Server/src/engine/math/Matrix3f.java

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//      Magicbane Emulator Project © 2013 - 2022
//                www.magicbane.com

 package engine.math;

import org.pmw.tinylog.Logger;

import java.nio.FloatBuffer;


/**
 * <code>Matrix3f</code> defines a 3x3 matrix. Matrix data is maintained
 * internally and is accessible via the get and set methods. Convenience methods
 * are used for matrix operations as well as generating a matrix from a given
 * set of values.
 * 
 */
public class Matrix3f {
	public float m00, m01, m02;
	public float m10, m11, m12;
	public float m20, m21, m22;

	/**
	 * Constructor instantiates a new <code>Matrix3f</code> object. The initial
	 * values for the matrix is that of the identity matrix.
	 * 
	 */
	public Matrix3f() {
		loadIdentity();
	}

	/**
	 * constructs a matrix with the given values.
	 * 
	 * @param m00
	 *            0x0 in the matrix.
	 * @param m01
	 *            0x1 in the matrix.
	 * @param m02
	 *            0x2 in the matrix.
	 * @param m10
	 *            1x0 in the matrix.
	 * @param m11
	 *            1x1 in the matrix.
	 * @param m12
	 *            1x2 in the matrix.
	 * @param m20
	 *            2x0 in the matrix.
	 * @param m21
	 *            2x1 in the matrix.
	 * @param m22
	 *            2x2 in the matrix.
	 */
	public Matrix3f(float m00, float m01, float m02, float m10, float m11,
			float m12, float m20, float m21, float m22) {

		this.m00 = m00;
		this.m01 = m01;
		this.m02 = m02;
		this.m10 = m10;
		this.m11 = m11;
		this.m12 = m12;
		this.m20 = m20;
		this.m21 = m21;
		this.m22 = m22;
	}

	/**
	 * Copy constructor that creates a new <code>Matrix3f</code> object that is
	 * the same as the provided matrix.
	 * 
	 * @param mat
	 *            the matrix to copy.
	 */
	public Matrix3f(Matrix3f mat) {
		copy(mat);
	}

	/**
	 * <code>copy</code> transfers the contents of a given matrix to this
	 * matrix. If a null matrix is supplied, this matrix is set to the identity
	 * matrix.
	 * 
	 * @param matrix
	 *            the matrix to copy.
	 */
	public void copy(Matrix3f matrix) {
		if (null == matrix) {
			loadIdentity();
		} else {
			m00 = matrix.m00;
			m01 = matrix.m01;
			m02 = matrix.m02;
			m10 = matrix.m10;
			m11 = matrix.m11;
			m12 = matrix.m12;
			m20 = matrix.m20;
			m21 = matrix.m21;
			m22 = matrix.m22;
		}
	}

	/**
	 * <code>get</code> retrieves a value from the matrix at the given position.
	 * If the position is invalid a <code>Exception</code> is thrown.
	 * 
	 * @param i
	 *            the row index.
	 * @param j
	 *            the column index.
	 * @return the value at (i, j).
	 * @throws Exception
	 */
	public float get(int i, int j) throws Exception {
		switch (i) {
		case 0:
			switch (j) {
			case 0:
				return m00;
			case 1:
				return m01;
			case 2:
				return m02;
			}
		case 1:
			switch (j) {
			case 0:
				return m10;
			case 1:
				return m11;
			case 2:
				return m12;
			}
		case 2:
			switch (j) {
			case 0:
				return m20;
			case 1:
				return m21;
			case 2:
				return m22;
			}
		}
		throw new Exception("Invalid indices into matrix.");
	}

