{$IF DEFINED(__MATRIX_HELPER_INTERFACE)}
  type __HELPER = type helper for __MAT
  public const
    {$IF __SIZE = 2}
      Identity: __MAT = ((1, 0), (0, 1));
    {$ELSEIF __SIZE = 3}
      Identity: __MAT = ((1, 0, 0), (0, 1, 0), (0, 0, 1));
    {$ELSEIF __SIZE = 4}
      Identity: __MAT = ((1, 0, 0, 0), (0, 1, 0, 0), (0, 0, 1, 0), (0, 0, 0, 1));
    {$ELSE}
      {$ERROR only vectors of size 2, 3 or 4 are supported}
    {$ENDIF}
  public
    function ToString(const aRound: Integer = -3): String; inline;
    function Transpose: __MAT; inline;
    function Determinant: Double; inline;
    function Invert: __MAT; inline;
    function Multiply(const m: __MAT): __MAT; inline;

    class function TryFromString(const s: String; out m: __MAT): Boolean; inline; static;
    class function FromString(const s: String): __MAT; inline; static;

    {$IF __SIZE = 3}
      function AxisX: __VEC3; inline;
      function AxisY: __VEC3; inline;
      function Position: __VEC3; inline;

      function Sub(const aCol, aRow: Integer): __IMPL.TMat2; inline;
      function Adjoint: __MAT; inline;
      function Translate(const v: __VEC2): __MAT; inline;
      function Translate(const x, y: __IMPL.TBaseType): __MAT; inline;
      function Scale(const v: __VEC2): __MAT; inline;
      function Scale(const v: __IMPL.TBaseType): __MAT; inline;
      function Shear(const v: __VEC2): __MAT; inline;
      function Shear(const x, y: __IMPL.TBaseType): __MAT; inline;
      function Rotate(const a: Double): __MAT; inline;

      class function Create(const x, y, z: __VEC3): __MAT; inline; static;
      class function CreateTranslate(const v: __VEC2): __MAT; inline; static;
      class function CreateTranslate(const x, y: __IMPL.TBaseType): __MAT; inline; static;
      class function CreateScale(const v: __VEC2): __MAT; inline; static;
      class function CreateScale(const v: __IMPL.TBaseType): __MAT; inline; static;
      class function CreateShear(const v: __VEC2): __MAT; inline; static;
      class function CreateShear(const x, y: __IMPL.TBaseType): __MAT; inline; static;
      class function CreateRotate(const a: Double): __MAT; inline; static;
    {$ELSEIF __SIZE = 4}
      function AxisX: __VEC4; inline;
      function AxisY: __VEC4; inline;
      function AxisZ: __VEC4; inline;
      function Position: __VEC4; inline;

      function Sub(const aCol, aRow: Integer): __IMPL.TMat3; inline;
      function Adjoint: __MAT; inline;
      function Translate(const v: __VEC3): __MAT; inline;
      function Translate(const x, y, z: __IMPL.TBaseType): __MAT; inline;
      function Scale(const v: __VEC3): __MAT; inline;
      function Scale(const v: __IMPL.TBaseType): __MAT; inline;
      function Rotate(const axis: __VEC3; const a: Double): __MAT; inline;

      class function Create(const x, y, z, w: __VEC4): __MAT; inline; static;
      class function CreateTranslate(const v: __VEC3): __MAT; inline; static;
      class function CreateTranslate(const x, y, z: __IMPL.TBaseType): __MAT; inline; static;
      class function CreateScale(const v: __VEC3): __MAT; inline; static;
      class function CreateScale(const v: __IMPL.TBaseType): __MAT; inline; static;
      class function CreateShear(const x, y, z: __VEC2): __MAT; inline; static;
      class function CreateShear(const xy, xz, yx, yz, zx, zy: __IMPL.TBaseType): __MAT; inline; static;
      class function CreateRotate(const axis: __VEC3; const a: Double): __MAT; inline; static;
    {$ENDIF}
  end;

  operator = (const m1, m2: __MAT): Boolean; inline;
  operator * (const m1, m2: __MAT): __MAT; inline;
  operator * (const m: __MAT; const v: __VEC): __VEC; inline;
  operator * (const s: __IMPL.TBaseType; const m: __MAT): __MAT; inline;
  operator * (const m: __MAT; const s: __IMPL.TBaseType): __MAT; inline;
{$ELSEIF DEFINED (__MATRIX_HELPER_IMPL)}
  operator = (const m1, m2: __MAT): Boolean;
  begin
    result := __IMPL.Equals(m1, m2);
  end;

