// TODO: get rid of instantiators in favor of aliases to reduce template bloat
module nxt.geometry;

import std.traits: isFloatingPoint, isNumeric, isSigned, isDynamicArray, isAssignable, isArray, CommonType, isInstanceOf;

version = use_cconv;            ///< Use cconv for faster compilation.
version = unittestAllInstances;

version(unittestAllInstances)
{
    static immutable defaultElementTypes = ["float", "double", "real"];
}
else
{
    static immutable defaultElementTypes = ["double"];
}

enum Orient { column, row } // Vector Orientation.

/** `D`-Dimensional Cartesian Point with Coordinate Type (Precision) `E`.
 */
struct Point(E, uint D)
if (D >= 1 /* && TODO: extend trait : isNumeric!E */)
{
    alias ElementType = E;

    this(T...)(T args)
    {
        foreach (immutable ix, arg; args)
        {
            _point[ix] = arg;
        }
    }

    /** Element data. */
    E[D] _point;
    enum dimension = D;

    @property void toString(scope void delegate(scope const(char)[]) @safe sink) const
    {
        sink(`Point(`);
        foreach (const ix, const e; _point)
        {
            if (ix != 0) { sink(","); }
            version(use_cconv)
            {
                import nxt.cconv : toStringInSink;
                toStringInSink(e, sink);
            }
            else
            {
                import std.conv : to;
                sink(to!string(e));
            }
        }
        sink(`)`);
    }

    @property string toMathML()() const
    {
        // opening
        string str = `<math><mrow>
  <mo>(</mo>
  <mtable>`;

        static foreach (i; 0 .. D)
        {
            str ~= `
    <mtr>
      <mtd>
        <mn>` ~ _point[i].toMathML ~ `</mn>
      </mtd>
    </mtr>`;
        }

        // closing
        str ~= `
  </mtable>
  <mo>)</mo>
</mrow></math>
`;
        return str;
    }

    /** Returns: Area 0 */
    @property E area() const { return 0; }

    inout(E)[] opSlice() inout { return _point[]; }

    /** Points +/- Vector => Point */
    auto opBinary(string op, F)(Vector!(F, D) r) const
        if ((op == "+") ||
            (op == "-"))
    {
        Point!(CommonType!(E, F), D) y;
        static foreach (i; 0 .. D)
        {
            y._point[i] = mixin("_point[i]" ~ op ~ "r._vector[i]");
        }
        return y;
    }
}

/** Instantiator for `Point`. */
auto point(Ts...)(Ts args)
if (!is(CommonType!Ts == void))
{
    return Point!(CommonType!Ts, args.length)(args);
}

version(unittest)
{
    alias vec2f = Vector!(float, 2, true);
    alias vec3f = Vector!(float, 3, true);

    alias vec2d = Vector!(float, 2, true);

    alias nvec2f = Vector!(float, 2, true);
}

/** `D`-Dimensional Vector with Coordinate/Element (Component) Type `E`.
 *
 * See_Also: http://physics.stackexchange.com/questions/16850/is-0-0-0-an-undefined-vector
 */
struct Vector(E, uint D,
              bool normalizedFlag = false, // `true` for unit vectors
              Orient orient = Orient.column)
if (D >= 1 &&
    (!normalizedFlag ||
     isFloatingPoint!E)) // only normalize fp for now
{
    // Construct from vector.
    this(V)(V vec)
    if (isVector!V &&
        // TOREVIEW: is(T.E : E) &&
        (V.dimension >= dimension))
    {
        static if (normalizedFlag)
        {
            if (vec.normalized)
            {
                immutable vec_norm = vec.magnitude;
                static foreach (i; 0 .. D)
                {
                    _vector[i] = vec._vector[i] / vec_norm;
                }
                return;
            }
        }
        static foreach (i; 0 .. D)
        {
            _vector[i] = vec._vector[i];
        }
    }

    /** Construct from Scalar `value`. */
    this(S)(S scalar)
    if (isAssignable!(E, S))
    {
        static if (normalizedFlag)
        {
            import std.math : sqrt;
            clear(1/sqrt(cast(E)D)); // TODO: costly
        }
        else
        {
            clear(scalar);
        }
    }

    /** Construct from combination of arguments. */
    this(Args...)(Args args) { construct!(0)(args); }

    enum dimension = D;