	/**
	 * <code>get(float[])</code> returns the matrix in row-major or column-major
	 * order.
	 * 
	 * @param data
	 *            The array to return the data into. This array can be 9 or 16
	 *            floats in size. Only the upper 3x3 are assigned to in the case
	 *            of a 16 element array.
	 * @param rowMajor
	 *            True for row major storage in the array (translation in
	 *            elements 3, 7, 11 for a 4x4), false for column major
	 *            (translation in elements 12, 13, 14 for a 4x4).
	 * @throws Exception
	 */
	public void get(float[] data, boolean rowMajor) throws Exception {
		if (data.length == 9) {
			if (rowMajor) {
				data[0] = m00;
				data[1] = m01;
				data[2] = m02;
				data[3] = m10;
				data[4] = m11;
				data[5] = m12;
				data[6] = m20;
				data[7] = m21;
				data[8] = m22;
			} else {
				data[0] = m00;
				data[1] = m10;
				data[2] = m20;
				data[3] = m01;
				data[4] = m11;
				data[5] = m21;
				data[6] = m02;
				data[7] = m12;
				data[8] = m22;
			}
		} else if (data.length == 16) {
			if (rowMajor) {
				data[0] = m00;
				data[1] = m01;
				data[2] = m02;
				data[4] = m10;
				data[5] = m11;
				data[6] = m12;
				data[8] = m20;
				data[9] = m21;
				data[10] = m22;
			} else {
				data[0] = m00;
				data[1] = m10;
				data[2] = m20;
				data[4] = m01;
				data[5] = m11;
				data[6] = m21;
				data[8] = m02;
				data[9] = m12;
				data[10] = m22;
			}
		} else {
			throw new Exception("Array size must be 9 or 16 in Matrix3f.get().");
		}
	}

	/**
	 * <code>getColumn</code> returns one of three columns specified by the
	 * parameter. This column is returned as a <code>Vector3f</code> object.
	 * 
	 * @param i
	 *            the column to retrieve. Must be between 0 and 2.
	 * @return the column specified by the index.
	 * @throws Exception
	 */
	public Vector3f getColumn(int i) throws Exception {
		return getColumn(i, null);
	}

	/**
	 * <code>getColumn</code> returns one of three columns specified by the
	 * parameter. This column is returned as a <code>Vector3f</code> object.
	 * 
	 * @param i
	 *            the column to retrieve. Must be between 0 and 2.
	 * @param store
	 *            the vector object to store the result in. if null, a new one
	 *            is created.
	 * @return the column specified by the index.
	 * @throws Exception
	 */
	public Vector3f getColumn(int i, Vector3f store) throws Exception {
		if (store == null)
			store = new Vector3f();
		switch (i) {
		case 0:
			store.x = m00;
			store.y = m10;
			store.z = m20;
			break;
		case 1:
			store.x = m01;
			store.y = m11;
			store.z = m21;
			break;
		case 2:
			store.x = m02;
			store.y = m12;
			store.z = m22;
			break;
		default:
			throw new Exception("Invalid column index. " + i);
		}
		return store;
	}

	/**
	 * <code>getColumn</code> returns one of three rows as specified by the
	 * parameter. This row is returned as a <code>Vector3f</code> object.
	 * 
	 * @param i
	 *            the row to retrieve. Must be between 0 and 2.
	 * @return the row specified by the index.
	 * @throws Exception
	 */
	public Vector3f getRow(int i) throws Exception {
		return getRow(i, null);
	}

	/**
	 * <code>getRow</code> returns one of three rows as specified by the
	 * parameter. This row is returned as a <code>Vector3f</code> object.
	 * 
	 * @param i
	 *            the row to retrieve. Must be between 0 and 2.
	 * @param store
	 *            the vector object to store the result in. if null, a new one
	 *            is created.
	 * @return the row specified by the index.
	 * @throws Exception
	 */
	public Vector3f getRow(int i, Vector3f store) throws Exception {
		if (store == null)
			store = new Vector3f();
		switch (i) {
		case 0:
			store.x = m00;
			store.y = m01;
			store.z = m02;
			break;
		case 1:
			store.x = m10;
			store.y = m11;
			store.z = m12;
			break;
		case 2:
			store.x = m20;
			store.y = m21;
			store.z = m22;
			break;
		default:
			throw new Exception("Invalid row index. " + i);
		}
		return store;
	}

	/**
	 * <code>fillFloatBuffer</code> fills a FloatBuffer object with the matrix
	 * data.
	 * 
	 * @param fb
	 *            the buffer to fill, starting at current position. Must have
	 *            room for 9 more floats.
	 * @return matrix data as a FloatBuffer. (position is advanced by 9 and any
	 *         limit set is not changed).
	 */
	public FloatBuffer fillFloatBuffer(FloatBuffer fb) {
		fb.put(m00).put(m01).put(m02);
		fb.put(m10).put(m11).put(m12);
		fb.put(m20).put(m21).put(m22);
		return fb;
	}

