/*
 * Copyright (c) 2011, 2015, Oracle and/or its affiliates. All rights reserved.
 * ORACLE PROPRIETARY/CONFIDENTIAL. Use is subject to license terms.
 *
 *
 *
 *
 *
 *
 *
 *
 *
 *
 *
 *
 *
 *
 *
 *
 *
 *
 *
 *
 */

package javafx.scene.transform;

import java.util.Iterator;

import com.sun.javafx.geometry.BoundsUtils;
import javafx.event.EventDispatchChain;

import javafx.scene.Node;

import com.sun.javafx.util.WeakReferenceQueue;
import com.sun.javafx.binding.ExpressionHelper;
import com.sun.javafx.event.EventHandlerManager;
import com.sun.javafx.geom.transform.Affine2D;
import com.sun.javafx.geom.transform.Affine3D;
import com.sun.javafx.geom.transform.AffineBase;
import com.sun.javafx.geom.transform.BaseTransform;
import com.sun.javafx.scene.transform.TransformUtils;
import java.lang.ref.SoftReference;
import javafx.beans.InvalidationListener;
import javafx.beans.property.ObjectProperty;
import javafx.beans.property.ReadOnlyBooleanProperty;
import javafx.beans.property.SimpleObjectProperty;
import javafx.beans.value.ChangeListener;
import javafx.event.Event;
import javafx.event.EventHandler;
import javafx.event.EventTarget;
import javafx.event.EventType;
import javafx.geometry.BoundingBox;
import javafx.geometry.Bounds;
import javafx.geometry.Point2D;
import javafx.geometry.Point3D;

// PENDING_DOC_REVIEW of this whole class
/**
 * This class is a base class for different affine transformations.
 * It provides factory methods for the simple transformations - rotating,
 * scaling, shearing, and translation. It allows to get the transformation
 * matrix elements for any transform.
 *
 * <p>Example:</p>
 *
 * <pre><code>
 *  Rectangle rect = new Rectangle(50,50, Color.RED);
 *  rect.getTransforms().add(new Rotate(45,0,0)); //rotate by 45 degrees
 * </code></pre>
 * @since JavaFX 2.0
 */
public abstract class Transform implements Cloneable, EventTarget {

    /* *************************************************************************
     *                                                                         *
     *                            Factories                                    *
     *                                                                         *
     **************************************************************************/

    /**
     * Returns a new {@code Affine} object from 12 number
     * values representing the 6 specifiable entries of the 3x4
     * Affine transformation matrix.
     *
     * @param mxx the X coordinate scaling element of the 3x4 matrix
     * @param myx the Y coordinate shearing element of the 3x4 matrix
     * @param mxy the X coordinate shearing element of the 3x4 matrix
     * @param myy the Y coordinate scaling element of the 3x4 matrix
     * @param tx the X coordinate translation element of the 3x4 matrix
     * @param ty the Y coordinate translation element of the 3x4 matrix
     * @return a new {@code Affine} object derived from specified parameters
     */
    public static Affine affine(
        double mxx, double myx, double mxy, double myy, double tx, double ty) {
        final Affine affine = new Affine();
        affine.setMxx(mxx);
        affine.setMxy(mxy);
        affine.setTx(tx);
        affine.setMyx(myx);
        affine.setMyy(myy);
        affine.setTy(ty);
        return affine;
    }


    /**
     * Returns a new {@code Affine} object from 12 number
     * values representing the 12 specifiable entries of the 3x4
     * Affine transformation matrix.
     *
     * @param mxx the X coordinate scaling element of the 3x4 matrix
     * @param mxy the XY element of the 3x4 matrix
     * @param mxz the XZ element of the 3x4 matrix
     * @param tx the X coordinate translation element of the 3x4 matrix
     * @param myx the YX element of the 3x4 matrix
     * @param myy the Y coordinate scaling element of the 3x4 matrix
     * @param myz the YZ element of the 3x4 matrix
     * @param ty the Y coordinate translation element of the 3x4 matrix
     * @param mzx the ZX element of the 3x4 matrix
     * @param mzy the ZY element of the 3x4 matrix
     * @param mzz the Z coordinate scaling element of the 3x4 matrix
     * @param tz the Z coordinate translation element of the 3x4 matrix
     * @return a new {@code Affine} object derived from specified parameters
     */
    public static Affine affine(
        double mxx, double mxy, double mxz, double tx,
        double myx, double myy, double myz, double ty,
        double mzx, double mzy, double mzz, double tz) {
        final Affine affine = new Affine();
        affine.setMxx(mxx);
        affine.setMxy(mxy);
        affine.setMxz(mxz);
        affine.setTx(tx);
        affine.setMyx(myx);
        affine.setMyy(myy);
        affine.setMyz(myz);
        affine.setTy(ty);
        affine.setMzx(mzx);
        affine.setMzy(mzy);
        affine.setMzz(mzz);
        affine.setTz(tz);
        return affine;
    }


    /**
     * Returns a {@code Translate} object representing a translation transformation.
     * <p>
     * This is equivalent to:
     * <pre>
     *    new Translate(x, y);
     * </pre>
     */
    public static Translate translate(double x, double y) {
        final Translate translate = new Translate();
        translate.setX(x);
        translate.setY(y);
        return translate;
    }


    /**
     * Returns a {@code Rotate} object that rotates coordinates around a pivot
     * point.
     * <p>
     * This is equivalent to:
     * <pre>
     *    new Rotate(angle, pivotX, pivotY);
     * </pre>
     */
    public static Rotate rotate(double angle, double pivotX, double pivotY) {
        final Rotate rotate = new Rotate();
        rotate.setAngle(angle);
        rotate.setPivotX(pivotX);
        rotate.setPivotY(pivotY);
        return rotate;
    }


    /**
     * Returns a {@code Scale} object representing a scaling transformation.
     * <p>
     * This is equivalent to:
     * <pre>
     *    new Scale(x, y);
     * </pre>
     */
    public static Scale scale(double x, double y) {
        final Scale scale = new Scale();
        scale.setX(x);
        scale.setY(y);
        return scale;
    }


    /**
     * Returns a {@code Scale} object representing a scaling transformation.
     * The returned scale operation will be about the given pivot point.
     * <p>
     * This is equivalent to:
     * <pre>
     *    new Scale(x, y, pivotX, pivotY);
     * </pre>
     */
    public static Scale scale(double x, double y, double pivotX, double pivotY) {
        final Scale scale = new Scale();
        scale.setX(x);
        scale.setY(y);
        scale.setPivotX(pivotX);
        scale.setPivotY(pivotY);
        return scale;
    }


    /**
     * Returns a {@code Shear} object representing a shearing transformation.
     * <p>
     * This is equivalent to:
     * <pre>
     *    new Shear(x, y);
     * </pre>
     */
    public static Shear shear(double x, double y) {
        final Shear shear = new Shear();
        shear.setX(x);
        shear.setY(y);
        return shear;
    }

    /**
     * Returns a {@code Shear} object representing a shearing transformation.
     * <p>
     * This is equivalent to:
     * <pre>
     *    new Shear(x, y, pivotX, pivotY);
     * </pre>
     */
    public static Shear shear(double x, double y, double pivotX, double pivotY) {
        final Shear shear = new Shear();
        shear.setX(x);
        shear.setY(y);
        shear.setPivotX(pivotX);
        shear.setPivotY(pivotY);
        return shear;
    }

    /**
     * For transforms with expensive inversion we cache the inverted matrix
     * once it is needed and computed for some operation.
     */
    private SoftReference<Transform> inverseCache = null;

    private WeakReferenceQueue impl_nodes = new WeakReferenceQueue();

    /* *************************************************************************
     *                                                                         *
     *                         Element getters                                 *
     *                                                                         *
     **************************************************************************/

    /**
     * Gets the X coordinate scaling element of the 3x4 matrix.
     *
     * @since JavaFX 2.2
     */
    public  double getMxx() {
        return 1.0;
    }

    /**
     * Gets the XY coordinate element of the 3x4 matrix.
     *
     * @since JavaFX 2.2
     */
    public  double getMxy() {
        return 0.0;
    }

    /**
     * Gets the XZ coordinate element of the 3x4 matrix.
     *
     * @since JavaFX 2.2
     */
    public  double getMxz() {
        return 0.0;
    }

    /**
     * Gets the X coordinate translation element of the 3x4 matrix.
     *
     * @since JavaFX 2.2
     */
    public  double getTx() {
        return 0.0;
    }

