module matrix_2d;

import Math = math;
import MemUtil = mem_util;

import matrix_3d;
import matrix_3x2d;

import vector_2d;


/*
 * The MIT License
 *
 * Copyright (c) 2020-2021 JOML
 %%$%# translated by jordan4ibanez
 *
 * Permission is hereby granted, free of charge, to any person obtaining a copy
 * of this software and associated documentation files (the "Software"), to deal
 * in the Software without restriction, including without limitation the rights
 * to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
 * copies of the Software, and to permit persons to whom the Software is
 * furnished to do so, subject to the following conditions:
 *
 * The above copyright notice and this permission notice shall be included in
 * all copies or substantial portions of the Software.
 *
 * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
 * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
 * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
 * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
 * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
 * OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
 * THE SOFTWARE.
 */


/**
 * Contains the definition of a 2x2 matrix of doubles, and associated functions to transform
 * it. The matrix is column-major to match OpenGL's interpretation, and it looks like this:
 * <p>
 *      m00  m10<br>
 *      m01  m11<br>
 *
 * @author Joseph Burton
 */
public struct Matrix2d {

    // Defaults to identity
    double m00 = 1.0;
    double m01 = 0.0;
    double m10 = 0.0;
    double m11 = 1.0;


    /**
     * Create a new {@link Matrix2d} and make it a copy of the given matrix.
     *
     * @param mat
     *          the {@link Matrix2d} to copy the values from
     */
    this(Matrix2d mat) {
        setMatrix2d(mat);
    }


    /**
     * Create a new {@link Matrix2d} and make it a copy of the upper left 2x2 of the given {@link Matrix3d}.
     *
     * @param mat
     *          the {@link Matrix3d} to copy the values from
     */
    this(Matrix3d mat) {
        setMatrix3d(mat);
    }


    /**
     * Create a new 2x2 matrix using the supplied double values. The order of the parameter is column-major,
     * so the first two parameters specify the two elements of the first column.
     *
     * @param m00
     *          the value of m00
     * @param m01
     *          the value of m01
     * @param m10
     *          the value of m10
     * @param m11
     *          the value of m11
     */
    this(double m00, double m01,
                    double m10, double m11) {
        this.m00 = m00;
        this.m01 = m01;
        this.m10 = m10;
        this.m11 = m11;
    }

    /**
     * Create a new {@link Matrix2d} and initialize its two columns using the supplied vectors.
     *
     * @param col0
     *          the first column
     * @param col1
     *          the second column
     */
    this(Vector2d col0, Vector2d col1) {
        m00 = col0.x;
        m01 = col0.y;
        m10 = col1.x;
        m11 = col1.y;
    }

    /**
     * Set the value of the matrix element at column 0 and row 0.
     *
     * @param m00
     *          the new value
     * @return this
     */
    ref public Matrix2d setm00(double m00) return {
        this.m00 = m00;
        return this;
    }
    /**
     * Set the value of the matrix element at column 0 and row 1.
     *
     * @param m01
     *          the new value
     * @return this
     */
    ref public Matrix2d setm01(double m01) return {
        this.m01 = m01;
        return this;
    }
    /**
     * Set the value of the matrix element at column 1 and row 0.
     *
     * @param m10
     *          the new value
     * @return this
     */
    ref public Matrix2d setm10(double m10) return {
        this.m10 = m10;
        return this;
    }
    /**
     * Set the value of the matrix element at column 1 and row 1.
     *
     * @param m11
     *          the new value
     * @return this
     */
    ref public Matrix2d setm11(double m11) return {
        this.m11 = m11;
        return this;
    }