    @property const
    {
        string orientationString()() { return orient == Orient.column ? `Column` : `Row`; }
        string joinString()() { return orient == Orient.column ? ` \\ ` : ` & `; }
    }

    @property void toString(scope void delegate(scope const(char)[]) @safe sink) const
    {
        sink(orientationString);
        sink(`Vector(`);
        foreach (const ix, const e; _vector)
        {
            if (ix != 0) { sink(","); }
            version(use_cconv)
            {
                import nxt.cconv : toStringInSink;
                toStringInSink(e, sink);
            }
            else
            {
                import std.conv : to;
                sink(to!string(e));
            }
        }
        sink(`)`);
    }

    /** Returns: LaTeX Encoding of Vector. http://www.thestudentroom.co.uk/wiki/LaTex#Matrices_and_Vectors */
    @property string toLaTeX()() const
    {
        return `\begin{pmatrix} ` ~ map!(to!string)(_vector[]).join(joinString) ~ ` \end{pmatrix}` ;
    }

    @property string toMathML()() const
    {
        // opening
        string str = `<math><mrow>
  <mo>⟨</mo>
  <mtable>`;

        if (orient == Orient.row)
        {
            str ~=  `
    <mtr>`;
        }

        static foreach (i; 0 .. D)
        {
            final switch (orient)
            {
            case Orient.column:
                str ~= `
    <mtr>
      <mtd>
        <mn>` ~ _vector[i].toMathML ~ `</mn>
      </mtd>
    </mtr>`;
                break;
            case Orient.row:
                str ~= `
      <mtd>
        <mn>` ~ _vector[i].toMathML ~ `</mn>
      </mtd>`;
                break;
            }
        }

        if (orient == Orient.row)
        {
            str ~=  `
    </mtr>`;
        }

        // closing
        str ~= `
  </mtable>
  <mo>⟩</mo>
</mrow></math>
`;
        return str;
    }

    auto randInPlace()(E scaling = 1)
    {
        import nxt.random_ex: randInPlace;
        static if (normalizedFlag &&
                   isFloatingPoint!E) // cannot use normalized() here (yet)
        {
            static if (D == 2)  // randomize on unit circle
            {
                alias P = real; // precision
                immutable angle = uniform(0, 2*cast(P)PI);
                _vector[0] = scaling*sin(angle);
                _vector[1] = scaling*cos(angle);
            }
            static if (D == 3)  // randomize on unit sphere: See_Also: http://mathworld.wolfram.com/SpherePointPicking.html
            {
                alias P = real; // precision
                immutable u = uniform(0, cast(P)1);
                immutable v = uniform(0, cast(P)1);
                immutable theta = 2*PI*u;
                immutable phi = acos(2*v-1);
                _vector[0] = scaling*cos(theta)*sin(phi);
                _vector[1] = scaling*sin(theta)*sin(phi);
                _vector[2] = scaling*cos(phi);
            }
            else
            {
                _vector.randInPlace();
                normalize(); // TODO: Turn this into D data restriction instead?
            }
        }
        else
        {
            _vector.randInPlace();
        }
    }

    /// Returns: `true` if all values are not `nan` nor `infinite`, otherwise `false`.
    @property bool ok()() const
    {
        static if (isFloatingPoint!E)
        {
            foreach (const ref v; _vector)
            {
                if (isNaN(v) ||
                    isInfinity(v))
                {
                    return false;
                }
            }
        }
        return true;
    }
    // NOTE: Disabled this because I want same behaviour as MATLAB: bool opCast(T : bool)() const { return ok; }
    bool opCast(T : bool)() const
    {
        return all!"a"(_vector[]);
    }

    /// Returns: Pointer to the coordinates.
    // @property auto value_ptr() { return _vector.ptr; }

    /// Sets all values to `value`.
    void clear(V)(V value)
    if (isAssignable!(E, V))
    {
        static foreach (i; 0 .. D)
        {
            _vector[i] = value;
        }
    }