    /**
     * Gets the YX coordinate element of the 3x4 matrix.
     *
     * @since JavaFX 2.2
     */
    public  double getMyx() {
        return 0.0;
    }

    /**
     * Gets the Y coordinate scaling element of the 3x4 matrix.
     *
     * @since JavaFX 2.2
     */
    public  double getMyy() {
        return 1.0;
    }

    /**
     * Gets the YZ coordinate element of the 3x4 matrix.
     *
     * @since JavaFX 2.2
     */
    public  double getMyz() {
        return 0.0;
    }

    /**
     * Gets the Y coordinate translation element of the 3x4 matrix.
     *
     * @since JavaFX 2.2
     */
    public  double getTy() {
        return 0.0;
    }

    /**
     * Gets the ZX coordinate element of the 3x4 matrix.
     *
     * @since JavaFX 2.2
     */
    public  double getMzx() {
        return 0.0;
    }

    /**
     * Gets the ZY coordinate element of the 3x4 matrix.
     *
     * @since JavaFX 2.2
     */
    public  double getMzy() {
        return 0.0;
    }

    /**
     * Gets the Z coordinate scaling element of the 3x4 matrix.
     *
     * @since JavaFX 2.2
     */
    public  double getMzz() {
        return 1.0;
    }

    /**
     * Gets the Z coordinate translation element of the 3x4 matrix.
     *
     * @since JavaFX 2.2
     */
    public  double getTz() {
        return 0.0;
    }

    /**
     * Gets the specified element of the transformation matrix.
     * @param type type of matrix to get the value from
     * @param row zero-based row number
     * @param column zero-based column number
     * @return value of the specified transformation matrix element
     * @throws IllegalArgumentException if a 2D matrix type is requested for
     *         a 3D transform
     * @throws IndexOutOfBoundsException if the indices are not within
     *         the specified matrix type
     * @throws NullPointerException if the specified {@code type} is null
     * @since JavaFX 8.0
     */
    public double getElement(MatrixType type, int row, int column) {
        if (row < 0 || row >= type.rows() || column < 0 || column >= type.columns()) {
            throw new IndexOutOfBoundsException("Index outside of affine "
                    + "matrix " + type + ": [" + row + ", " + column + "]");
        }
        switch(type) {
            case MT_2D_2x3:
                // fall-through
            case MT_2D_3x3:
                if (!isType2D()) {
                    throw new IllegalArgumentException("Cannot access 2D matrix "
                            + "of a 3D transform");
                }
                switch(row) {
                    case 0:
                        switch(column) {
                            case 0: return getMxx();
                            case 1: return getMxy();
                            case 2: return getTx();
                        }
                    case 1:
                        switch(column) {
                            case 0: return getMyx();
                            case 1: return getMyy();
                            case 2: return getTy();
                        }
                    case 2:
                        switch(column) {
                            case 0: return 0.0;
                            case 1: return 0.0;
                            case 2: return 1.0;
                        }
                }
                break;
            case MT_3D_3x4:
                // fall-through
            case MT_3D_4x4:
                switch(row) {
                    case 0:
                        switch(column) {
                            case 0: return getMxx();
                            case 1: return getMxy();
                            case 2: return getMxz();
                            case 3: return getTx();
                        }
                    case 1:
                        switch(column) {
                            case 0: return getMyx();
                            case 1: return getMyy();
                            case 2: return getMyz();
                            case 3: return getTy();
                        }
                    case 2:
                        switch(column) {
                            case 0: return getMzx();
                            case 1: return getMzy();
                            case 2: return getMzz();
                            case 3: return getTz();
                        }
                    case 3:
                        switch(column) {
                            case 0: return 0.0;
                            case 1: return 0.0;
                            case 2: return 0.0;
                            case 3: return 1.0;
                        }
                }
                break;
        }
        // cannot reach here
        throw new InternalError("Unsupported matrix type " + type);
    }

    /* *************************************************************************
     *                                                                         *
     *                           State getters                                 *
     *                                                                         *
     **************************************************************************/

    /**
     * Computes if this transform is currently a 2D transform (has no effect
     * in the direction of Z axis).
     * Used by the subclasses to effectively provide value of the type2D
     * property.
     * @return true if this transform is currently 2D-only
     */
    boolean computeIs2D() {
        return getMxz() == 0.0 && getMzx() == 0.0 && getMzy() == 0.0 &&
                    getMzz() == 1.0 && getTz() == 0.0;
    }

    /**
     * Computes if this transform is currently an identity (has
     * no effect in any direction).
     * Used by the subclasses to effectively provide value of the identity
     * property.
     * @return true if this transform is currently an identity transform
     */
    boolean computeIsIdentity() {
        return
            getMxx() == 1.0 && getMxy() == 0.0 && getMxz() == 0.0 && getTx() == 0.0 &&
            getMyx() == 0.0 && getMyy() == 1.0 && getMyz() == 0.0 && getTy() == 0.0 &&
            getMzx() == 0.0 && getMzy() == 0.0 && getMzz() == 1.0 && getTz() == 0.0;
    }

    /**
     * Computes determinant of the transformation matrix.
     * Among other things, determinant can be used for testing this transform's
     * invertibility - it is invertible if determinant is not equal to zero.
     * @return Determinant of the transformation matrix
     * @since JavaFX 8.0
     */
    public double determinant() {
        final double myx = getMyx();
        final double myy = getMyy();
        final double myz = getMyz();
        final double mzx = getMzx();
        final double mzy = getMzy();
        final double mzz = getMzz();

        return (getMxx() * (myy * mzz - mzy * myz) +
                getMxy() * (myz * mzx - mzz * myx) +
                getMxz() * (myx * mzy - mzx * myy));
    }

    /**
     * Determines if this is currently a 2D transform.
     * Transform is 2D if it has no effect along the Z axis.
     * @since JavaFX 8.0
     */
    private LazyBooleanProperty type2D;

    public final boolean isType2D() {
        return type2D == null ? computeIs2D() : type2D.get();
    }

    public final ReadOnlyBooleanProperty type2DProperty() {
        if (type2D == null) {
            type2D = new LazyBooleanProperty() {

                @Override
                protected boolean computeValue() {
                    return computeIs2D();
                }

                @Override
                public Object getBean() {
                    return Transform.this;
                }

                @Override
                public String getName() {
                    return "type2D";
                }
            };
        }
        return type2D;
    }

    /**
     * Determines if this is currently an identity transform.
     * Identity transform has no effect on the transformed nodes.
     * @since JavaFX 8.0
     */
    private LazyBooleanProperty identity;

    public final boolean isIdentity() {
        return identity == null ? computeIsIdentity() : identity.get();
    }

    public final ReadOnlyBooleanProperty identityProperty() {
        if (identity == null) {
            identity = new LazyBooleanProperty() {

                @Override
                protected boolean computeValue() {
                    return computeIsIdentity();
                }

                @Override
                public Object getBean() {
                    return Transform.this;
                }

                @Override
                public String getName() {
                    return "identity";
                }
            };
        }
        return identity;
    }

    /**
     * Lazily computed read-only boolean property implementation.
     * Used for type2D and identity properties.
     */
    private static abstract class LazyBooleanProperty
            extends ReadOnlyBooleanProperty {

        private ExpressionHelper<Boolean> helper;
        private boolean valid;
        private boolean value;

        @Override
        public void addListener(InvalidationListener listener) {
            helper = ExpressionHelper.addListener(helper, this, listener);
        }

        @Override
        public void removeListener(InvalidationListener listener) {
            helper = ExpressionHelper.removeListener(helper, listener);
        }

        @Override
        public void addListener(ChangeListener<? super Boolean> listener) {
            helper = ExpressionHelper.addListener(helper, this, listener);
        }

        @Override
        public void removeListener(ChangeListener<? super Boolean> listener) {
            helper = ExpressionHelper.removeListener(helper, listener);
        }

        @Override
        public boolean get() {
            if (!valid) {
                value = computeValue();
                valid = true;
            }

            return value;
        }

        public void invalidate() {
            if (valid) {
                valid = false;
                ExpressionHelper.fireValueChangedEvent(helper);
            }
        }

        protected abstract boolean computeValue();
    }

    /**
     * Transforms the specified point by this transform and by the specified
     * transform and returns distance of the result points. Used for similarTo
     * method. Has to be used only for 2D transforms (otherwise throws an
     * exception).
     * @param t the other transform
     * @param x point's X coordinate
     * @param y point's Y coordinate
     * @return distance of the transformed points
     */
    private double transformDiff(Transform t, double x, double y) {
        final Point2D byThis = transform(x, y);
        final Point2D byOther = t.transform(x, y);
        return byThis.distance(byOther);
    }