    /**
     * Set the value of the matrix element at column 0 and row 0.
     *
     * @param m00
     *          the new value
     * @return this
     */
    ref Matrix2d _m00(double m00) return {
        this.m00 = m00;
        return this;
    }
    /**
     * Set the value of the matrix element at column 0 and row 1.
     *
     * @param m01
     *          the new value
     * @return this
     */
    ref Matrix2d _m01(double m01) return {
        this.m01 = m01;
        return this;
    }
    /**
     * Set the value of the matrix element at column 1 and row 0.
     *
     * @param m10
     *          the new value
     * @return this
     */
    ref Matrix2d _m10(double m10) return {
        this.m10 = m10;
        return this;
    }
    /**
     * Set the value of the matrix element at column 1 and row 1.
     *
     * @param m11
     *          the new value
     * @return this
     */
    ref Matrix2d _m11(double m11) return {
        this.m11 = m11;
        return this;
    }

    /**
     * Set the elements of this matrix to the ones in <code>m</code>.
     *
     * @param m
     *          the matrix to copy the elements from
     * @return this
     */
    ref public Matrix2d set(Matrix2d m) return {
        setMatrix2d(m);
        return this;
    }
    private void setMatrix2d(Matrix2d mat) {
        m00 = mat.m00;
        m01 = mat.m01;
        m10 = mat.m10;
        m11 = mat.m11;
    }


    /**
     * Set the elements of this matrix to the left 2x2 submatrix of <code>m</code>.
     *
     * @param m
     *          the matrix to copy the elements from
     * @return this
     */
    ref public Matrix2d set(Matrix3x2d m) return {
        setMatrix3x2d(m);
        return this;
    }
    private void setMatrix3x2d(Matrix3x2d mat) {
        m00 = mat.m00;
        m01 = mat.m01;
        m10 = mat.m10;
        m11 = mat.m11;
    }

    /**
     * Set the elements of this matrix to the upper left 2x2 of the given {@link Matrix3d}.
     *
     * @param m
     *          the {@link Matrix3d} to copy the values from
     * @return this
     */
    ref public Matrix2d set(Matrix3d m) return {
        setMatrix3d(m);
        return this;
    }
    private void setMatrix3d(Matrix3d mat) {
        m00 = mat.m00;
        m01 = mat.m01;
        m10 = mat.m10;
        m11 = mat.m11;
    }


    /**
     * Multiply this matrix by the supplied <code>right</code> matrix.
     * <p>
     * If <code>M</code> is <code>this</code> matrix and <code>R</code> the <code>right</code> matrix,
     * then the new matrix will be <code>M * R</code>. So when transforming a
     * vector <code>v</code> with the new matrix by using <code>M * R * v</code>, the
     * transformation of the right matrix will be applied first!
     *
     * @param right
     *          the right operand of the matrix multiplication
     * @return this
     */
    ref public Matrix2d mul(Matrix2d right) return {
        this.mul(right, this);
        return this;
    }

    public Matrix2d mul(Matrix2d right, ref Matrix2d dest) {
        double nm00 = m00 * right.m00 + m10 * right.m01;
        double nm01 = m01 * right.m00 + m11 * right.m01;
        double nm10 = m00 * right.m10 + m10 * right.m11;
        double nm11 = m01 * right.m10 + m11 * right.m11;
        dest.m00 = nm00;
        dest.m01 = nm01;
        dest.m10 = nm10;
        dest.m11 = nm11;
        return dest;
    }

    /**
     * Pre-multiply this matrix by the supplied <code>left</code> matrix and store the result in <code>this</code>.
     * <p>
     * If <code>M</code> is <code>this</code> matrix and <code>L</code> the <code>left</code> matrix,
     * then the new matrix will be <code>L * M</code>. So when transforming a
     * vector <code>v</code> with the new matrix by using <code>L * M * v</code>, the
     * transformation of <code>this</code> matrix will be applied first!
     *
     * @param left
     *          the left operand of the matrix multiplication
     * @return this
     */
    ref public Matrix2d mulLocal(Matrix2d left) return {
        this.mulLocal(left, this);
        return this;
    }

    public Matrix2d mulLocal(Matrix2d left, ref Matrix2d dest) {
        double nm00 = left.m00 * m00 + left.m10 * m01;
        double nm01 = left.m01 * m00 + left.m11 * m01;
        double nm10 = left.m00 * m10 + left.m10 * m11;
        double nm11 = left.m01 * m10 + left.m11 * m11;
        dest.m00 = nm00;
        dest.m01 = nm01;
        dest.m10 = nm10;
        dest.m11 = nm11;
        return dest;
    }