	/**
	 * 
	 * <code>setColumn</code> sets a particular column of this matrix to that
	 * represented by the provided vector.
	 * 
	 * @param i
	 *            the column to set.
	 * @param column
	 *            the data to set.
	 * @throws Exception
	 */
	public void setColumn(int i, Vector3f column) throws Exception {

		if (column == null) {
			return;
		}
		switch (i) {
		case 0:
			m00 = column.x;
			m10 = column.y;
			m20 = column.z;
			break;
		case 1:
			m01 = column.x;
			m11 = column.y;
			m21 = column.z;
			break;
		case 2:
			m02 = column.x;
			m12 = column.y;
			m22 = column.z;
			break;
		default:
			throw new Exception("Invalid column index. " + i);
		}
	}

	/**
	 * 
	 * <code>setRow</code> sets a particular row of this matrix to that
	 * represented by the provided vector.
	 * 
	 * @param i
	 *            the row to set.
	 * @param row
	 *            the data to set.
	 * @throws Exception
	 */
	public void setRow(int i, Vector3f row) throws Exception {

		if (row == null) {
			return;
		}
		switch (i) {
		case 0:
			m00 = row.x;
			m01 = row.y;
			m02 = row.z;
			break;
		case 1:
			m10 = row.x;
			m11 = row.y;
			m12 = row.z;
			break;
		case 2:
			m20 = row.x;
			m21 = row.y;
			m22 = row.z;
			break;
		default:
			throw new Exception("Invalid row index. " + i);
		}
	}

	/**
	 * <code>set</code> places a given value into the matrix at the given
	 * position. If the position is invalid a <code>Exception</code> is thrown.
	 * 
	 * @param i
	 *            the row index.
	 * @param j
	 *            the column index.
	 * @param value
	 *            the value for (i, j).
	 * @throws Exception
	 */
	public void set(int i, int j, float value) throws Exception {
		switch (i) {
		case 0:
			switch (j) {
			case 0:
				m00 = value;
				return;
			case 1:
				m01 = value;
				return;
			case 2:
				m02 = value;
				return;
			}
		case 1:
			switch (j) {
			case 0:
				m10 = value;
				return;
			case 1:
				m11 = value;
				return;
			case 2:
				m12 = value;
				return;
			}
		case 2:
			switch (j) {
			case 0:
				m20 = value;
				return;
			case 1:
				m21 = value;
				return;
			case 2:
				m22 = value;
				return;
			}
		}
		throw new Exception("Invalid indices into matrix.");
	}

	/**
	 * 
	 * <code>set</code> sets the values of the matrix to those supplied by the
	 * 3x3 two dimenion array.
	 * 
	 * @param matrix
	 *            the new values of the matrix.
	 * @throws Exception
	 *             if the array is not of size 9.
	 */
	public void set(float[][] matrix) throws Exception {
		if (matrix.length != 3 || matrix[0].length != 3) {
			throw new Exception("Array must be of size 9.");
		}

		m00 = matrix[0][0];
		m01 = matrix[0][1];
		m02 = matrix[0][2];
		m10 = matrix[1][0];
		m11 = matrix[1][1];
		m12 = matrix[1][2];
		m20 = matrix[2][0];
		m21 = matrix[2][1];
		m22 = matrix[2][2];
	}

	/**
	 * Recreate Matrix using the provided axis.
	 * 
	 * @param uAxis
	 *            Vector3f
	 * @param vAxis
	 *            Vector3f
	 * @param wAxis
	 *            Vector3f
	 */
	public void fromAxes(Vector3f uAxis, Vector3f vAxis, Vector3f wAxis) {
		m00 = uAxis.x;
		m10 = uAxis.y;
		m20 = uAxis.z;

		m01 = vAxis.x;
		m11 = vAxis.y;
		m21 = vAxis.z;

		m02 = wAxis.x;
		m12 = wAxis.y;
		m22 = wAxis.z;
	}

	/**
	 * <code>set</code> sets the values of this matrix from an array of values
	 * assuming that the data is rowMajor order;
	 * 
	 * @param matrix
	 *            the matrix to set the value to.
	 * @throws Exception
	 */
	public void set(float[] matrix) throws Exception {
		set(matrix, true);
	}