    /**
     * Transforms the specified point by this transform and by the specified
     * transform and returns distance of the result points. Used for similarTo
     * method.
     * @param t the other transform
     * @param x point's X coordinate
     * @param y point's Y coordinate
     * @param z point's Z coordinate
     * @return distance of the transformed points
     */
    private double transformDiff(Transform t, double x, double y, double z) {
        final Point3D byThis = transform(x, y, z);
        final Point3D byOther = t.transform(x, y, z);
        return byThis.distance(byOther);
    }

    /**
     * Checks if this transform is similar to the specified transform.
     * The two transforms are considered similar if any point from
     * {@code range} is transformed by them to points that are no farther
     * than {@code maxDelta} from each other.
     * @param transform transform to be compared to this transform
     * @param range region of interest on which the two transforms are compared
     * @param maxDelta maximum allowed distance for the results of transforming
     *                 any single point from {@code range} by the two transforms
     * @return true if the transforms are similar according to the specified
     *              criteria
     * @throws NullPointerException if the specified {@code transform}
     *         or {@code range} is null
     * @since JavaFX 8.0
     */
    public boolean similarTo(Transform transform, Bounds range, double maxDelta) {

        double cornerX, cornerY, cornerZ;

        if (isType2D() && transform.isType2D()) {
            cornerX = range.getMinX();
            cornerY = range.getMinY();

            if (transformDiff(transform, cornerX, cornerY) > maxDelta) {
                return false;
            }

            cornerY = range.getMaxY();
            if (transformDiff(transform, cornerX, cornerY) > maxDelta) {
                return false;
            }

            cornerX = range.getMaxX();
            cornerY = range.getMinY();
            if (transformDiff(transform, cornerX, cornerY) > maxDelta) {
                return false;
            }

            cornerY = range.getMaxY();
            if (transformDiff(transform, cornerX, cornerY) > maxDelta) {
                return false;
            }

            return true;
        }

        cornerX = range.getMinX();
        cornerY = range.getMinY();
        cornerZ = range.getMinZ();
        if (transformDiff(transform, cornerX, cornerY, cornerZ) > maxDelta) {
            return false;
        }

        cornerY = range.getMaxY();
        if (transformDiff(transform, cornerX, cornerY, cornerZ) > maxDelta) {
            return false;
        }

        cornerX = range.getMaxX();
        cornerY = range.getMinY();
        if (transformDiff(transform, cornerX, cornerY, cornerZ) > maxDelta) {
            return false;
        }

        cornerY = range.getMaxY();
        if (transformDiff(transform, cornerX, cornerY, cornerZ) > maxDelta) {
            return false;
        }

        if (range.getDepth() != 0.0) {
            cornerX = range.getMinX();
            cornerY = range.getMinY();
            cornerZ = range.getMaxZ();
            if (transformDiff(transform, cornerX, cornerY, cornerZ) > maxDelta) {
                return false;
            }

            cornerY = range.getMaxY();
            if (transformDiff(transform, cornerX, cornerY, cornerZ) > maxDelta) {
                return false;
            }

            cornerX = range.getMaxX();
            cornerY = range.getMinY();
            if (transformDiff(transform, cornerX, cornerY, cornerZ) > maxDelta) {
                return false;
            }

            cornerY = range.getMaxY();
            if (transformDiff(transform, cornerX, cornerY, cornerZ) > maxDelta) {
                return false;
            }
        }

        return true;
    }

    /* *************************************************************************
     *                                                                         *
     *                           Array getters                                 *
     *                                                                         *
     **************************************************************************/

    /**
     * Core of the toArray implementation for the 2D case.
     * All of the checks has been made by the enclosing method as well as
     * the constant elements filled, this method only fills the varying
     * elements to the array. Used by subclasses to fill
     * the elements efficiently.
     * @param array array to be filled with the 6 2D elements
     */
    void fill2DArray(double[] array) {
        array[0] = getMxx();
        array[1] = getMxy();
        array[2] = getTx();
        array[3] = getMyx();
        array[4] = getMyy();
        array[5] = getTy();
    }

    /**
     * Core of the toArray implementation for the 3D case.
     * All of the checks has been made by the enclosing method as well as
     * the constant elements filled, this method only fills the varying
     * elements to the array. Used by subclasses to fill
     * the elements efficiently.
     * @param array array to be filled with the 12 3D elements
     */
    void fill3DArray(double[] array) {
        array[0] = getMxx();
        array[1] = getMxy();
        array[2] = getMxz();
        array[3] = getTx();
        array[4] = getMyx();
        array[5] = getMyy();
        array[6] = getMyz();
        array[7] = getTy();
        array[8] = getMzx();
        array[9] = getMzy();
        array[10] = getMzz();
        array[11] = getTz();
    }

    /**
     * Returns an array containing the flattened transformation matrix.
     * If the requested matrix type fits in the specified array, it is returned
     * therein. Otherwise, a new array is created.
     * @param type matrix type to be filled in the array
     * @param array array into which the elements of the matrix are to be
     *              stored, if it is non-null and big enough; otherwise,
     *              a new array is created for this purpose.
     * @return an array containing the elements of the requested matrix type
     *         representing this transform
     * @throws IllegalArgumentException if a 2D matrix type is requested for
     *         a 3D transform
     * @throws NullPointerException if the specified {@code type} is null
     * @since JavaFX 8.0
     */
    public double[] toArray(MatrixType type, double[] array) {
        checkRequestedMAT(type);

        if (array == null || array.length < type.elements()) {
            array = new double[type.elements()];
        }

        switch (type) {
            case MT_2D_3x3:
                array[6] = 0.0;
                array[7] = 0.0;
                array[8] = 1.0;
                // fall-through
            case MT_2D_2x3:
                fill2DArray(array);
                break;
            case MT_3D_4x4:
                array[12] = 0.0;
                array[13] = 0.0;
                array[14] = 0.0;
                array[15] = 1.0;
                // fall-through
            case MT_3D_3x4:
                fill3DArray(array);
                break;
            default:
                throw new InternalError("Unsupported matrix type " + type);
        }

        return array;
    }

    /**
     * Returns an array containing the flattened transformation matrix.
     * @param type matrix type to be filled in the array
     * @return an array containing the elements of the requested matrix type
     *         representing this transform
     * @throws IllegalArgumentException if a 2D matrix type is requested for
     *         a 3D transform
     * @throws NullPointerException if the specified {@code type} is null
     * @since JavaFX 8.0
     */
    public double[] toArray(MatrixType type) {
        return toArray(type, null);
    }

    /**
     * Returns an array containing a row of the transformation matrix.
     * If the row of the requested matrix type fits in the specified array,
     * it is returned therein. Otherwise, a new array is created.
     * @param type matrix type whose row is to be filled in the array
     * @param row zero-based index of the row
     * @param array array into which the elements of the row are to be
     *              stored, if it is non-null and big enough; otherwise,
     *              a new array is created for this purpose.
     * @return an array containing the requested row of the requested matrix
     *         type representing this transform
     * @throws IllegalArgumentException if a 2D matrix type is requested for
     *         a 3D transform
     * @throws IndexOutOfBoundsException if the {@code row} index is not within
     *         the number of rows of the specified matrix type
     * @throws NullPointerException if the specified {@code type} is null
     * @since JavaFX 8.0
     */
    public double[] row(MatrixType type, int row, double[] array) {

        checkRequestedMAT(type);

        if (row < 0 || row >= type.rows()) {
            throw new IndexOutOfBoundsException(
                    "Cannot get row " + row + " from " + type);
        }

        if (array == null || array.length < type.columns()) {
            array = new double[type.columns()];
        }

        switch(type) {
            case MT_2D_2x3:
            case MT_2D_3x3:
                switch (row) {
                    case 0:
                        array[0] = getMxx();
                        array[1] = getMxy();
                        array[2] = getTx();
                        break;
                    case 1:
                        array[0] = getMyx();
                        array[1] = getMyy();
                        array[2] = getTy();
                        break;
                    case 2:
                        array[0] = 0.0;
                        array[1] = 0.0;
                        array[2] = 1.0;
                        break;
                }
                break;
            case MT_3D_3x4:
            case MT_3D_4x4:
                switch (row) {
                    case 0:
                        array[0] = getMxx();
                        array[1] = getMxy();
                        array[2] = getMxz();
                        array[3] = getTx();
                        break;
                    case 1:
                        array[0] = getMyx();
                        array[1] = getMyy();
                        array[2] = getMyz();
                        array[3] = getTy();
                        break;
                    case 2:
                        array[0] = getMzx();
                        array[1] = getMzy();
                        array[2] = getMzz();
                        array[3] = getTz();
                        break;
                    case 3:
                        array[0] = 0.0;
                        array[1] = 0.0;
                        array[2] = 0.0;
                        array[3] = 1.0;
                        break;
                }
                break;
            default:
                throw new InternalError("Unsupported row " + row + " of " + type);
        }
        return array;
    }