    /**
     * Set the values within this matrix to the supplied double values. The result looks like this:
     * <p>
     * m00, m10<br>
     * m01, m11<br>
     *
     * @param m00
     *          the new value of m00
     * @param m01
     *          the new value of m01
     * @param m10
     *          the new value of m10
     * @param m11
     *          the new value of m11
     * @return this
     */
    ref public Matrix2d set(double m00, double m01,
                        double m10, double m11) return {
        this.m00 = m00;
        this.m01 = m01;
        this.m10 = m10;
        this.m11 = m11;
        return this;
    }
    /**
     * Set the two columns of this matrix to the supplied vectors, respectively.
     *
     * @param col0
     *          the first column
     * @param col1
     *          the second column
     * @return this
     */
    ref public Matrix2d set(Vector2d col0, Vector2d col1) return {
        m00 = col0.x;
        m01 = col0.y;
        m10 = col1.x;
        m11 = col1.y;
        return this;
    }

    public double determinant() {
        return m00 * m11 - m10 * m01;
    }

    /**
     * Invert this matrix.
     *
     * @return this
     */
    ref public Matrix2d invert() return {
        this.invert(this);
        return this;
    }

    public Matrix2d invert(ref Matrix2d dest) {
        double s = 1.0 / determinant();
        double nm00 = m11 * s;
        double nm01 = -m01 * s;
        double nm10 = -m10 * s;
        double nm11 = m00 * s;
        dest.m00 = nm00;
        dest.m01 = nm01;
        dest.m10 = nm10;
        dest.m11 = nm11;
        return dest;
    }

    /**
     * Transpose this matrix.
     *
     * @return this
     */
    ref public Matrix2d transpose() return {
        this.transpose(this);
        return this;
    }

    public Matrix2d transpose(ref Matrix2d dest) {
        dest.set(m00, m10,
                m01, m11);
        return dest;
    }

   
    /**
     * Get the current values of <code>this</code> matrix and store them into
     * <code>dest</code>.
     * <p>
     * This is the reverse method of {@link #set(Matrix2d)} and allows to obtain
     * intermediate calculation results when chaining multiple transformations.
     *
     * @see #set(Matrix2d)
     *
     * @param dest
     *          the destination matrix
     * @return the passed in destination
     */
    public Matrix2d get(ref Matrix2d dest) {
        return dest.set(this);
    }

    public Matrix3x2d get(ref Matrix3x2d dest) {
        return dest.set(this);
    }

    public Matrix3d get(ref Matrix3d dest) {
        return dest.set(this);
    }

    public double getRotation() {
        return cast(double) Math.atan2(m01, m11);
    }

    /**
     * Set all values within this matrix to zero.
     *
     * @return this
     */
    ref public Matrix2d zero() return {
        MemUtil.zero(this);
        return this;
    }

    /**
     * Set this matrix to the identity.
     *
     * @return this
     */
    ref public Matrix2d identity() return {
        m00 = 1.0;
        m01 = 0.0;
        m10 = 0.0;
        m11 = 1.0;
        return this;
    }

    public Matrix2d scale(Vector2d xy, ref Matrix2d dest) {
        return scale(xy.x, xy.y, dest);
    }

    /**
     * Apply scaling to this matrix by scaling the base axes by the given <code>xy.x</code> and
     * <code>xy.y</code> factors, respectively.
     * <p>
     * If <code>M</code> is <code>this</code> matrix and <code>S</code> the scaling matrix,
     * then the new matrix will be <code>M * S</code>. So when transforming a
     * vector <code>v</code> with the new matrix by using <code>M * S * v</code>, the
     * scaling will be applied first!
     *
     * @param xy
     *            the factors of the x and y component, respectively
     * @return this
     */
    ref public Matrix2d scale(Vector2d xy) return {
        this.scale(xy.x, xy.y, this);
        return this;
    }

    public Matrix2d scale(double x, double y, ref Matrix2d dest) {
        // scale matrix elements:
        // m00 = x, m11 = y
        // all others = 0
        dest.m00 = m00 * x;
        dest.m01 = m01 * x;
        dest.m10 = m10 * y;
        dest.m11 = m11 * y;
        return dest;
    }