    /** Returns: Whole Internal Array of E. */
    auto opSlice()
    {
        return _vector[];
    }
    /** Returns: Slice of Internal Array of E. */
    auto opSlice(uint off, uint len)
    {
        return _vector[off .. len];
    }
    /** Returns: Reference to Internal Vector Element. */
    ref inout(E) opIndex(uint i) inout
    {
        return _vector[i];
    }

    bool opEquals(S)(in S scalar) const
    if (isAssignable!(E, S)) // TODO: is(typeof(E.init != S.init))
    {
        static foreach (i; 0 .. D)
        {
            if (_vector[i] != scalar)
            {
                return false;
            }
        }
        return true;
    }

    bool opEquals(F)(in F vec) const
    if (isVector!F &&
        dimension == F.dimension) // TOREVIEW: Use isEquable instead?
    {
        return _vector == vec._vector;
    }

    bool opEquals(F)(const F[] array) const
    if (isAssignable!(E, F) &&
        !isArray!F &&
        !isVector!F) // TOREVIEW: Use isNotEquable instead?
    {
        if (array.length != dimension)
        {
            return false;
        }
        static foreach (i; 0 .. D)
        {
            if (_vector[i] != array[i])
            {
                return false;
            }
        }
        return true;
    }

    static void isCompatibleVectorImpl(uint d)(Vector!(E, d) vec) if (d <= dimension) {}
    static void isCompatibleMatrixImpl(uint r, uint c)(Matrix!(E, r, c) m) {}

    enum isCompatibleVector(T) = is(typeof(isCompatibleVectorImpl(T.init)));
    enum isCompatibleMatrix(T) = is(typeof(isCompatibleMatrixImpl(T.init)));

    private void construct(uint i)()
    {
        static assert(i == D, "Not enough arguments passed to constructor");
    }
    private void construct(uint i, T, Tail...)(T head, Tail tail)
    {
        static        if (i >= D)
        {
            static assert(0, "Too many arguments passed to constructor");
        }
        else static if (is(T : E))
        {
            _vector[i] = head;
            construct!(i + 1)(tail);
        }
        else static if (isDynamicArray!T)
        {
            static assert((Tail.length == 0) && (i == 0), "Dynamic array can not be passed together with other arguments");
            _vector[] = head[];
        }
        else static if (__traits(isStaticArray, T))
        {
            _vector[i .. i + T.length] = head[];
            construct!(i + T.length)(tail);
        }
        else static if (isCompatibleVector!T)
        {
            _vector[i .. i + T.dimension] = head._vector[];
            construct!(i + T.dimension)(tail);
        }
        else
        {
            static assert(0, "Vector constructor argument must be of type " ~ E.stringof ~ " or Vector, not " ~ T.stringof);
        }
    }

    // private void dispatchImpl(int i, string s, int size)(ref E[size] result) const {
    //     static if (s.length > 0) {
    //         result[i] = _vector[coordToIndex!(s[0])];
    //         dispatchImpl!(i + 1, s[1..$])(result);
    //     }
    // }

    // /// Implements dynamic swizzling.
    // /// Returns: a Vector
    // @property Vector!(E, s.length) opDispatch(string s)() const {
    //     E[s.length] ret;
    //     dispatchImpl!(0, s)(ret);
    //     Vector!(E, s.length) ret_vec;
    //     ret_vec._vector = ret;
    //     return ret_vec;
    // }

    ref inout(Vector) opUnary(string op : "+")() inout { return this; }

    Vector opUnary(string op : "-")() const
    if (isSigned!(E))
    {
        Vector y;
        static foreach (i; 0 .. D)
        {
            y._vector[i] = - _vector[i];
        }
        return y;
    }

    auto opBinary(string op, T)(in T rhs) const
    if (op == "+" || op == "-" &&
        isInstanceOf!(Vector, T) &&
        dimension && T.dimension)
    {
        Vector!(CommonType!(E, F), D) y;
        static foreach (i; 0 .. D)
        {
            y._vector[i] = mixin("_vector[i]" ~ op ~ "rhs._vector[i]");
        }
        return y;
    }

    Vector opBinary(string op : "*", F)(in F r) const
    {
        Vector!(CommonType!(E, F), D, normalizedFlag) y;
        static foreach (i; 0 .. dimension)
        {
            y._vector[i] = _vector[i] * r;
        }
        return y;
    }