    /**
     * Returns an array containing a row of the transformation matrix.
     * @param type matrix type whose row is to be filled in the array
     * @param row zero-based index of the row
     * @return an array containing the requested row of the requested matrix
     *         type representing this transform
     * @throws IllegalArgumentException if a 2D matrix type is requested for
     *         a 3D transform
     * @throws IndexOutOfBoundsException if the {@code row} index is not within
     *         the number of rows of the specified matrix type
     * @throws NullPointerException if the specified {@code type} is null
     * @since JavaFX 8.0
     */
    public double[] row(MatrixType type, int row) {
        return row(type, row, null);
    }

    /**
     * Returns an array containing a column of the transformation matrix.
     * If the column of the requested matrix type fits in the specified array,
     * it is returned therein. Otherwise, a new array is created.
     * @param type matrix type whose column is to be filled in the array
     * @param column zero-based index of the column
     * @param array array into which the elements of the column are to be
     *              stored, if it is non-null and big enough; otherwise,
     *              a new array is created for this purpose.
     * @return an array containing the requested column of the requested matrix
     *         type representing this transform
     * @throws IllegalArgumentException if a 2D matrix type is requested for
     *         a 3D transform
     * @throws IndexOutOfBoundsException if the {@code column} index
     *         is not within the number of columns of the specified matrix type
     * @throws NullPointerException if the specified {@code type} is null
     * @since JavaFX 8.0
     */
    public double[] column(MatrixType type, int column, double[] array) {

        checkRequestedMAT(type);

        if (column < 0 || column >= type.columns()) {
            throw new IndexOutOfBoundsException(
                    "Cannot get row " + column + " from " + type);
        }

        if (array == null || array.length < type.rows()) {
            array = new double[type.rows()];
        }

        switch(type) {
            case MT_2D_2x3:
                switch (column) {
                    case 0:
                        array[0] = getMxx();
                        array[1] = getMyx();
                        break;
                    case 1:
                        array[0] = getMxy();
                        array[1] = getMyy();
                        break;
                    case 2:
                        array[0] = getTx();
                        array[1] = getTy();
                        break;
                }
                break;
            case MT_2D_3x3:
                switch (column) {
                    case 0:
                        array[0] = getMxx();
                        array[1] = getMyx();
                        array[2] = 0.0;
                        break;
                    case 1:
                        array[0] = getMxy();
                        array[1] = getMyy();
                        array[2] = 0.0;
                        break;
                    case 2:
                        array[0] = getTx();
                        array[1] = getTy();
                        array[2] = 1.0;
                        break;
                }
                break;
            case MT_3D_3x4:
                switch (column) {
                    case 0:
                        array[0] = getMxx();
                        array[1] = getMyx();
                        array[2] = getMzx();
                        break;
                    case 1:
                        array[0] = getMxy();
                        array[1] = getMyy();
                        array[2] = getMzy();
                        break;
                    case 2:
                        array[0] = getMxz();
                        array[1] = getMyz();
                        array[2] = getMzz();
                        break;
                    case 3:
                        array[0] = getTx();
                        array[1] = getTy();
                        array[2] = getTz();
                        break;
                }
                break;
            case MT_3D_4x4:
                switch (column) {
                    case 0:
                        array[0] = getMxx();
                        array[1] = getMyx();
                        array[2] = getMzx();
                        array[3] = 0.0;
                        break;
                    case 1:
                        array[0] = getMxy();
                        array[1] = getMyy();
                        array[2] = getMzy();
                        array[3] = 0.0;
                        break;
                    case 2:
                        array[0] = getMxz();
                        array[1] = getMyz();
                        array[2] = getMzz();
                        array[3] = 0.0;
                        break;
                    case 3:
                        array[0] = getTx();
                        array[1] = getTy();
                        array[2] = getTz();
                        array[3] = 1.0;
                        break;
                }
                break;
            default:
                throw new InternalError("Unsupported column " + column + " of "
                        + type);
        }
        return array;
    }

    /**
     * Returns an array containing a column of the transformation matrix.
     * @param type matrix type whose column is to be filled in the array
     * @param column zero-based index of the column
     * @return an array containing the requested column of the requested matrix
     *         type representing this transform
     * @throws IllegalArgumentException if a 2D matrix type is requested for
     *         a 3D transform
     * @throws IndexOutOfBoundsException if the {@code column} index
     *         is not within the number of columns of the specified matrix type
     * @throws NullPointerException if the specified {@code type} is null
     * @since JavaFX 8.0
     */
    public double[] column(MatrixType type, int column) {
        return column(type, column, null);
    }

    /* *************************************************************************
     *                                                                         *
     *                         Transform creators                              *
     *                                                                         *
     **************************************************************************/

    /**
     * Returns the concatenation of this transform and the specified transform.
     * Applying the resulting transform to a node has the same effect as
     * adding the two transforms to its {@code getTransforms()} list,
     * {@code this} transform first and the specified {@code transform} second.
     * @param transform transform to be concatenated with this transform
     * @return The concatenated transform
     * @throws NullPointerException if the specified {@code transform} is null
     * @since JavaFX 8.0
     */
    public Transform createConcatenation(Transform transform) {
        final double txx = transform.getMxx();
        final double txy = transform.getMxy();
        final double txz = transform.getMxz();
        final double ttx = transform.getTx();
        final double tyx = transform.getMyx();
        final double tyy = transform.getMyy();
        final double tyz = transform.getMyz();
        final double tty = transform.getTy();
        final double tzx = transform.getMzx();
        final double tzy = transform.getMzy();
        final double tzz = transform.getMzz();
        final double ttz = transform.getTz();
        return new Affine(
            (getMxx() * txx + getMxy() * tyx + getMxz() * tzx),
            (getMxx() * txy + getMxy() * tyy + getMxz() * tzy),
            (getMxx() * txz + getMxy() * tyz + getMxz() * tzz),
            (getMxx() * ttx + getMxy() * tty + getMxz() * ttz + getTx()),
            (getMyx() * txx + getMyy() * tyx + getMyz() * tzx),
            (getMyx() * txy + getMyy() * tyy + getMyz() * tzy),
            (getMyx() * txz + getMyy() * tyz + getMyz() * tzz),
            (getMyx() * ttx + getMyy() * tty + getMyz() * ttz + getTy()),
            (getMzx() * txx + getMzy() * tyx + getMzz() * tzx),
            (getMzx() * txy + getMzy() * tyy + getMzz() * tzy),
            (getMzx() * txz + getMzy() * tyz + getMzz() * tzz),
            (getMzx() * ttx + getMzy() * tty + getMzz() * ttz + getTz()));
    }

    /**
     * Returns the inverse transform of this transform.
     * @return the inverse transform
     * @throws NonInvertibleTransformException if this transform
     *         cannot be inverted
     * @since JavaFX 8.0
     */
    public Transform createInverse() throws NonInvertibleTransformException {
        return getInverseCache().clone();
    }

    /**
     * Returns a deep copy of this transform.
     * @return a copy of this transform
     * @since JavaFX 8.0
     */
    @Override
    public Transform clone() {
        return TransformUtils.immutableTransform(this);
    }

    /* *************************************************************************
     *                                                                         *
     *                     Transform, Inverse Transform                        *
     *                                                                         *
     **************************************************************************/

    /**
     * Transforms the specified point by this transform.
     * This method can be used only for 2D transforms.
     * @param x the X coordinate of the point
     * @param y the Y coordinate of the point
     * @return the transformed point
     * @throws IllegalStateException if this is a 3D transform
     * @since JavaFX 8.0
     */
    public Point2D transform(double x, double y) {
        ensureCanTransform2DPoint();

        return new Point2D(
            getMxx() * x + getMxy() * y + getTx(),
            getMyx() * x + getMyy() * y + getTy());
    }