	/**
	 * <code>set</code> sets the values of this matrix from an array of values;
	 * 
	 * @param matrix
	 *            the matrix to set the value to.
	 * @param rowMajor
	 *            whether the incoming data is in row or column major order.
	 */
	public void set(float[] matrix, boolean rowMajor) throws Exception {
		if (matrix.length != 9)
			throw new Exception("Array must be of size 9.");

		if (rowMajor) {
			m00 = matrix[0];
			m01 = matrix[1];
			m02 = matrix[2];
			m10 = matrix[3];
			m11 = matrix[4];
			m12 = matrix[5];
			m20 = matrix[6];
			m21 = matrix[7];
			m22 = matrix[8];
		} else {
			m00 = matrix[0];
			m01 = matrix[3];
			m02 = matrix[6];
			m10 = matrix[1];
			m11 = matrix[4];
			m12 = matrix[7];
			m20 = matrix[2];
			m21 = matrix[5];
			m22 = matrix[8];
		}
	}

	/**
	 * 
	 * <code>set</code> defines the values of the matrix based on a supplied
	 * <code>Quaternion</code>. It should be noted that all previous values will
	 * be overridden.
	 * 
	 * @param quaternion
	 *            the quaternion to create a rotational matrix from.
	 */
	public void set(Quaternion quaternion) {
		quaternion.toRotationMatrix(this);
	}

	/**
	 * <code>loadIdentity</code> sets this matrix to the identity matrix. Where
	 * all values are zero except those along the diagonal which are one.
	 * 
	 */
	public void loadIdentity() {
		m01 = m02 = m10 = m12 = m20 = m21 = 0;
		m00 = m11 = m22 = 1;
	}

	/**
	 * @return true if this matrix is identity
	 */
	public boolean isIdentity() {
		return (m00 == 1 && m01 == 0 && m02 == 0)
				&& (m10 == 0 && m11 == 1 && m12 == 0)
				&& (m20 == 0 && m21 == 0 && m22 == 1);
	}

	/**
	 * <code>fromAngleAxis</code> sets this matrix4f to the values specified by
	 * an angle and an axis of rotation. This method creates an object, so use
	 * fromAngleNormalAxis if your axis is already normalized.
	 * 
	 * @param angle
	 *            the angle to rotate (in radians).
	 * @param axis
	 *            the axis of rotation.
	 */
	public void fromAngleAxis(float angle, Vector3f axis) {
		Vector3f normAxis = axis.normalize();
		fromAngleNormalAxis(angle, normAxis);
	}

	/**
	 * <code>fromAngleNormalAxis</code> sets this matrix4f to the values
	 * specified by an angle and a normalized axis of rotation.
	 * 
	 * @param angle
	 *            the angle to rotate (in radians).
	 * @param axis
	 *            the axis of rotation (already normalized).
	 */
	public void fromAngleNormalAxis(float angle, Vector3f axis) {
		float fCos = FastMath.cos(angle);
		float fSin = FastMath.sin(angle);
		float fOneMinusCos = ((float) 1.0) - fCos;
		float fX2 = axis.x * axis.x;
		float fY2 = axis.y * axis.y;
		float fZ2 = axis.z * axis.z;
		float fXYM = axis.x * axis.y * fOneMinusCos;
		float fXZM = axis.x * axis.z * fOneMinusCos;
		float fYZM = axis.y * axis.z * fOneMinusCos;
		float fXSin = axis.x * fSin;
		float fYSin = axis.y * fSin;
		float fZSin = axis.z * fSin;

		m00 = fX2 * fOneMinusCos + fCos;
		m01 = fXYM - fZSin;
		m02 = fXZM + fYSin;
		m10 = fXYM + fZSin;
		m11 = fY2 * fOneMinusCos + fCos;
		m12 = fYZM - fXSin;
		m20 = fXZM - fYSin;
		m21 = fYZM + fXSin;
		m22 = fZ2 * fOneMinusCos + fCos;
	}

	/**
	 * <code>mult</code> multiplies this matrix by a given matrix. The result
	 * matrix is returned as a new object. If the given matrix is null, a null
	 * matrix is returned.
	 * 
	 * @param mat
	 *            the matrix to multiply this matrix by.
	 * @return the result matrix.
	 */
	public Matrix3f mult(Matrix3f mat) {
		return mult(mat, null);
	}