    /**
     * Apply scaling to this matrix by scaling the base axes by the given x and
     * y factors.
     * <p>
     * If <code>M</code> is <code>this</code> matrix and <code>S</code> the scaling matrix,
     * then the new matrix will be <code>M * S</code>. So when transforming a
     * vector <code>v</code> with the new matrix by using <code>M * S * v</code>
     * , the scaling will be applied first!
     *
     * @param x
     *            the factor of the x component
     * @param y
     *            the factor of the y component
     * @return this
     */
    ref public Matrix2d scale(double x, double y) return {
        this.scale(x, y, this);
        return this;
    }

    public Matrix2d scale(double xy, ref Matrix2d dest) {
        return scale(xy, xy, dest);
    }

    /**
     * Apply scaling to this matrix by uniformly scaling all base axes by the given <code>xy</code> factor.
     * <p>
     * If <code>M</code> is <code>this</code> matrix and <code>S</code> the scaling matrix,
     * then the new matrix will be <code>M * S</code>. So when transforming a
     * vector <code>v</code> with the new matrix by using <code>M * S * v</code>
     * , the scaling will be applied first!
     *
     * @see #scale(double, double)
     *
     * @param xy
     *            the factor for all components
     * @return this
     */
    ref public Matrix2d scale(double xy) return {
        return scale(xy, xy);
    }

    public Matrix2d scaleLocal(double x, double y, ref Matrix2d dest) {
        dest.m00 = x * m00;
        dest.m01 = y * m01;
        dest.m10 = x * m10;
        dest.m11 = y * m11;
        return dest;
    }

    /**
     * Pre-multiply scaling to this matrix by scaling the base axes by the given x and
     * y factors.
     * <p>
     * If <code>M</code> is <code>this</code> matrix and <code>S</code> the scaling matrix,
     * then the new matrix will be <code>S * M</code>. So when transforming a
     * vector <code>v</code> with the new matrix by using <code>S * M * v</code>, the
     * scaling will be applied last!
     *
     * @param x
     *            the factor of the x component
     * @param y
     *            the factor of the y component
     * @return this
     */
    ref public Matrix2d scaleLocal(double x, double y) return {
        this.scaleLocal(x, y, this);
        return this;
    }

    /**
     * Set this matrix to be a simple scale matrix, which scales all axes uniformly by the given factor.
     * <p>
     * The resulting matrix can be multiplied against another transformation
     * matrix to obtain an additional scaling.
     * <p>
     * In order to post-multiply a scaling transformation directly to a
     * matrix, use {@link #scale(double) scale()} instead.
     *
     * @see #scale(double)
     *
     * @param factor
     *             the scale factor in x and y
     * @return this
     */
    ref public Matrix2d scaling(double factor) return {
        MemUtil.zero(this);
        m00 = factor;
        m11 = factor;
        return this;
    }

    /**
     * Set this matrix to be a simple scale matrix.
     *
     * @param x
     *             the scale in x
     * @param y
     *             the scale in y
     * @return this
     */
    ref public Matrix2d scaling(double x, double y) return {
        MemUtil.zero(this);
        m00 = x;
        m11 = y;
        return this;
    }

    /**
     * Set this matrix to be a simple scale matrix which scales the base axes by <code>xy.x</code> and <code>xy.y</code> respectively.
     * <p>
     * The resulting matrix can be multiplied against another transformation
     * matrix to obtain an additional scaling.
     * <p>
     * In order to post-multiply a scaling transformation directly to a
     * matrix use {@link #scale(Vector2d) scale()} instead.
     *
     * @see #scale(Vector2d)
     *
     * @param xy
     *             the scale in x and y respectively
     * @return this
     */
    ref public Matrix2d scaling(Vector2d xy) return {
        return scaling(xy.x, xy.y);
    }