    /**
     * Transforms the specified point by this transform.
     * This method can be used only for 2D transforms.
     * @param point the point to be transformed
     * @return the transformed point
     * @throws IllegalStateException if this is a 3D transform
     * @throws NullPointerException if the specified {@code point} is null
     * @since JavaFX 8.0
     */
    public Point2D transform(Point2D point) {
        return transform(point.getX(), point.getY());
    }

    /**
     * Transforms the specified point by this transform.
     * @param x the X coordinate of the point
     * @param y the Y coordinate of the point
     * @param z the Z coordinate of the point
     * @return the transformed point
     * @since JavaFX 8.0
     */
    public Point3D transform(double x, double y, double z) {
        return new Point3D(
            getMxx() * x + getMxy() * y + getMxz() * z + getTx(),
            getMyx() * x + getMyy() * y + getMyz() * z + getTy(),
            getMzx() * x + getMzy() * y + getMzz() * z + getTz());
    }

    /**
     * Transforms the specified point by this transform.
     * @param point the point to be transformed
     * @return the transformed point
     * @throws NullPointerException if the specified {@code point} is null
     * @since JavaFX 8.0
     */
    public Point3D transform(Point3D point) {
        return transform(point.getX(), point.getY(), point.getZ());
    }

    /**
     * Transforms the specified bounds by this transform.
     * @param bounds the bounds to be transformed
     * @return the transformed bounds
     * @since JavaFX 8.0
     */
    public Bounds transform(Bounds bounds) {
        if (isType2D() && (bounds.getMinZ() == 0) && (bounds.getMaxZ() == 0)) {
            Point2D p1 = transform(bounds.getMinX(), bounds.getMinY());
            Point2D p2 = transform(bounds.getMaxX(), bounds.getMinY());
            Point2D p3 = transform(bounds.getMaxX(), bounds.getMaxY());
            Point2D p4 = transform(bounds.getMinX(), bounds.getMaxY());

            return BoundsUtils.createBoundingBox(p1, p2, p3, p4);
        }
        Point3D p1 = transform(bounds.getMinX(), bounds.getMinY(), bounds.getMinZ());
        Point3D p2 = transform(bounds.getMinX(), bounds.getMinY(), bounds.getMaxZ());
        Point3D p3 = transform(bounds.getMinX(), bounds.getMaxY(), bounds.getMinZ());
        Point3D p4 = transform(bounds.getMinX(), bounds.getMaxY(), bounds.getMaxZ());
        Point3D p5 = transform(bounds.getMaxX(), bounds.getMaxY(), bounds.getMinZ());
        Point3D p6 = transform(bounds.getMaxX(), bounds.getMaxY(), bounds.getMaxZ());
        Point3D p7 = transform(bounds.getMaxX(), bounds.getMinY(), bounds.getMinZ());
        Point3D p8 = transform(bounds.getMaxX(), bounds.getMinY(), bounds.getMaxZ());

        return BoundsUtils.createBoundingBox(p1, p2, p3, p4, p5, p6, p7, p8);
    }

    /**
     * Core of the transform2DPoints method.
     * All the checks has been performed and the care of the overlaps has been
     * taken by the enclosing method, this method only transforms the points
     * and fills them to the array. Used by the subclasses to perform
     * the transform efficiently.
     */
    void transform2DPointsImpl(double[] srcPts, int srcOff,
            double[] dstPts, int dstOff, int numPts) {
        final double xx = getMxx();
        final double xy = getMxy();
        final double tx = getTx();
        final double yx = getMyx();
        final double yy = getMyy();
        final double ty = getTy();

        while (--numPts >= 0) {
            final double x = srcPts[srcOff++];
            final double y = srcPts[srcOff++];

            dstPts[dstOff++] = xx * x + xy * y + tx;
            dstPts[dstOff++] = yx * x + yy * y + ty;
        }
    }

    /**
     * Core of the transform3DPoints method.
     * All the checks has been performed and the care of the overlaps has been
     * taken by the enclosing method, this method only transforms the points
     * and fills them to the array. Used by the subclasses to perform
     * the transform efficiently.
     */
    void transform3DPointsImpl(double[] srcPts, int srcOff,
            double[] dstPts, int dstOff, int numPts) {

        final double xx = getMxx();
        final double xy = getMxy();
        final double xz = getMxz();
        final double tx = getTx();
        final double yx = getMyx();
        final double yy = getMyy();
        final double yz = getMyz();
        final double ty = getTy();
        final double zx = getMzx();
        final double zy = getMzy();
        final double zz = getMzz();
        final double tz = getTz();

        while (--numPts >= 0) {
            final double x = srcPts[srcOff++];
            final double y = srcPts[srcOff++];
            final double z = srcPts[srcOff++];

            dstPts[dstOff++] = xx * x + xy * y + xz * z + tx;
            dstPts[dstOff++] = yx * x + yy * y + yz * z + ty;
            dstPts[dstOff++] = zx * x + zy * y + zz * z + tz;
        }
    }

    /**
     * Transforms an array of coordinates by this transform.
     * The two coordinate array sections can be exactly the same or
     * can be overlapping sections of the same array without affecting the
     * validity of the results.
     * This method ensures that no source coordinates are overwritten by a
     * previous operation before they can be transformed.
     * The coordinates are stored in the arrays starting at the specified
     * offset in the order <code>[x0, y0, x1, y1, ..., xn, yn]</code>.
     * This method can be used only for 2D transforms.
     * @param srcPts the array containing the source point coordinates.
     * Each point is stored as a pair of x,&nbsp;y coordinates.
     * @param srcOff the offset to the first point to be transformed
     * in the source array
     * @param dstPts the array into which the transformed point coordinates
     * are returned.  Each point is stored as a pair of x,&nbsp;y
     * coordinates.
     * @param dstOff the offset to the location of the first
     * transformed point that is stored in the destination array
     * @param numPts the number of points to be transformed
     * @throws IllegalStateException if this is a 3D transform
     * @throws NullPointerException if {@code srcPts} or (@code dstPts} is null
     * @since JavaFX 8.0
     */
    public void transform2DPoints(double[] srcPts, int srcOff,
                          double[] dstPts, int dstOff,
                          int numPts) {

        if (srcPts == null || dstPts == null) {
            throw new NullPointerException();
        }

        if (!isType2D()) {
            throw new IllegalStateException("Cannot transform 2D points "
                    + "with a 3D transform");
        }

        // deal with overlapping arrays
        srcOff = getFixedSrcOffset(srcPts, srcOff, dstPts, dstOff, numPts, 2);

        // do the transformations
        transform2DPointsImpl(srcPts, srcOff, dstPts, dstOff, numPts);
    }

    /**
     * Transforms an array of floating point coordinates by this transform.
     * The three coordinate array sections can be exactly the same or
     * can be overlapping sections of the same array without affecting the
     * validity of the results.
     * This method ensures that no source coordinates are overwritten by a
     * previous operation before they can be transformed.
     * The coordinates are stored in the arrays starting at the specified
     * offset in the order <code>[x0, y0, z0, x1, y1, z1, ..., xn, yn, zn]</code>.
     * @param srcPts the array containing the source point coordinates.
     * Each point is stored as a tiplet of x,&nbsp;y,&nbsp;z coordinates.
     * @param srcOff the offset to the first point to be transformed
     * in the source array
     * @param dstPts the array into which the transformed point coordinates
     * are returned.  Each point is stored as a triplet of x,&nbsp;y,&nbsp;z
     * coordinates.
     * @param dstOff the offset to the location of the first
     * transformed point that is stored in the destination array
     * @param numPts the number of points to be transformed
     * @throws NullPointerException if {@code srcPts} or (@code dstPts} is null
     * @since JavaFX 8.0
     */
    public void transform3DPoints(double[] srcPts, int srcOff,
                          double[] dstPts, int dstOff,
                          int numPts) {

        if (srcPts == null || dstPts == null) {
            throw new NullPointerException();
        }

        // deal with overlapping arrays
        srcOff = getFixedSrcOffset(srcPts, srcOff, dstPts, dstOff, numPts, 3);

        // do the transformations
        transform3DPointsImpl(srcPts, srcOff, dstPts, dstOff, numPts);
    }