	/**
	 * <code>mult</code> multiplies this matrix by a given matrix. The result
	 * matrix is returned as a new object.
	 * 
	 * @param mat
	 *            the matrix to multiply this matrix by.
	 * @param product
	 *            the matrix to store the result in. if null, a new matrix3f is
	 *            created. It is safe for mat and product to be the same object.
	 * @return a matrix3f object containing the result of this operation
	 */
	public Matrix3f mult(Matrix3f mat, Matrix3f product) {

		float temp00, temp01, temp02;
		float temp10, temp11, temp12;
		float temp20, temp21, temp22;

		if (product == null)
			product = new Matrix3f();
		temp00 = m00 * mat.m00 + m01 * mat.m10 + m02 * mat.m20;
		temp01 = m00 * mat.m01 + m01 * mat.m11 + m02 * mat.m21;
		temp02 = m00 * mat.m02 + m01 * mat.m12 + m02 * mat.m22;
		temp10 = m10 * mat.m00 + m11 * mat.m10 + m12 * mat.m20;
		temp11 = m10 * mat.m01 + m11 * mat.m11 + m12 * mat.m21;
		temp12 = m10 * mat.m02 + m11 * mat.m12 + m12 * mat.m22;
		temp20 = m20 * mat.m00 + m21 * mat.m10 + m22 * mat.m20;
		temp21 = m20 * mat.m01 + m21 * mat.m11 + m22 * mat.m21;
		temp22 = m20 * mat.m02 + m21 * mat.m12 + m22 * mat.m22;

		product.m00 = temp00;
		product.m01 = temp01;
		product.m02 = temp02;
		product.m10 = temp10;
		product.m11 = temp11;
		product.m12 = temp12;
		product.m20 = temp20;
		product.m21 = temp21;
		product.m22 = temp22;

		return product;
	}

	/**
	 * <code>mult</code> multiplies this matrix by a given <code>Vector3f</code>
	 * object. The result vector is returned. If the given vector is null, null
	 * will be returned.
	 * 
	 * @param vec
	 *            the vector to multiply this matrix by.
	 * @return the result vector.
	 */
	public Vector3f mult(Vector3f vec) {
		return mult(vec, null);
	}

	/**
	 * Multiplies this 3x3 matrix by the 1x3 Vector vec and stores the result in
	 * product.
	 * 
	 * @param vec
	 *            The Vector3f to multiply.
	 * @param product
	 *            The Vector3f to store the result, it is safe for this to be
	 *            the same as vec.
	 * @return The given product vector.
	 */
	public Vector3f mult(Vector3f vec, Vector3f product) {

		if (null == product) {
			product = new Vector3f();
		}

		float x = vec.x;
		float y = vec.y;
		float z = vec.z;

		product.x = m00 * x + m01 * y + m02 * z;
		product.y = m10 * x + m11 * y + m12 * z;
		product.z = m20 * x + m21 * y + m22 * z;
		return product;
	}

	/**
	 * <code>multLocal</code> multiplies this matrix internally by a given float
	 * scale factor.
	 * 
	 * @param scale
	 *            the value to scale by.
	 * @return this Matrix3f
	 */
	public Matrix3f multLocal(float scale) {
		m00 *= scale;
		m01 *= scale;
		m02 *= scale;
		m10 *= scale;
		m11 *= scale;
		m12 *= scale;
		m20 *= scale;
		m21 *= scale;
		m22 *= scale;
		return this;
	}

	/**
	 * <code>multLocal</code> multiplies this matrix by a given
	 * <code>Vector3f</code> object. The result vector is stored inside the
	 * passed vector, then returned . If the given vector is null, null will be
	 * returned.
	 * 
	 * @param vec
	 *            the vector to multiply this matrix by.
	 * @return The passed vector after multiplication
	 */
	public Vector3f multLocal(Vector3f vec) {
		if (vec == null)
			return null;
		float x = vec.x;
		float y = vec.y;
		vec.x = m00 * x + m01 * y + m02 * vec.z;
		vec.y = m10 * x + m11 * y + m12 * vec.z;
		vec.z = m20 * x + m21 * y + m22 * vec.z;
		return vec;
	}

	/**
	 * <code>mult</code> multiplies this matrix by a given matrix. The result
	 * matrix is saved in the current matrix. If the given matrix is null,
	 * nothing happens. The current matrix is returned. This is equivalent to
	 * this*=mat
	 * 
	 * @param mat
	 *            the matrix to multiply this matrix by.
	 * @return This matrix, after the multiplication
	 */
	public Matrix3f multLocal(Matrix3f mat) {

		return mult(mat, this);
	}

	/**
	 * Transposes this matrix in place. Returns this matrix for chaining
	 * 
	 * @return This matrix after transpose
	 * @throws Exception
	 */
	public Matrix3f transposeLocal() throws Exception {
		float[] tmp = new float[9];
		get(tmp, false);
		set(tmp, true);
		return this;
	}