    /**
     * Set this matrix to a rotation matrix which rotates the given radians about the origin.
     * <p>
     * The produced rotation will rotate a vector counter-clockwise around the origin.
     * <p>
     * The resulting matrix can be multiplied against another transformation
     * matrix to obtain an additional rotation.
     * <p>
     * In order to post-multiply a rotation transformation directly to a
     * matrix, use {@link #rotate(double) rotate()} instead.
     *
     * @see #rotate(double)
     *
     * @param angle
     *          the angle in radians
     * @return this
     */
    ref public Matrix2d rotation(double angle) return {
        double sin = Math.sin(angle);
        double cos = Math.cosFromSin(sin, angle);
        m00 = cos;
        m01 = sin;
        m10 = -sin;
        m11 = cos;
        return this;
    }

    public Vector2d transform(Vector2d v) {
        return v.mul(this);
    }

    public Vector2d transform(Vector2d v, ref Vector2d dest) {
        v.mul(this, dest);
        return dest;
    }

    public Vector2d transform(double x, double y, ref Vector2d dest) {
        dest.set(m00 * x + m10 * y,
                m01 * x + m11 * y);
        return dest;
    }

    public Vector2d transformTranspose(Vector2d v) {
        return v.mulTranspose(this);
    }

    public Vector2d transformTranspose(Vector2d v, ref Vector2d dest) {
        v.mulTranspose(this, dest);
        return dest;
    }

    public Vector2d transformTranspose(double x, double y, ref Vector2d dest) {
        dest.set(m00 * x + m01 * y,
                m10 * x + m11 * y);
        return dest;
    }

    /**
     * Apply rotation about the origin to this matrix by rotating the given amount of radians.
     * <p>
     * The produced rotation will rotate a vector counter-clockwise around the origin.
     * <p>
     * If <code>M</code> is <code>this</code> matrix and <code>R</code> the rotation matrix,
     * then the new matrix will be <code>M * R</code>. So when transforming a
     * vector <code>v</code> with the new matrix by using <code>M * R * v</code>
     * , the rotation will be applied first!
     * <p>
     * Reference: <a href="https://en.wikipedia.org/wiki/Rotation_matrix#In_two_dimensions">http://en.wikipedia.org</a>
     *
     * @param angle
     *            the angle in radians
     * @return this
     */
    ref public Matrix2d rotate(double angle) return {
        this.rotate(angle, this);
        return this;
    }

    public Matrix2d rotate(double angle, ref Matrix2d dest) {
        double s = Math.sin(angle);
        double c = Math.cosFromSin(s, angle);
        // rotation matrix elements:
        // m00 = c, m01 = s, m10 = -s, m11 = c
        double nm00 = m00 * c + m10 * s;
        double nm01 = m01 * c + m11 * s;
        double nm10 = m10 * c - m00 * s;
        double nm11 = m11 * c - m01 * s;
        dest.m00 = nm00;
        dest.m01 = nm01;
        dest.m10 = nm10;
        dest.m11 = nm11;
        return dest;
    }

    /**
     * Pre-multiply a rotation to this matrix by rotating the given amount of radians about the origin.
     * <p>
     * The produced rotation will rotate a vector counter-clockwise around the origin.
     * <p>
     * If <code>M</code> is <code>this</code> matrix and <code>R</code> the rotation matrix,
     * then the new matrix will be <code>R * M</code>. So when transforming a
     * vector <code>v</code> with the new matrix by using <code>R * M * v</code>, the
     * rotation will be applied last!
     * <p>
     * In order to set the matrix to a rotation matrix without pre-multiplying the rotation
     * transformation, use {@link #rotation(double) rotation()}.
     * <p>
     * Reference: <a href="https://en.wikipedia.org/wiki/Rotation_matrix#In_two_dimensions">http://en.wikipedia.org</a>
     *
     * @see #rotation(double)
     *
     * @param angle
     *            the angle in radians to rotate about the X axis
     * @return this
     */
    ref public Matrix2d rotateLocal(double angle) return {
        this.rotateLocal(angle, this);
        return this;
    }