  operator * (const m1, m2: __MAT): __MAT;
  begin
    result := __IMPL.Multiply(m1, m2);
  end;

  operator * (const m: __MAT; const v: __VEC): __VEC;
  begin
    result := __IMPL.Multiply(m, v);
  end;

  operator * (const s: __IMPL.TBaseType; const m: __MAT): __MAT;
  begin
    result := __IMPL.Multiply(m, s);
  end;

  operator * (const m: __MAT; const s: __IMPL.TBaseType): __MAT;
  begin
    result := __IMPL.Multiply(m, s);
  end;

  function __HELPER.ToString(const aRound: Integer = -3): String;
  begin
    result := __IMPL.ToString(self, aRound);
  end;

  function __HELPER.Transpose: __MAT;
  begin
    result := __IMPL.Transpose(self);
  end;

  function __HELPER.Determinant: Double;
  begin
    result := __IMPL.Determinant(self);
  end;

  function __HELPER.Invert: __MAT;
  begin
    result := __IMPL.Invert(self);
  end;

  function __HELPER.Multiply(const m: __MAT): __MAT;
  begin
    result := __IMPL.Multiply(self, m);
  end;

  class function __HELPER.TryFromString(const s: String; out m: __MAT): Boolean;
  begin
    result := __IMPL.TryFromString(s, m);
  end;

  class function __HELPER.FromString(const s: String): __MAT;
  begin
    if not __IMPL.TryFromString(s, result) then
      result := Identity;
  end;

  {$IF __SIZE = 3}
    function __HELPER.AxisX: __VEC3;
    begin
      result := self[0];
    end;

    function __HELPER.AxisY: __VEC3;
    begin
      result := self[1];
    end;

    function __HELPER.Position: __VEC3;
    begin
      result := self[2];
    end;

    function __HELPER.Sub(const aCol, aRow: Integer): __IMPL.TMat2;
    begin
      result := __IMPL.Sub(self, aCol, aRow);
    end;

    function __HELPER.Adjoint: __MAT;
    begin
      result := __IMPL.Adjoint(self);
    end;

    function __HELPER.Translate(const v: __VEC2): __MAT;
    begin
      result := __IMPL.Multiply(self, __IMPL.CreateTranslate(v));
    end;

    function __HELPER.Translate(const x, y: __IMPL.TBaseType): __MAT;
    begin
      result := __IMPL.Multiply(self, __IMPL.CreateTranslate(__IMPL.TVectorHelper.Vector2(x, y)));
    end;

    function __HELPER.Scale(const v: __VEC2): __MAT;
    begin
      result := __IMPL.Multiply(self, __IMPL.CreateScale(v));
    end;

    function __HELPER.Scale(const v: __IMPL.TBaseType): __MAT;
    begin
      result := __IMPL.Multiply(self, __IMPL.CreateScale(__IMPL.TVectorHelper.Vector2(v, v)));
    end;

    function __HELPER.Shear(const v: __VEC2): __MAT;
    begin
      result := __IMPL.Multiply(self, __IMPL.CreateShear(v));
    end;

    function __HELPER.Shear(const x, y: __IMPL.TBaseType): __MAT;
    begin
      result := __IMPL.Multiply(self, __IMPL.CreateShear(__IMPL.TVectorHelper.Vector2(x, y)));
    end;

    function __HELPER.Rotate(const a: Double): __MAT;
    begin
      result := __IMPL.Multiply(self, __IMPL.CreateRotate(a));
    end;

    class function __HELPER.Create(const x, y, z: __VEC3): __MAT;
    begin
      result := __IMPL.Create(x, y, z);
    end;

    class function __HELPER.CreateTranslate(const v: __VEC2): __MAT;
    begin
      result := __IMPL.CreateTranslate(v);
    end;

    class function __HELPER.CreateTranslate(const x, y: __IMPL.TBaseType): __MAT;
    begin
      result := __IMPL.CreateTranslate(__IMPL.TVectorHelper.Vector2(x, y));
    end;

    class function __HELPER.CreateScale(const v: __VEC2): __MAT;
    begin
      result := __IMPL.CreateScale(v);
    end;