	/**
	 * Inverts this matrix as a new Matrix3f.
	 * 
	 * @return The new inverse matrix
	 */
	public Matrix3f invert() {
		return invert(null);
	}

	/**
	 * Inverts this matrix and stores it in the given store.
	 * 
	 * @return The store
	 */
	public Matrix3f invert(Matrix3f store) {
		if (store == null)
			store = new Matrix3f();

		float det = determinant();
		if (FastMath.abs(det) <= 0)
			return store.zero();

		store.m00 = m11 * m22 - m12 * m21;
		store.m01 = m02 * m21 - m01 * m22;
		store.m02 = m01 * m12 - m02 * m11;
		store.m10 = m12 * m20 - m10 * m22;
		store.m11 = m00 * m22 - m02 * m20;
		store.m12 = m02 * m10 - m00 * m12;
		store.m20 = m10 * m21 - m11 * m20;
		store.m21 = m01 * m20 - m00 * m21;
		store.m22 = m00 * m11 - m01 * m10;

		store.multLocal(1f / det);
		return store;
	}

	/**
	 * Inverts this matrix locally.
	 * 
	 * @return this
	 */
	public Matrix3f invertLocal() {
		float det = determinant();
		if (FastMath.abs(det) <= FastMath.FLT_EPSILON)
			return zero();

		float f00 = m11 * m22 - m12 * m21;
		float f01 = m02 * m21 - m01 * m22;
		float f02 = m01 * m12 - m02 * m11;
		float f10 = m12 * m20 - m10 * m22;
		float f11 = m00 * m22 - m02 * m20;
		float f12 = m02 * m10 - m00 * m12;
		float f20 = m10 * m21 - m11 * m20;
		float f21 = m01 * m20 - m00 * m21;
		float f22 = m00 * m11 - m01 * m10;

		m00 = f00;
		m01 = f01;
		m02 = f02;
		m10 = f10;
		m11 = f11;
		m12 = f12;
		m20 = f20;
		m21 = f21;
		m22 = f22;

		multLocal(1f / det);
		return this;
	}

	/**
	 * Returns a new matrix representing the adjoint of this matrix.
	 * 
	 * @return The adjoint matrix
	 */
	public Matrix3f adjoint() {
		return adjoint(null);
	}

	/**
	 * Places the adjoint of this matrix in store (creates store if null.)
	 * 
	 * @param store
	 *            The matrix to store the result in. If null, a new matrix is
	 *            created.
	 * @return store
	 */
	public Matrix3f adjoint(Matrix3f store) {
		if (store == null)
			store = new Matrix3f();

		store.m00 = m11 * m22 - m12 * m21;
		store.m01 = m02 * m21 - m01 * m22;
		store.m02 = m01 * m12 - m02 * m11;
		store.m10 = m12 * m20 - m10 * m22;
		store.m11 = m00 * m22 - m02 * m20;
		store.m12 = m02 * m10 - m00 * m12;
		store.m20 = m10 * m21 - m11 * m20;
		store.m21 = m01 * m20 - m00 * m21;
		store.m22 = m00 * m11 - m01 * m10;

		return store;
	}

	/**
	 * <code>determinant</code> generates the determinate of this matrix.
	 * 
	 * @return the determinate
	 */
	public float determinant() {
		float fCo00 = m11 * m22 - m12 * m21;
		float fCo10 = m12 * m20 - m10 * m22;
		float fCo20 = m10 * m21 - m11 * m20;
        return m00 * fCo00 + m01 * fCo10 + m02 * fCo20;
	}

	/**
	 * Sets all of the values in this matrix to zero.
	 * 
	 * @return this matrix
	 */
	public Matrix3f zero() {
		m00 = m01 = m02 = m10 = m11 = m12 = m20 = m21 = m22 = 0.0f;
		return this;
	}

	/**
	 * <code>add</code> adds the values of a parameter matrix to this matrix.
	 * 
	 * @param mat
	 *            the matrix to add to this.
	 */
	public void add(Matrix3f mat) {
		m00 += mat.m00;
		m01 += mat.m01;
		m02 += mat.m02;
		m10 += mat.m10;
		m11 += mat.m11;
		m12 += mat.m12;
		m20 += mat.m20;
		m21 += mat.m21;
		m22 += mat.m22;
	}