    public Matrix2d rotateLocal(double angle, ref Matrix2d dest) {
        double s = Math.sin(angle);
        double c = Math.cosFromSin(s, angle);
        // rotation matrix elements:
        // m00 = c, m01 = s, m10 = -s, m11 = c
        double nm00 = c * m00 - s * m01;
        double nm01 = s * m00 + c * m01;
        double nm10 = c * m10 - s * m11;
        double nm11 = s * m10 + c * m11;
        dest.m00 = nm00;
        dest.m01 = nm01;
        dest.m10 = nm10;
        dest.m11 = nm11;
        return dest;
    }

    public Vector2d getRow(int row, ref Vector2d dest) {
        switch (row) {
            case 0:
                dest.x = m00;
                dest.y = m10;
                break;
            case 1:
                dest.x = m01;
                dest.y = m11;
                break;
            default: {}
        }
        return dest;
    }

    /**
     * Set the row at the given <code>row</code> index, starting with <code>0</code>.
     *
     * @param row
     *          the row index in <code>[0..1]</code>
     * @param src
     *          the row components to set
     * @return this
     * @throws IndexOutOfBoundsException if <code>row</code> is not in <code>[0..1]</code>
     */
    ref public Matrix2d setRow(int row, Vector2d src) return {
        return setRow(row, src.x, src.y);
    }

    /**
     * Set the row at the given <code>row</code> index, starting with <code>0</code>.
     *
     * @param row
     *          the row index in <code>[0..1]</code>
     * @param x
     *          the first element in the row
     * @param y
     *          the second element in the row
     * @return this
     * @throws IndexOutOfBoundsException if <code>row</code> is not in <code>[0..1]</code>
     */
    ref public Matrix2d setRow(int row, double x, double y) return {
        switch (row) {
            case 0:
                this.m00 = x;
                this.m10 = y;
                break;
            case 1:
                this.m01 = x;
                this.m11 = y;
                break;
            default:{}
        }
        return this;
    }

    public Vector2d getColumn(int column, ref Vector2d dest){
        switch (column) {
            case 0:
                dest.x = m00;
                dest.y = m01;
                break;
            case 1:
                dest.x = m10;
                dest.y = m11;
                break;
            default:{}
        }
        return dest;
    }

    /**
     * Set the column at the given <code>column</code> index, starting with <code>0</code>.
     *
     * @param column
     *          the column index in <code>[0..1]</code>
     * @param src
     *          the column components to set
     * @return this
     * @throws IndexOutOfBoundsException if <code>column</code> is not in <code>[0..1]</code>
     */
    ref public Matrix2d setColumn(int column, Vector2d src) return {
        return setColumn(column, src.x, src.y);
    }

    /**
     * Set the column at the given <code>column</code> index, starting with <code>0</code>.
     *
     * @param column
     *          the column index in <code>[0..1]</code>
     * @param x
     *          the first element in the column
     * @param y
     *          the second element in the column
     * @return this
     * @throws IndexOutOfBoundsException if <code>column</code> is not in <code>[0..1]</code>
     */
    ref public Matrix2d setColumn(int column, double x, double y) return {
        switch (column) {
            case 0:
                this.m00 = x;
                this.m01 = y;
                break;
            case 1:
                this.m10 = x;
                this.m11 = y;
                break;
            default: {}
        }
        return this;
    }

    public double get(int column, int row) {
        switch (column) {
            case 0:
                switch (row) {
                    case 0:
                        return m00;
                    case 1:
                        return m01;
                    default:
                        break;
                }
                break;
            case 1:
                switch (row) {
                    case 0:
                        return m10;
                    case 1:
                        return m11;
                    default:
                        break;
                }
                break;
            default:{}
        }
        return 0;
    }