    class function __HELPER.CreateScale(const v: __IMPL.TBaseType): __MAT;
    begin
      result := __IMPL.CreateScale(__IMPL.TVectorHelper.Vector2(v, v));
    end;

    class function __HELPER.CreateShear(const v: __VEC2): __MAT;
    begin
      result := __IMPL.CreateShear(v);
    end;

    class function __HELPER.CreateShear(const x, y: __IMPL.TBaseType): __MAT;
    begin
      result := __IMPL.CreateShear(__IMPL.TVectorHelper.Vector2(x, y));
    end;

    class function __HELPER.CreateRotate(const a: Double): __MAT;
    begin
      result := __IMPL.CreateRotate(a);
    end;
  {$ELSEIF __SIZE = 4}
    function __HELPER.AxisX: __VEC4;
    begin
      result := self[0];
    end;

    function __HELPER.AxisY: __VEC4;
    begin
      result := self[1];
    end;

    function __HELPER.AxisZ: __VEC4;
    begin
      result := self[2];
    end;

    function __HELPER.Position: __VEC4;
    begin
      result := self[3];
    end;

    function __HELPER.Sub(const aCol, aRow: Integer): __IMPL.TMat3;
    begin
      result := __IMPL.Sub(self, aRow, aCol);
    end;

    function __HELPER.Adjoint: __MAT;
    begin
      result := __IMPL.Adjoint(self);
    end;

    function __HELPER.Translate(const v: __VEC3): __MAT;
    begin
      result := __IMPL.Multiply(self, __IMPL.CreateTranslate(v));
    end;

    function __HELPER.Translate(const x, y, z: __IMPL.TBaseType): __MAT;
    begin
      result := __IMPL.Multiply(self, __IMPL.CreateTranslate(__IMPL.TVectorHelper.Vector3(x, y, z)));
    end;

    function __HELPER.Scale(const v: __VEC3): __MAT;
    begin
      result := __IMPL.Multiply(self, __IMPL.CreateScale(v));
    end;

    function __HELPER.Scale(const v: __IMPL.TBaseType): __MAT;
    begin
      result := __IMPL.Multiply(self, __IMPL.CreateScale(__IMPL.TVectorHelper.Vector3(v, v, v)));
    end;

    function __HELPER.Rotate(const axis: __VEC3; const a: Double): __MAT;
    begin
      result := __IMPL.Multiply(self, __IMPL.CreateRotate(axis, a));
    end;

    class function __HELPER.Create(const x, y, z, w: __VEC4): __MAT;
    begin
      result := __IMPL.Create(x, y, z, w);
    end;

    class function __HELPER.CreateTranslate(const v: __VEC3): __MAT;
    begin
      result := __IMPL.CreateTranslate(v);
    end;

    class function __HELPER.CreateTranslate(const x, y, z: __IMPL.TBaseType): __MAT;
    begin
      result := __IMPL.CreateTranslate(__IMPL.TVectorHelper.Vector3(x, y, z));
    end;

    class function __HELPER.CreateScale(const v: __VEC3): __MAT;
    begin
      result := __IMPL.CreateScale(v);
    end;

    class function __HELPER.CreateScale(const v: __IMPL.TBaseType): __MAT;
    begin
      result := __IMPL.CreateScale(__IMPL.TVectorHelper.Vector3(v, v, v));
    end;

    class function __HELPER.CreateShear(const x, y, z: __VEC2): __MAT;
    begin
      result := __IMPL.CreateShear(x, y, z);
    end;

    class function __HELPER.CreateShear(const xy, xz, yx, yz, zx, zy: __IMPL.TBaseType): __MAT;
    begin
      result := __IMPL.CreateShear(
        __IMPL.TVectorHelper.Vector2(xy, xz),
        __IMPL.TVectorHelper.Vector2(yx, yz),
        __IMPL.TVectorHelper.Vector2(zx, zy));
    end;

    class function __HELPER.CreateRotate(const axis: __VEC3; const a: Double): __MAT;
    begin
      result := __IMPL.CreateRotate(axis, a);
    end;
  {$ENDIF}
{$ENDIF}

{$UNDEF __IMPL}
{$UNDEF __SIZE}
{$UNDEF __VEC}
{$UNDEF __MAT}
{$UNDEF __HELPER}