    Vector!(CommonType!(E, F), D) opBinary(string op : "*", F)(in Vector!(F, D) r) const
    {
        // MATLAB-style Product Behaviour
        static if (orient == Orient.column &&
                   r.orient == Orient.row)
        {
            return outer(this, r);
        }
        else static if (orient == Orient.row &&
                        r.orient == Orient.column)
        {
            return dot(this, r);
        }
        else
        {
            static assert(0, "Incompatible vector dimensions.");
        }
    }

    /** Multiply with right-hand-side `rhs`. */
    Vector!(E, T.rows) opBinary(string op : "*", T)(in T rhs) const
    if (isCompatibleMatrix!T &&
        (T.cols == dimension))
    {
        Vector!(E, T.rows) ret;
        ret.clear(0);
        static foreach (c; 0 .. T.cols)
        {
            static foreach (r; 0 ..  T.rows)
            {
                ret._vector[r] += _vector[c] * rhs.at(r,c);
            }
        }
        return ret;
    }

    /** Multiply with left-hand-side `lhs`. */
    version(none)               // TODO: activate
    auto opBinaryRight(string op, T)(in T lhs) const
    if (!isInstanceOf!(Vector, T) &&
        !isMatrix!T &&
        !isQuaternion!T)
    {
        return this.opBinary!(op)(lhs);
    }

    /** TODO: Suitable Restrictions on F. */
    void opOpAssign(string op, F)(in F r)
        /* if ((op == "+") || (op == "-") || (op == "*") || (op == "%") || (op == "/") || (op == "^^")) */
    {
        static foreach (i; 0 .. dimension)
        {
            mixin("_vector[i]" ~ op ~ "= r;");
        }
    }
    unittest
    {
        auto v2 = vec2f(1, 3);
        v2 *= 5.0f; assert(v2[] == [5, 15].s);
        v2 ^^= 2; assert(v2[] == [25, 225].s);
        v2 /= 5; assert(v2[] == [5, 45].s);
    }

    void opOpAssign(string op)(in Vector r)
    if ((op == "+") ||
        (op == "-"))
    {
        static foreach (i; 0 .. dimension)
        {
            mixin("_vector[i]" ~ op ~ "= r._vector[i];");
        }
    }

    /// Returns: Non-Rooted `N` - Norm of `x`.
    auto nrnNorm(uint N)() const
    if (isNumeric!E && N >= 1)
    {
        static if (isFloatingPoint!E)
        {
            real y = 0;                 // TOREVIEW: Use maximum precision for now
        }
        else
        {
            E y = 0;                // TOREVIEW: Use other precision for now
        }
        static foreach (i; 0 .. D)
        {
            y += _vector[i] ^^ N;
        }
        return y;
    }

    /// Returns: Squared Magnitude of x.
    @property real magnitudeSquared()() const
    if (isNumeric!E)
    {
        static if (normalizedFlag) // cannot use normalized() here (yet)
        {
            return 1;
        }
        else
        {
            return nrnNorm!2;
        }
    }

    /// Returns: Magnitude of x.
    @property real magnitude()() const
    if (isNumeric!E)
    {
        static if (normalizedFlag) // cannot use normalized() here (yet)
        {
            return 1;
        }
        else
        {
            import std.math : sqrt;
            return sqrt(magnitudeSquared);
        }
    }
    alias norm = magnitude;

    static if (isFloatingPoint!E)
    {
        /// Normalize `this`.
        void normalize()()
        {
            if (this != 0)         // zero vector have zero magnitude
            {
                immutable m = this.magnitude;
                static foreach (i; 0 .. D)
                {
                    _vector[i] /= m;
                }
            }
        }

        /// Returns: normalizedFlag Copy of this Vector.
        @property Vector normalized()() const
        {
            Vector y = this;
            y.normalize();
            return y;
        }

        unittest
        {
            static if (D == 2 && !normalizedFlag)
            {
                assert(Vector(3, 4).magnitude == 5);
            }
        }
    }

    /// Returns: Vector Index at Character Coordinate `coord`.
    private @property ref inout(E) get_(char coord)() inout
    {
        return _vector[coordToIndex!coord];
    }