	/**
	 * <code>transpose</code> <b>locally</b> transposes this Matrix. This is
	 * inconsistent with general value vs local semantics, but is preserved for
	 * backwards compatibility. Use transposeNew() to transpose to a new object
	 * (value).
	 * 
	 * @return this object for chaining.
	 * @throws Exception
	 */
	public Matrix3f transpose() throws Exception {
		return transposeLocal();
	}

	/**
	 * <code>transposeNew</code> returns a transposed version of this matrix.
	 * 
	 * @return The new Matrix3f object.
	 */
	public Matrix3f transposeNew() {
        return new Matrix3f(m00, m10, m20, m01, m11, m21, m02, m12, m22);
	}

	/**
	 * <code>toString</code> returns the string representation of this object.
	 * It is in a format of a 3x3 matrix. For example, an identity matrix would
	 * be represented by the following string. com.jme.math.Matrix3f <br>
	 * [<br>
	 * 1.0 0.0 0.0 <br>
	 * 0.0 1.0 0.0 <br>
	 * 0.0 0.0 1.0 <br>
	 * ]<br>
	 * 
	 * @return the string representation of this object.
	 */
	@Override
	public String toString() {
		StringBuffer result = new StringBuffer("com.jme.math.Matrix3f\n[\n");
		result.append(' ');
		result.append(m00);
		result.append("  ");
		result.append(m01);
		result.append("  ");
		result.append(m02);
		result.append(" \n");
		result.append(' ');
		result.append(m10);
		result.append("  ");
		result.append(m11);
		result.append("  ");
		result.append(m12);
		result.append(" \n");
		result.append(' ');
		result.append(m20);
		result.append("  ");
		result.append(m21);
		result.append("  ");
		result.append(m22);
		result.append(" \n]");
		return result.toString();
	}

	/**
	 * 
	 * <code>hashCode</code> returns the hash code value as an integer and is
	 * supported for the benefit of hashing based collection classes such as
	 * Hashtable, HashMap, HashSet etc.
	 * 
	 * @return the hashcode for this instance of Matrix4f.
	 * @see java.lang.Object#hashCode()
	 */
	@Override
	public int hashCode() {
		int hash = 37;
		hash = 37 * hash + Float.floatToIntBits(m00);
		hash = 37 * hash + Float.floatToIntBits(m01);
		hash = 37 * hash + Float.floatToIntBits(m02);

		hash = 37 * hash + Float.floatToIntBits(m10);
		hash = 37 * hash + Float.floatToIntBits(m11);
		hash = 37 * hash + Float.floatToIntBits(m12);

		hash = 37 * hash + Float.floatToIntBits(m20);
		hash = 37 * hash + Float.floatToIntBits(m21);
		hash = 37 * hash + Float.floatToIntBits(m22);

		return hash;
	}

	/**
	 * are these two matrices the same? they are is they both have the same mXX
	 * values.
	 * 
	 * @param o
	 *            the object to compare for equality
	 * @return true if they are equal
	 */
	@Override
	public boolean equals(Object o) {
		if (!(o instanceof Matrix3f) || o == null) {
			return false;
		}

		if (this == o) {
			return true;
		}

		Matrix3f comp = (Matrix3f) o;
		if (Float.compare(m00, comp.m00) != 0)
			return false;
		if (Float.compare(m01, comp.m01) != 0)
			return false;
		if (Float.compare(m02, comp.m02) != 0)
			return false;

		if (Float.compare(m10, comp.m10) != 0)
			return false;
		if (Float.compare(m11, comp.m11) != 0)
			return false;
		if (Float.compare(m12, comp.m12) != 0)
			return false;

		if (Float.compare(m20, comp.m20) != 0)
			return false;
		if (Float.compare(m21, comp.m21) != 0)
			return false;
		return Float.compare(m22, comp.m22) == 0;
	}

