001,
D2331 is abs(L23 - L31),
D2331<0.00000001,
D3112 is abs(L31 - L12),
D3112<0.00000001.
Now, if I run that against my points above I get this:
?- points_main(Xs).
Xs = [[j1, j2, j3], [j1, j3, j2], [j2, j1, j3], [j2, j3, j1], [j3, j1, j2], [j3, j2, j1]].
All combinations of the above three points - so, yes, they are all equilateral triangles.
If I run against your original points, as expected, there are no equilateral triangles.
A few side notes.
(1) I removed all of the assert code. It wasn't helpful nor necessary to get your code working.
(2) you could define my j3 point as point(j3,0.5,X) :- X is sqrt(3)/2. and your original maths would work. However, this is just lucky. When dealing will floating-point numbers you can never be sure that two numbers are equal even though they should be.
(3) I introduced P1 \= P2, etc, to prevent the points unifying to themselves. That's why you got [a,a,a],... etc.