    /// Coordinate Character c to Index
    template coordToIndex(char c)
    {
        static if ((c == 'x'))
        {
            enum coordToIndex = 0;
        }
        else static if ((c == 'y'))
        {
            enum coordToIndex = 1;
        }
        else static if ((c == 'z'))
        {
            static assert(D >= 3, "The " ~ c ~ " property is only available on vectors with a third dimension.");
            enum coordToIndex = 2;
        }
        else static if ((c == 'w'))
        {
            static assert(D >= 4, "The " ~ c ~ " property is only available on vectors with a fourth dimension.");
            enum coordToIndex = 3;
        }
        else
        {
            static assert(0, "Accepted coordinates are x, s, r, u, y, g, t, v, z, p, b, w, q and a not " ~ c ~ ".");
        }
    }

    /// Updates the vector with the values from other.
    void update(in Vector!(E, D) other) { _vector = other._vector; }

    static if (D == 2)
    {
        void set(E x, E y)
        {
            _vector[0] = x;
            _vector[1] = y;
        }
    }
    else static if (D == 3)
    {
        void set(E x, E y, E z)
        {
            _vector[0] = x;
            _vector[1] = y;
            _vector[2] = z;
        }
    }
    else static if (D == 4)
    {
        void set(E x, E y, E z, E w)
        {
            _vector[0] = x;
            _vector[1] = y;
            _vector[2] = z;
            _vector[3] = w;
        }
    }

    static if (D >= 1) { alias x = get_!'x'; }
    static if (D >= 2) { alias y = get_!'y'; }
    static if (D >= 3) { alias z = get_!'z'; }
    static if (D >= 4) { alias w = get_!'w'; }

    static if (isNumeric!E)
    {
        /* Need these conversions when E is for instance ubyte.
           See this commit: https://github.com/Dav1dde/gl3n/commit/2504003df4f8a091e58a3d041831dc2522377f95 */
        static immutable E0 = E(0);
        static immutable E1 = E(1);
        static if (dimension == 2)
        {
            static immutable Vector e1 = Vector(E1, E0); /// canonical basis for Euclidian space
            static immutable Vector e2 = Vector(E0, E1); /// ditto
        }
        else static if (dimension == 3)
        {
            static immutable Vector e1 = Vector(E1, E0, E0); /// canonical basis for Euclidian space
            static immutable Vector e2 = Vector(E0, E1, E0); /// ditto
            static immutable Vector e3 = Vector(E0, E0, E1); /// ditto
        }
        else static if (dimension == 4)
        {
            static immutable Vector e1 = Vector(E1, E0, E0, E0); /// canonical basis for Euclidian space
            static immutable Vector e2 = Vector(E0, E1, E0, E0); /// ditto
            static immutable Vector e3 = Vector(E0, E0, E1, E0); /// ditto
            static immutable Vector e4 = Vector(E0, E0, E0, E1); /// ditto
        }
    }

    version(none)
    @safe pure nothrow @nogc unittest
    {
        static if (isNumeric!E)
        {
            assert(vec2.e1[] == [1, 0].s);
            assert(vec2.e2[] == [0, 1].s);

            assert(vec3.e1[] == [1, 0, 0].s);
            assert(vec3.e2[] == [0, 1, 0].s);
            assert(vec3.e3[] == [0, 0, 1].s);

            assert(vec4.e1[] == [1, 0, 0, 0].s);
            assert(vec4.e2[] == [0, 1, 0, 0].s);
            assert(vec4.e3[] == [0, 0, 1, 0].s);
            assert(vec4.e4[] == [0, 0, 0, 1].s);
        }
    }

    /** Element data. */
    E[D] _vector;

    unittest
    {
        // static if (isSigned!(E)) { assert(-Vector!(E,D)(+2),
        //                                   +Vector!(E,D)(-2)); }
    }

}

auto rowVector(Ts...)(Ts args)
if (!is(CommonType!Ts == void))
{
    return Vector!(CommonType!Ts, args.length)(args);
}
alias vector = rowVector; // TODO: Should rowVector or columnVector be default?

auto columnVector(Ts...)(Ts args)
if (!is(CommonType!Ts == void))
{
    return Vector!(CommonType!Ts, args.length, false, Orient.column)(args);
}

///
@safe pure nothrow @nogc unittest
{
    assert(point(1, 2) + vector(1, 2) == point(2, 4));
    assert(point(1, 2) - vector(1, 2) == point(0, 0));
}

version(unittest)
{
    import std.conv : to;
    import nxt.array_help : s;
}