:- use_module(library(record)).

/* comment */
:- record vector(x:float=0.0,y:float=0.0,z:float=0.0).

add_vectors(C,A,B) :-
    vector_x(A,X1),
    vector_y(A,Y1),
    vector_z(A,Z1),
    vector_x(B,X2),
    vector_y(B,Y2),
    vector_z(B,Z2),
    X is X1 + X2, 
    Y is Y1 + Y2, 
    Z is Z1 + Z2,
    make_vector([x(X),y(Y),z(Z)],C).

subtract_vectors(C,A,B) :-
    vector_x(A,X1),
    vector_y(A,Y1),
    vector_z(A,Z1),
    vector_x(B,X2),
    vector_y(B,Y2),
    vector_z(B,Z2),
    X is X1 - X2, 
    Y is Y1 - Y2, 
    Z is Z1 - Z2,
    make_vector([x(X),y(Y),z(Z)],C).

dot_vectors(C,A,B) :- 
    vector_x(A,X1),
    vector_y(A,Y1),
    vector_z(A,Z1),
    vector_x(B,X2),
    vector_y(B,Y2),
    vector_z(B,Z2),
    C is X1 * X2 + Y1 * Y2 + Z1 * Z2. 

cross_vectors(C,A,B) :- 
    vector_x(A,X1),
    vector_y(A,Y1),
    vector_z(A,Z1),
    vector_x(B,X2),
    vector_y(B,Y2),
    vector_z(B,Z2),
    X is Y1 * Z2 - Y2 * Z1, 
    Y is -(X1 * Z2 - X2 * Z1),
    Z is X1 * Y2 - X2 * Y1,
    make_vector([x(X),y(Y),z(Z)],C).

magnitude(C,A) :-
    dot_vectors(B,A,A),
    C is sqrt(B).

direction_r(C,A) :-
    vector_x(A,X1),
    vector_y(A,Y1),
    C is atan2(Y1,X1).
    
direction_d(C,A) :-
    direction_r(B,A),
    C is B * 90.0 / asin(1.0).

problem_05 :-
    write("Problem 5\n"),
    make_vector([x(4.0),y(-3.0),z(0.0)],A),
    make_vector([x(6.0),y(8.0),z(0.0)], B),
    make_vector([x(2.0),y(-3.0),z(7.0)], F),
    make_vector([x(12.0),y(45.0),z(-8.0)], G),
    make_vector([x(-5.0),y(-3.0),z(42.0)], H),

    vector_x(A,DJD),
    write("DJD = "),
    write(DJD),nl,
    write("A = "),
    write(A),nl,
    write("B = "),
    write(B),nl,
    add_vectors(C,A,B),
    write("C = A + B = "),
    write(C),nl,
    subtract_vectors(D,B,A),
    write("D = B - A = "),
    write(D),nl,
    subtract_vectors(E,A,B),
    write("E = A - B = "),
    write(E),nl,
    write("F = "),
    write(F),nl,
    write("G = "),
    write(G),nl,
    write("H = "),
    write(H),nl,
    magnitude(MA,A),
    write("Magnitude A = "),
    write(MA),nl,
    magnitude(MB,B),
    write("Magnitude B = "),
    write(MB),nl,
    magnitude(MC,C),
    write("Magnitude C = "),
    write(MC),nl,
    magnitude(MD,D),
    write("Magnitude D = "),
    write(MD),nl,
    magnitude(ME,E),
    write("Magnitude E = "),
    write(ME),nl,
    direction_r(DA_r,A),
    write("Direction in radians A = "),
    write(DA_r),nl,
    direction_r(DB_r,B),
    write("Direction in radians B = "),
    write(DB_r),nl,
    direction_r(DC_r,C),
    write("Direction in radians C = "),
    write(DC_r),nl,
    direction_r(DD_r,D),
    write("Direction in radians D = "),
    write(DD_r),nl,
    direction_r(DE_r,E),
    write("Direction in radians E = "),
    write(DE_r),nl,
    direction_d(DA_d,A),
    write("Direction in degrees A = "),
    write(DA_d),nl,
    direction_d(DB_d,B),
    write("Direction in degrees B = "),
    write(DB_d),nl,
    direction_d(DC_d,C),
    write("Direction in degrees C = "),
    write(DC_d),nl,
    direction_d(DD_d,D),
    write("Direction in degrees D = "),
    write(DD_d),nl,
    direction_d(DE_d,E),
    write("Direction in degrees E = "),
    write(DE_d),nl,
    dot_vectors(AdA,A,A),
    write("A dot A = "),
    write(AdA),nl,
    dot_vectors(AdB,A,B),
    write("A dot B = "),
    write(AdB),nl,
    dot_vectors(BdA,B,A),
    write("B dot A = "),
    write(BdA),nl,
    dot_vectors(AdC,A,C),
    write("A dot C = "),
    write(AdC),nl,
    dot_vectors(DdA,D,A),
    write("D dot A = "),
    write(DdA),nl,
    dot_vectors(AdE,A,E),
    write("A dot E = "),
    write(AdE),nl,
    dot_vectors(EdA,E,A),
    write("E dot A = "),
    write(EdA),nl,

    cross_vectors(AcA,A,A),
    write("A cross A = "),
    write(AcA),nl,
    cross_vectors(AcB,A,B),
    write("A cross B = "),
    write(AcB),nl,
    cross_vectors(BcA,B,A),
    write("B cross A = "),
    write(BcA),nl,
    cross_vectors(AcC,A,C),
    write("A cross C = "),
    write(AcC),nl,
    cross_vectors(DcA,D,A),
    write("D cross A = "),
    write(DcA),nl,
    cross_vectors(AcE,A,E),
    write("A cross E = "),
    write(AcE),nl,
    cross_vectors(EcA,E,A),
    write("E cross A = "),
    write(EcA),nl,
    cross_vectors(FcG,F,G),
    write("F cross G = "),
    write(FcG),nl,
    cross_vectors(FcH,F,H),
    write("F cross H = "),
    write(FcH),nl,
    cross_vectors(GcH,G,H),
    write("G cross H = "),
    write(GcH),nl,
    cross_vectors(GcF,G,F),
    write("G cross F = "),
    write(GcF),nl,
    cross_vectors(HcF,H,F),
    write("H cross F = "),
    write(HcF),nl,
    cross_vectors(HcG,H,G),
    write("H cross G = "),
    write(HcG),nl.