    /**
     * Set the matrix element at the given column and row to the specified value.
     *
     * @param column
     *          the colum index in <code>[0..1]</code>
     * @param row
     *          the row index in <code>[0..1]</code>
     * @param value
     *          the value
     * @return this
     */
    ref public Matrix2d set(int column, int row, double value) return {
        switch (column) {
            case 0:
                switch (row) {
                    case 0:
                        this.m00 = value;
                        return this;
                    case 1:
                        this.m01 = value;
                        return this;
                    default:
                        break;
                }
                break;
            case 1:
                switch (row) {
                    case 0:
                        this.m10 = value;
                        return this;
                    case 1:
                        this.m11 = value;
                        return this;
                    default:
                        break;
                }
                break;
            default:{}
        }
        return this;
    }

    /**
     * Set <code>this</code> matrix to its own normal matrix.
     * <p>
     * Please note that, if <code>this</code> is an orthogonal matrix or a matrix whose columns are orthogonal vectors,
     * then this method <i>need not</i> be invoked, since in that case <code>this</code> itself is its normal matrix.
     * In this case, use {@link #set(Matrix2d)} to set a given Matrix2d to this matrix.
     *
     * @see #set(Matrix2d)
     *
     * @return this
     */
    ref public Matrix2d normal() return {
        this.normal(this);
        return this;
    }

    /**
     * Compute a normal matrix from <code>this</code> matrix and store it into <code>dest</code>.
     * <p>
     * Please note that, if <code>this</code> is an orthogonal matrix or a matrix whose columns are orthogonal vectors,
     * then this method <i>need not</i> be invoked, since in that case <code>this</code> itself is its normal matrix.
     * In this case, use {@link #set(Matrix2d)} to set a given Matrix2d to this matrix.
     *
     * @see #set(Matrix2d)
     *
     * @param dest
     *             will hold the result
     * @return dest
     */
    public Matrix2d normal(ref Matrix2d dest) {
        double det = m00 * m11 - m10 * m01;
        double s = 1.0 / det;
        /* Invert and transpose in one go */
        double nm00 = m11 * s;
        double nm01 = -m10 * s;
        double nm10 = -m01 * s;
        double nm11 = m00 * s;
        dest.m00 = nm00;
        dest.m01 = nm01;
        dest.m10 = nm10;
        dest.m11 = nm11;
        return dest;
    }

    public Vector2d getScale(ref Vector2d dest) {
        dest.x = Math.sqrt(m00 * m00 + m01 * m01);
        dest.y = Math.sqrt(m10 * m10 + m11 * m11);
        return dest;
    }

    public Vector2d positiveX(Vector2d dir) {
        if (m00 * m11 < m01 * m10) { // negative determinant?
            dir.x = -m11;
            dir.y = m01;
        } else {
            dir.x = m11;
            dir.y = -m01;
        }
        return dir.normalize(dir);
    }

    public Vector2d normalizedPositiveX(Vector2d dir) {
        if (m00 * m11 < m01 * m10) { // negative determinant?
            dir.x = -m11;
            dir.y = m01;
        } else {
            dir.x = m11;
            dir.y = -m01;
        }
        return dir;
    }

    public Vector2d positiveY(Vector2d dir) {
        if (m00 * m11 < m01 * m10) { // negative determinant?
            dir.x = m10;
            dir.y = -m00;
        } else {
            dir.x = -m10;
            dir.y = m00;
        }
        return dir.normalize(dir);
    }

    public Vector2d normalizedPositiveY(Vector2d dir) {
        if (m00 * m11 < m01 * m10) { // negative determinant?
            dir.x = m10;
            dir.y = -m00;
        } else {
            dir.x = -m10;
            dir.y = m00;
        }
        return dir;
    }

