j3ml/include/J3ML/LinearAlgebra/Matrix3x3.h

#pragma once

#include <J3ML/LinearAlgebra.h>
#include <J3ML/LinearAlgebra/Vector2.h>
#include <J3ML/LinearAlgebra/Vector3.h>
#include <J3ML/LinearAlgebra/Quaternion.h>

namespace LinearAlgebra {
    /// A 3-by-3 matrix for linear transformations of 3D geometry.
    /* This can represent any kind of linear transformations of 3D geometry, which include
     * rotation, scale, shear, mirroring, and orthographic projection.
     * A 3x3 matrix cannot represent translation, which requires a 3x4, or perspective projection (4x4).
     * The elements of this matrix are
     *  m_00, m_01, m_02
     *  m_10, m_11, m_12
     *  m_20, m_21, m_22
     *
     *  The element m_yx is the value on the row y and column x.
     *  You can access m_yx using the double-bracket notation m[y][x], or using the member function At.
     *
     *  @note The member functions in this class use the convention that transforms are applied to
     *  vectors in the form M * v. This means that "Matrix3x3 M, M1, M2; M = M1 * M2;" gives a transformation M
     *  that applies M2 first, followed by M1 second
     */
    class Matrix3x3 {
    public:
        enum { Rows = 3 };
        enum { Cols = 3 };

        static const Matrix3x3 Zero;
        static const Matrix3x3 Identity;
        static const Matrix3x3 NaN;

        Matrix3x3() {}
        Matrix3x3(float val);
        Matrix3x3(float m00, float m01, float m02, float m10, float m11, float m12, float m20, float m21, float m22);
        Matrix3x3(const Vector3& r1, const Vector3& r2, const Vector3& r3);
        explicit Matrix3x3(const Quaternion& orientation);

        static Matrix3x3 RotateX(float radians);
        static Matrix3x3 RotateY(float radians);
        static Matrix3x3 RotateZ(float radians);

        Vector3 GetRow(int index) const;
        Vector3 GetColumn(int index) const;

        float &At(int row, int col);
        float At(int x, int y) const;

        void SetRotatePart(const Vector3& a, float angle);

        /// Creates a new M3x3 that rotates about the given axis by the given angle
        static Matrix3x3 RotateAxisAngle(const Vector3& axis, float angleRadians);

        static Matrix3x3 RotateFromTo(const Vector3& source, const Vector3& direction)
        {

        }

        void SetRow(int i, const Vector3 &vector3);
        void SetColumn(int i, const Vector3& vector);
        void SetAt(int x, int y, float value);

        void Orthonormalize(int c0, int c1, int c2)
        {
            Vector3 v0 = GetColumn(c0);
            Vector3 v1 = GetColumn(c1);
            Vector3 v2 = GetColumn(c2);
            Vector3::Orthonormalize(v0, v1, v2);
            SetColumn(c0, v0);
            SetColumn(c1, v1);
            SetColumn(c2, v2);
        }

        static Matrix3x3 LookAt(const Vector3& forward, const Vector3& target, const Vector3& localUp, const Vector3& worldUp);

        static Matrix3x3 FromQuat(const Quaternion& orientation);

        Quaternion ToQuat() const;

        /// Creates a new Matrix3x3 as a combination of rotation and scale.
        // This function creates a new matrix M in the form M = R * S
        // where R is a rotation matrix and S is a scale matrix.
        // Transforming a vector v using this matrix computes the vector
        // v' == M * v == R*S*v == (R * (S * v)) which means the scale operation
        // is applied to the vector first, followed by rotation, and finally translation
        static Matrix3x3 FromRS(const Quaternion& rotate, const Vector3& scale);
        static Matrix3x3 FromRS(const Matrix3x3 &rotate, const Vector3& scale);


        /// Creates a new transformation matrix that scales by the given factors.
        // This matrix scales with respect to origin.
        static Matrix3x3 Scale(float sx, float sy, float sz);
        static Matrix3x3 Scale(const Vector3& scale);

        /// Returns the main diagonal.
        Vector3 Diagonal() const;
        /// Returns the local +X/+Y/+Z axis in world space.
        /// This is the same as transforming the vector{1,0,0} by this matrix.
        Vector3 WorldX() const;
        /// Returns the local +Y axis in world space.
        /// This is the same as transforming the vector{0,1,0} by this matrix.
        Vector3 WorldY() const;
        /// Returns the local +Z axis in world space.
        /// This is the same as transforming the vector{0,0,1} by this matrix.
        Vector3 WorldZ() const;

        /// Computes the determinant of this matrix.
        // If the determinant is nonzero, this matrix is invertible.
        // If the determinant is negative, this matrix performs reflection about some axis.
        // From http://msdn.microsoft.com/en-us/library/bb204853(VS.85).aspx :
        // "If the determinant is positive, the basis is said to be "positively" oriented (or right-handed).
        // If the determinant is negative, the basis is said to be "negatively" oriented (or left-handed)."
        // @note This function computes 9 LOADs, 9 MULs and 5 ADDs. */
        float Determinant() const;

        // Returns an inverted copy of this matrix. This
        Matrix3x3 Inverse() const;

        // Returns a transposed copy of this matrix.
        Matrix3x3 Transpose() const;

        // Transforms the given vectors by this matrix M, i.e. returns M * (x,y,z)
        Vector2 Transform(const Vector2& rhs) const;
        Vector3 Transform(const Vector3& rhs) const;

        Vector3 operator[](int row) const
        {
            return Vector3{elems[row][0], elems[row][1], elems[row][2]};
        }

        Vector3 operator * (const Vector3& rhs) const;
        Matrix3x3 operator * (const Matrix3x3& rhs) const;

    protected:
        float elems[3][3];
    };
}