    /**
     * Transforms the relative magnitude vector by this transform.
     * The vector is transformed without applying the translation components
     * of the affine transformation matrix.
     * This method can be used only for a 2D transform.
     * @param x vector magnitude in the direction of the X axis
     * @param y vector magnitude in the direction of the Y axis
     * @return the transformed relative magnitude vector represented
     *         by a {@code Point2D} instance
     * @throws IllegalStateException if this is a 3D transform
     * @since JavaFX 8.0
     */
    public Point2D deltaTransform(double x, double y) {
        ensureCanTransform2DPoint();

        return new Point2D(
            getMxx() * x + getMxy() * y,
            getMyx() * x + getMyy() * y);
    }

    /**
     * Transforms the relative magnitude vector represented by the specified
     * {@code Point2D} instance by this transform.
     * The vector is transformed without applying the translation components
     * of the affine transformation matrix.
     * This method can be used only for a 2D transform.
     * @param point the relative magnitude vector
     * @return the transformed relative magnitude vector represented
     *         by a {@code Point2D} instance
     * @throws IllegalStateException if this is a 3D transform
     * @throws NullPointerException if the specified {@code point} is null
     * @since JavaFX 8.0
     */
    public Point2D deltaTransform(Point2D point) {
        return deltaTransform(point.getX(), point.getY());
    }

    /**
     * Transforms the relative magnitude vector by this transform.
     * The vector is transformed without applying the translation components
     * of the affine transformation matrix.
     * @param x vector magnitude in the direction of the X axis
     * @param y vector magnitude in the direction of the Y axis
     * @return the transformed relative magnitude vector represented
     *         by a {@code Point3D} instance
     * @since JavaFX 8.0
     */
    public Point3D deltaTransform(double x, double y, double z) {
        return new Point3D(
            getMxx() * x + getMxy() * y + getMxz() * z,
            getMyx() * x + getMyy() * y + getMyz() * z,
            getMzx() * x + getMzy() * y + getMzz() * z);
    }

    /**
     * Transforms the relative magnitude vector represented by the specified
     * {@code Point3D} instance by this transform.
     * The vector is transformed without applying the translation components
     * of the affine transformation matrix.
     * @param point the relative magnitude vector
     * @return the transformed relative magnitude vector represented
     *         by a {@code Point3D} instance
     * @throws NullPointerException if the specified {@code point} is null
     * @since JavaFX 8.0
     */
    public Point3D deltaTransform(Point3D point) {
        return deltaTransform(point.getX(), point.getY(), point.getZ());
    }

    /**
     * Transforms the specified point by the inverse of this transform.
     * This method can be used only for 2D transforms.
     * @param x the X coordinate of the point
     * @param y the Y coordinate of the point
     * @return the inversely transformed point
     * @throws IllegalStateException if this is a 3D transform
     * @throws NonInvertibleTransformException if this transform
     *         cannot be inverted
     * @since JavaFX 8.0
     */
    public Point2D inverseTransform(double x, double y)
            throws NonInvertibleTransformException {

        ensureCanTransform2DPoint();

        return getInverseCache().transform(x, y);
    }

    /**
     * Transforms the specified point by the inverse of this transform.
     * This method can be used only for 2D transforms.
     * @param point the point to be transformed
     * @return the inversely transformed point
     * @throws IllegalStateException if this is a 3D transform
     * @throws NonInvertibleTransformException if this transform
     *         cannot be inverted
     * @throws NullPointerException if the specified {@code point} is null
     * @since JavaFX 8.0
     */
    public Point2D inverseTransform(Point2D point)
            throws NonInvertibleTransformException {
        return inverseTransform(point.getX(), point.getY());
    }

    /**
     * Transforms the specified point by the inverse of this transform.
     * @param x the X coordinate of the point
     * @param y the Y coordinate of the point
     * @param z the Z coordinate of the point
     * @return the inversely transformed point
     * @throws NonInvertibleTransformException if this transform
     *         cannot be inverted
     * @since JavaFX 8.0
     */
    public Point3D inverseTransform(double x, double y, double z)
            throws NonInvertibleTransformException {

        return getInverseCache().transform(x, y, z);
    }

    /**
     * Transforms the specified point by the inverse of this transform.
     * @param point the point to be transformed
     * @return the inversely transformed point
     * @throws NonInvertibleTransformException if this transform
     *         cannot be inverted
     * @throws NullPointerException if the specified {@code point} is null
     * @since JavaFX 8.0
     */
    public Point3D inverseTransform(Point3D point)
            throws NonInvertibleTransformException {
        return inverseTransform(point.getX(), point.getY(), point.getZ());
    }

    /**
     * Transforms the specified bounds by the inverse of this transform.
     * @param bounds the bounds to be transformed
     * @return the inversely transformed bounds
     * @throws NonInvertibleTransformException if this transform
     *         cannot be inverted
     * @throws NullPointerException if the specified {@code bounds} is null
     * @since JavaFX 8.0
     */
    public Bounds inverseTransform(Bounds bounds)
            throws NonInvertibleTransformException {
        if (isType2D() && (bounds.getMinZ() == 0) && (bounds.getMaxZ() == 0)) {
            Point2D p1 = inverseTransform(bounds.getMinX(), bounds.getMinY());
            Point2D p2 = inverseTransform(bounds.getMaxX(), bounds.getMinY());
            Point2D p3 = inverseTransform(bounds.getMaxX(), bounds.getMaxY());
            Point2D p4 = inverseTransform(bounds.getMinX(), bounds.getMaxY());

            return BoundsUtils.createBoundingBox(p1, p2, p3, p4);
        }
        Point3D p1 = inverseTransform(bounds.getMinX(), bounds.getMinY(), bounds.getMinZ());
        Point3D p2 = inverseTransform(bounds.getMinX(), bounds.getMinY(), bounds.getMaxZ());
        Point3D p3 = inverseTransform(bounds.getMinX(), bounds.getMaxY(), bounds.getMinZ());
        Point3D p4 = inverseTransform(bounds.getMinX(), bounds.getMaxY(), bounds.getMaxZ());
        Point3D p5 = inverseTransform(bounds.getMaxX(), bounds.getMaxY(), bounds.getMinZ());
        Point3D p6 = inverseTransform(bounds.getMaxX(), bounds.getMaxY(), bounds.getMaxZ());
        Point3D p7 = inverseTransform(bounds.getMaxX(), bounds.getMinY(), bounds.getMinZ());
        Point3D p8 = inverseTransform(bounds.getMaxX(), bounds.getMinY(), bounds.getMaxZ());

        return BoundsUtils.createBoundingBox(p1, p2, p3, p4, p5, p6, p7, p8);

    }

    /**
     * Core of the inverseTransform2DPoints method.
     * All the checks has been performed and the care of the overlaps has been
     * taken by the enclosing method, this method only transforms the points
     * and fills them to the array. Used by the subclasses to perform
     * the transform efficiently.
     */
    void inverseTransform2DPointsImpl(double[] srcPts, int srcOff,
            double[] dstPts, int dstOff, int numPts)
            throws NonInvertibleTransformException {

        getInverseCache().transform2DPointsImpl(srcPts, srcOff,
                dstPts, dstOff, numPts);
    }

    /**
     * Core of the inverseTransform3DPoints method.
     * All the checks has been performed and the care of the overlaps has been
     * taken by the enclosing method, this method only transforms the points
     * and fills them to the array. Used by the subclasses to perform
     * the transform efficiently.
     */
    void inverseTransform3DPointsImpl(double[] srcPts, int srcOff,
            double[] dstPts, int dstOff, int numPts)
            throws NonInvertibleTransformException {

        getInverseCache().transform3DPointsImpl(srcPts, srcOff,
                dstPts, dstOff, numPts);
    }