    public int hashCode() {
        immutable int prime = 31;
        int result = 1;
        long temp;
        temp = Math.doubleToLongBits(m00);
        result = prime * result + cast(int) ((temp >>> 32) ^ temp);
        temp = Math.doubleToLongBits(m01);
        result = prime * result + cast(int) ((temp >>> 32) ^ temp);
        temp = Math.doubleToLongBits(m10);
        result = prime * result + cast(int) ((temp >>> 32) ^ temp);
        temp = Math.doubleToLongBits(m11);
        result = prime * result + cast(int) ((temp >>> 32) ^ temp);
        return result;
    }

    public bool equals(Matrix2d m, double delta) {
        if (this == m)
            return true;
        if (!Math.equals(m00, m.m00, delta))
            return false;
        if (!Math.equals(m01, m.m01, delta))
            return false;
        if (!Math.equals(m10, m.m10, delta))
            return false;
        if (!Math.equals(m11, m.m11, delta))
            return false;
        return true;
    }

    /**
     * Exchange the values of <code>this</code> matrix with the given <code>other</code> matrix.
     *
     * @param other
     *          the other matrix to exchange the values with
     * @return this
     */
    ref public Matrix2d swap(ref Matrix2d other) return {
        MemUtil.swap(this, other);
        return this;
    }

    /**
     * Component-wise add <code>this</code> and <code>other</code>.
     *
     * @param other
     *          the other addend
     * @return this
     */
    ref public Matrix2d add(Matrix2d other) return {
        this.add(other, this);
        return this;
    }

    public Matrix2d add(Matrix2d other, ref Matrix2d dest) {
        dest.m00 = m00 + other.m00;
        dest.m01 = m01 + other.m01;
        dest.m10 = m10 + other.m10;
        dest.m11 = m11 + other.m11;
        return dest;
    }

    /**
     * Component-wise subtract <code>subtrahend</code> from <code>this</code>.
     *
     * @param subtrahend
     *          the subtrahend
     * @return this
     */
    ref public Matrix2d sub(Matrix2d subtrahend) return {
        this.sub(subtrahend, this);
        return this;
    }

    public Matrix2d sub(Matrix2d other, ref Matrix2d dest) {
        dest.m00 = m00 - other.m00;
        dest.m01 = m01 - other.m01;
        dest.m10 = m10 - other.m10;
        dest.m11 = m11 - other.m11;
        return dest;
    }

    /**
     * Component-wise multiply <code>this</code> by <code>other</code>.
     *
     * @param other
     *          the other matrix
     * @return this
     */
    public Matrix2d mulComponentWise(Matrix2d other) {
        return sub(other, this);
    }

    public Matrix2d mulComponentWise(Matrix2d other, ref Matrix2d dest) {
        dest.m00 = m00 * other.m00;
        dest.m01 = m01 * other.m01;
        dest.m10 = m10 * other.m10;
        dest.m11 = m11 * other.m11;
        return dest;
    }

    /**
     * Linearly interpolate <code>this</code> and <code>other</code> using the given interpolation factor <code>t</code>
     * and store the result in <code>this</code>.
     * <p>
     * If <code>t</code> is <code>0.0</code> then the result is <code>this</code>. If the interpolation factor is <code>1.0</code>
     * then the result is <code>other</code>.
     *
     * @param other
     *          the other matrix
     * @param t
     *          the interpolation factor between 0.0 and 1.0
     * @return this
     */
    public Matrix2d lerp(Matrix2d other, double t) {
        return lerp(other, t, this);
    }

    public Matrix2d lerp(Matrix2d other, double t, ref Matrix2d dest) {
        dest.m00 = Math.fma(other.m00 - m00, t, m00);
        dest.m01 = Math.fma(other.m01 - m01, t, m01);
        dest.m10 = Math.fma(other.m10 - m10, t, m10);
        dest.m11 = Math.fma(other.m11 - m11, t, m11);
        return dest;
    }

    public bool isFinite() {
        return Math.isFinite(m00) && Math.isFinite(m01) &&
               Math.isFinite(m10) && Math.isFinite(m11);
    }
}