	/**
	 * A function for creating a rotation matrix that rotates a vector called
	 * "start" into another vector called "end".
	 * 
	 * @param start
	 *            normalized non-zero starting vector
	 * @param end
	 *            normalized non-zero ending vector
	 * @throws Exception
	 * @see "Tomas Miller, John Hughes \"Efficiently Building a Matrix to Rotate
	 *      \ One Vector to Another\" Journal of Graphics Tools, 4(4):1-4, 1999"
	 */
	public void fromStartEndVectors(Vector3f start, Vector3f end)
			throws Exception {
		Vector3f v = new Vector3f();
		float e, h, f;

		start.cross(end, v);
		e = start.dot(end);
		f = (e < 0) ? -e : e;

		// if "from" and "to" vectors are nearly parallel
		if (f > 1.0f - FastMath.ZERO_TOLERANCE) {
			Vector3f u = new Vector3f();
			Vector3f x = new Vector3f();
			float c1, c2, c3; /* coefficients for later use */
			int i, j;

			x.x = (start.x > 0.0) ? start.x : -start.x;
			x.y = (start.y > 0.0) ? start.y : -start.y;
			x.z = (start.z > 0.0) ? start.z : -start.z;

			if (x.x < x.y) {
				if (x.x < x.z) {
					x.x = 1.0f;
					x.y = x.z = 0.0f;
				} else {
					x.z = 1.0f;
					x.x = x.y = 0.0f;
				}
			} else {
				if (x.y < x.z) {
					x.y = 1.0f;
					x.x = x.z = 0.0f;
				} else {
					x.z = 1.0f;
					x.x = x.y = 0.0f;
				}
			}

			u.x = x.x - start.x;
			u.y = x.y - start.y;
			u.z = x.z - start.z;
			v.x = x.x - end.x;
			v.y = x.y - end.y;
			v.z = x.z - end.z;

			c1 = 2.0f / u.dot(u);
			c2 = 2.0f / v.dot(v);
			c3 = c1 * c2 * u.dot(v);

			for (i = 0; i < 3; i++) {
				for (j = 0; j < 3; j++) {
					float val = -c1 * u.get(i) * u.get(j) - c2 * v.get(i)
							* v.get(j) + c3 * v.get(i) * u.get(j);
					set(i, j, val);
				}
				float val = get(i, i);
				set(i, i, val + 1.0f);
			}
		} else {
			// the most common case, unless "start"="end", or "start"=-"end"
			float hvx, hvz, hvxy, hvxz, hvyz;
			h = 1.0f / (1.0f + e);
			hvx = h * v.x;
			hvz = h * v.z;
			hvxy = hvx * v.y;
			hvxz = hvx * v.z;
			hvyz = hvz * v.y;
			set(0, 0, e + hvx * v.x);
			set(0, 1, hvxy - v.z);
			set(0, 2, hvxz + v.y);

			set(1, 0, hvxy + v.z);
			set(1, 1, e + h * v.y * v.y);
			set(1, 2, hvyz - v.x);

			set(2, 0, hvxz - v.y);
			set(2, 1, hvyz + v.x);
			set(2, 2, e + hvz * v.z);
		}
	}

	/**
	 * <code>scale</code> scales the operation performed by this matrix on a
	 * per-component basis.
	 * 
	 * @param scale
	 *            The scale applied to each of the X, Y and Z output values.
	 */
	public void scale(Vector3f scale) {
		m00 *= scale.x;
		m10 *= scale.x;
		m20 *= scale.x;
		m01 *= scale.y;
		m11 *= scale.y;
		m21 *= scale.y;
		m02 *= scale.z;
		m12 *= scale.z;
		m22 *= scale.z;
	}

	static boolean equalIdentity(Matrix3f mat) {
		if (Math.abs(mat.m00 - 1) > 1e-4)
			return false;
		if (Math.abs(mat.m11 - 1) > 1e-4)
			return false;
		if (Math.abs(mat.m22 - 1) > 1e-4)
			return false;

		if (Math.abs(mat.m01) > 1e-4)
			return false;
		if (Math.abs(mat.m02) > 1e-4)
			return false;

		if (Math.abs(mat.m10) > 1e-4)
			return false;
		if (Math.abs(mat.m12) > 1e-4)
			return false;

		if (Math.abs(mat.m20) > 1e-4)
			return false;
		return !(Math.abs(mat.m21) > 1e-4);
	}

	@Override
	public Matrix3f clone() {
		try {
			return (Matrix3f) super.clone();
		} catch (CloneNotSupportedException e) {
			Logger.error( e);
			throw new AssertionError(); // can not happen
		}
	}
}