    /**
     * Transforms an array of coordinates by the inverse of this transform.
     * The two coordinate array sections can be exactly the same or
     * can be overlapping sections of the same array without affecting the
     * validity of the results.
     * This method ensures that no source coordinates are overwritten by a
     * previous operation before they can be transformed.
     * The coordinates are stored in the arrays starting at the specified
     * offset in the order <code>[x0, y0, x1, y1, ..., xn, yn]</code>.
     * This method can be used only for 2D transforms.
     * @param srcPts the array containing the source point coordinates.
     * Each point is stored as a pair of x,&nbsp;y coordinates.
     * @param srcOff the offset to the first point to be transformed
     * in the source array
     * @param dstPts the array into which the transformed point coordinates
     * are returned.  Each point is stored as a pair of x,&nbsp;y
     * coordinates.
     * @param dstOff the offset to the location of the first
     * transformed point that is stored in the destination array
     * @param numPts the number of points to be transformed
     * @throws IllegalStateException if this is a 3D transform
     * @throws NonInvertibleTransformException if this transform
     *         cannot be inverted
     * @throws NullPointerException if {@code srcPts} or (@code dstPts} is null
     * @since JavaFX 8.0
     */
    public void inverseTransform2DPoints(double[] srcPts, int srcOff,
                          double[] dstPts, int dstOff,
                          int numPts) throws NonInvertibleTransformException{

        if (srcPts == null || dstPts == null) {
            throw new NullPointerException();
        }

        if (!isType2D()) {
            throw new IllegalStateException("Cannot transform 2D points "
                    + "with a 3D transform");
        }

        // deal with overlapping arrays
        srcOff = getFixedSrcOffset(srcPts, srcOff, dstPts, dstOff, numPts, 2);

        // do the transformations
        inverseTransform2DPointsImpl(srcPts, srcOff, dstPts, dstOff, numPts);
    }

    /**
     * Transforms an array of floating point coordinates by the inverse
     * of this transform.
     * The three coordinate array sections can be exactly the same or
     * can be overlapping sections of the same array without affecting the
     * validity of the results.
     * This method ensures that no source coordinates are overwritten by a
     * previous operation before they can be transformed.
     * The coordinates are stored in the arrays starting at the specified
     * offset in the order <code>[x0, y0, z0, x1, y1, z1, ..., xn, yn, zn]</code>.
     * @param srcPts the array containing the source point coordinates.
     * Each point is stored as a triplet of x,&nbsp;y,&nbsp;z coordinates.
     * @param srcOff the offset to the first point to be transformed
     * in the source array
     * @param dstPts the array into which the transformed point coordinates
     * are returned.  Each point is stored as a triplet of x,&nbsp;y,&nbsp;z
     * coordinates.
     * @param dstOff the offset to the location of the first
     * transformed point that is stored in the destination array
     * @param numPts the number of points to be transformed
     * @throws NonInvertibleTransformException if this transform
     *         cannot be inverted
     * @throws NullPointerException if {@code srcPts} or (@code dstPts} is null
     * @since JavaFX 8.0
     */
    public void inverseTransform3DPoints(double[] srcPts, int srcOff,
                          double[] dstPts, int dstOff,
                          int numPts) throws NonInvertibleTransformException {

        if (srcPts == null || dstPts == null) {
            throw new NullPointerException();
        }

        // deal with overlapping arrays
        srcOff = getFixedSrcOffset(srcPts, srcOff, dstPts, dstOff, numPts, 3);

        // do the transformations
        inverseTransform3DPointsImpl(srcPts, srcOff, dstPts, dstOff, numPts);
    }

    /**
     * Transforms the relative magnitude vector by the inverse of this transform.
     * The vector is transformed without applying the translation components
     * of the affine transformation matrix.
     * This method can be used only for a 2D transform.
     * @param x vector magnitude in the direction of the X axis
     * @param y vector magnitude in the direction of the Y axis
     * @return the inversely transformed relative magnitude vector represented
     *         by a {@code Point2D} instance
     * @throws IllegalStateException if this is a 3D transform
     * @throws NonInvertibleTransformException if this transform
     *         cannot be inverted
     * @since JavaFX 8.0
     */
    public Point2D inverseDeltaTransform(double x, double y)
            throws NonInvertibleTransformException {

        ensureCanTransform2DPoint();

        return getInverseCache().deltaTransform(x, y);
    }

    /**
     * Transforms the relative magnitude vector represented by the specified
     * {@code Point2D} instance by the inverse of this transform.
     * The vector is transformed without applying the translation components
     * of the affine transformation matrix.
     * This method can be used only for a 2D transform.
     * @param point the relative magnitude vector
     * @return the inversely transformed relative magnitude vector represented
     *         by a {@code Point2D} instance
     * @throws IllegalStateException if this is a 3D transform
     * @throws NonInvertibleTransformException if this transform
     *         cannot be inverted
     * @throws NullPointerException if the specified {@code point} is null
     * @since JavaFX 8.0
     */
    public Point2D inverseDeltaTransform(Point2D point)
            throws NonInvertibleTransformException {
        return inverseDeltaTransform(point.getX(), point.getY());
    }

    /**
     * Transforms the relative magnitude vector by the inverse of this transform.
     * The vector is transformed without applying the translation components
     * of the affine transformation matrix.
     * @param x vector magnitude in the direction of the X axis
     * @param y vector magnitude in the direction of the Y axis
     * @return the inversely transformed relative magnitude vector represented
     *         by a {@code Point3D} instance
     * @throws NonInvertibleTransformException if this transform
     *         cannot be inverted
     * @since JavaFX 8.0
     */
    public Point3D inverseDeltaTransform(double x, double y, double z)
            throws NonInvertibleTransformException {

        return getInverseCache().deltaTransform(x, y, z);
    }

    /**
     * Transforms the relative magnitude vector represented by the specified
     * {@code Point3D} instance by the inverse of this transform.
     * The vector is transformed without applying the translation components
     * of the affine transformation matrix.
     * @param point the relative magnitude vector
     * @return the inversely transformed relative magnitude vector represented
     *         by a {@code Point3D} instance
     * @throws NonInvertibleTransformException if this transform
     *         cannot be inverted
     * @throws NullPointerException if the specified {@code point} is null
     * @since JavaFX 8.0
     */
    public Point3D inverseDeltaTransform(Point3D point)
            throws NonInvertibleTransformException {
        return inverseDeltaTransform(point.getX(), point.getY(), point.getZ());
    }

    /**
     * Helper method for transforming arrays of points that deals with
     * overlapping arrays.
     * @return the (if necessary fixed) srcOff
     */
    private int getFixedSrcOffset(double[] srcPts, int srcOff,
            double[] dstPts, int dstOff,
            int numPts, int dimensions) {

        if (dstPts == srcPts &&
            dstOff > srcOff && dstOff < srcOff + numPts * dimensions)
        {
            // If the arrays overlap partially with the destination higher
            // than the source and we transform the coordinates normally
            // we would overwrite some of the later source coordinates
            // with results of previous transformations.
            // To get around this we use arraycopy to copy the points
            // to their final destination with correct overwrite
            // handling and then transform them in place in the new
            // safer location.
            System.arraycopy(srcPts, srcOff, dstPts, dstOff, numPts * dimensions);
            return dstOff;
        }

        return srcOff;
    }

    /* *************************************************************************
     *                                                                         *
     *                         Event Dispatch                                  *
     *                                                                         *
     **************************************************************************/

    private EventHandlerManager internalEventDispatcher;
    private EventHandlerManager getInternalEventDispatcher() {
        if (internalEventDispatcher == null) {
            internalEventDispatcher = new EventHandlerManager(this);
        }
        return internalEventDispatcher;
    }
    private ObjectProperty<EventHandler<? super TransformChangedEvent>>
            onTransformChanged;

    @Override
    public EventDispatchChain buildEventDispatchChain(EventDispatchChain tail) {
        return internalEventDispatcher == null
                ? tail : tail.append(getInternalEventDispatcher());
    }

    /**
     * <p>
     * Registers an event handler to this transform. Any event filters are first
     * processed, then the specified onFoo event handlers, and finally any
     * event handlers registered by this method.
     * </p><p>
     * Currently the only event delivered to a {@code Transform} is the
     * {@code TransformChangedEvent} with it's single type
     * {@code TRANSFORM_CHANGED}.
     * </p>
     *
     * @param <T> the specific event class of the handler
     * @param eventType the type of the events to receive by the handler
     * @param eventHandler the handler to register
     * @throws NullPointerException if the event type or handler is null
     * @since JavaFX 8.0
     */
    public final <T extends Event> void addEventHandler(
            final EventType<T> eventType,
            final EventHandler<? super T> eventHandler) {
        getInternalEventDispatcher()
                .addEventHandler(eventType, eventHandler);
        // need to validate all properties to get the change events
        validate();
    }

    /**
     * Unregisters a previously registered event handler from this transform.
     * One handler might have been registered for different event types, so the
     * caller needs to specify the particular event type from which to
     * unregister the handler.
     *
     * @param <T> the specific event class of the handler
     * @param eventType the event type from which to unregister
     * @param eventHandler the handler to unregister
     * @throws NullPointerException if the event type or handler is null
     * @since JavaFX 8.0
     */
    public final <T extends Event> void removeEventHandler(
            final EventType<T> eventType,
            final EventHandler<? super T> eventHandler) {
        getInternalEventDispatcher()
                .removeEventHandler(eventType, eventHandler);
    }

    /**
     * <p>
     * Registers an event filter to this transform. Registered event filters get
     * an event before any associated event handlers.
     * </p><p>
     * Currently the only event delivered to a {@code Transform} is the
     * {@code TransformChangedEvent} with it's single type
     * {@code TRANSFORM_CHANGED}.
     * <p>
     *
     * @param <T> the specific event class of the filter
     * @param eventType the type of the events to receive by the filter
     * @param eventFilter the filter to register
     * @throws NullPointerException if the event type or filter is null
     * @since JavaFX 8.0
     */
    public final <T extends Event> void addEventFilter(
            final EventType<T> eventType,
            final EventHandler<? super T> eventFilter) {
        getInternalEventDispatcher()
                .addEventFilter(eventType, eventFilter);
        // need to validate all properties to get the change events
        validate();
    }

    /**
     * Unregisters a previously registered event filter from this transform. One
     * filter might have been registered for different event types, so the
     * caller needs to specify the particular event type from which to
     * unregister the filter.
     *
     * @param <T> the specific event class of the filter
     * @param eventType the event type from which to unregister
     * @param eventFilter the filter to unregister
     * @throws NullPointerException if the event type or filter is null
     * @since JavaFX 8.0
     */
    public final <T extends Event> void removeEventFilter(
            final EventType<T> eventType,
            final EventHandler<? super T> eventFilter) {
        getInternalEventDispatcher()
                .removeEventFilter(eventType, eventFilter);
    }

    /**
     * Sets the onTransformChanged event handler which is called whenever
     * the transform changes any of its parameters.
     *
     * @param value the event handler, can be null to clear it
     * @since JavaFX 8.0
     */
    public final void setOnTransformChanged(
            EventHandler<? super TransformChangedEvent> value) {
        onTransformChangedProperty().set(value);
        // need to validate all properties to get the change events
        validate();
    }

    /**
     * Gets the onTransformChanged event handler.
     * @return the event handler previously set by {@code setOnTransformChanged}
     * method, null if the handler is not set.
     * @since JavaFX 8.0
     */
    public final EventHandler<? super TransformChangedEvent> getOnTransformChanged() {
        return (onTransformChanged == null) ? null : onTransformChanged.get();
    }

    /**
     * The onTransformChanged event handler is called whenever the transform
     * changes any of its parameters.
     * @since JavaFX 8.0
     */
    public final ObjectProperty<EventHandler<? super TransformChangedEvent>>
            onTransformChangedProperty() {
        if (onTransformChanged == null) {

            onTransformChanged = new SimpleObjectProperty<EventHandler
                    <? super TransformChangedEvent>>(this, "onTransformChanged") {

                @Override protected void invalidated() {
                    getInternalEventDispatcher().setEventHandler(
                            TransformChangedEvent.TRANSFORM_CHANGED, get());
                }
            };
        }

        return onTransformChanged;
    }

    /* *************************************************************************
     *                                                                         *
     *                    Internal implementation stuff                        *
     *                                                                         *
     **************************************************************************/

    /**
     * Makes sure the specified matrix type can be requested from this transform.
     * Is used for convenience in various methods that accept
     * the MatrixType argument.
     * @param type matrix type to check
     * @throws IllegalArgumentException if this is a 3D transform and
     *                                  a 2D type is requested
     */
    void checkRequestedMAT(MatrixType type) throws IllegalArgumentException{
        if (type.is2D() && !isType2D()) {
            throw new IllegalArgumentException("Cannot access 2D matrix "
                    + "for a 3D transform");
        }
    }

    /**
     * Makes sure this is a 2D transform.
     * Is used for convenience in various 2D point transformation methods.
     * @throws IllegalStateException if this is a 2D transform
     */
    void ensureCanTransform2DPoint() throws IllegalStateException {
        if (!isType2D()) {
            throw new IllegalStateException("Cannot transform 2D point "
                    + "with a 3D transform");
        }
    }

    /**
     * Needed for the proper delivery of the TransformChangedEvent.
     * If the members are invalid, the transformChanged() notification
     * is not called and the event is not delivered. To avoid that
     * we need to manually validate all properties. Subclasses validate
     * their specific properties.
     */
    void validate() {
        getMxx(); getMxy(); getMxz(); getTx();
        getMyx(); getMyy(); getMyz(); getTy();
        getMzx(); getMzy(); getMzz(); getTz();
    }

    /**
     * @treatAsPrivate implementation detail
     * @deprecated This is an internal API that is not intended for use and will be removed in the next version
     */
    @Deprecated
    public abstract void impl_apply(Affine3D t);

    /**
     * @treatAsPrivate implementation detail
     * @deprecated This is an internal API that is not intended for use and will be removed in the next version
     */
    @Deprecated
    public abstract BaseTransform impl_derive(BaseTransform t);

    /**
     * @treatAsPrivate implementation detail
     * @deprecated This is an internal API that is not intended for use and will be removed in the next version
     */
    @Deprecated
    public void impl_add(final Node node) {
        impl_nodes.add(node);
    }

    /**
     * @treatAsPrivate implementation detail
     * @deprecated This is an internal API that is not intended for use and will be removed in the next version
     */
    @Deprecated
    public void impl_remove(final Node node) {
        impl_nodes.remove(node);
    }

    /**
     * This method must be called by all transforms whenever any of their
     * parameters changes. It is typically called when any of the transform's
     * properties is invalidated (it is OK to skip the call if an invalid
     * property is set).
     * @since JavaFX 8.0
     */
    protected void transformChanged() {
        inverseCache = null;
        final Iterator iterator = impl_nodes.iterator();
        while (iterator.hasNext()) {
            ((Node) iterator.next()).impl_transformsChanged();
        }

        if (type2D != null) {
            type2D.invalidate();
        }

        if (identity != null) {
            identity.invalidate();
        }

        if (internalEventDispatcher != null) {
            // need to validate all properties for the event to be fired next time
            validate();
            Event.fireEvent(this, new TransformChangedEvent(this, this));
        }
    }

    /**
     * Visitor from {@code Affine} class which provides an efficient
     * {@code append} operation for the subclasses.
     * @param a {@code Affine} instance to append to
     */
    void appendTo(Affine a) {
        a.append(getMxx(), getMxy(), getMxz(), getTx(),
                 getMyx(), getMyy(), getMyz(), getTy(),
                 getMzx(), getMzy(), getMzz(), getTz());
    }

    /**
     * Visitor from {@code Affine} class which provides an efficient
     * {@code prepend} operation for the subclasses.
     * @param a {@code Affine} instance to prepend to
     */
    void prependTo(Affine a) {
        a.prepend(getMxx(), getMxy(), getMxz(), getTx(),
                  getMyx(), getMyy(), getMyz(), getTy(),
                  getMzx(), getMzy(), getMzz(), getTz());
    }

    /**
     * <p>
     * Gets the inverse transform cache.
     * </p><p>
     * Computing the inverse transform is generally an expensive operation,
     * so once it is needed we cache the result (throwing it away when the
     * transform changes). The subclasses may avoid using the cache if their
     * inverse can be computed quickly on the fly.
     * </p><p>
     * This method computes the inverse if the cache is not valid.
     * </p>
     * @return the cached inverse transformation
     * @throws NonInvertibleTransformException if this transform
     *         cannot be inverted
     */
    private Transform getInverseCache() throws NonInvertibleTransformException {
        if (inverseCache == null || inverseCache.get() == null) {
            Affine inv = new Affine(
                    getMxx(), getMxy(), getMxz(), getTx(),
                    getMyx(), getMyy(), getMyz(), getTy(),
                    getMzx(), getMzy(), getMzz(), getTz());
            inv.invert();
            inverseCache = new SoftReference<Transform>(inv);
            return inv;
        }

        return inverseCache.get();
    }

    /**
     * Used only by tests to emulate garbage collecting the soft references
     */
    void clearInverseCache() {
        if (inverseCache != null) {
            inverseCache.clear();
        }
    }
}
