/*******************************************************************************
* Copyright 2011 See AUTHORS file.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
******************************************************************************/
package com.badlogic.gdx.math;
import java.io.Serializable;
/** Encapsulates a <a href="http://en.wikipedia.org/wiki/Row-major_order#Column-major_order">column major</a> 4 by 4 matrix. Like
* the {@link Vector3} class it allows the chaining of methods by returning a reference to itself. For example:
*
* <pre>
* Matrix4 mat = new Matrix4().trn(position).mul(camera.combined);
* </pre>
*
* @author badlogicgames@gmail.com */
public class Matrix4 implements Serializable {
private static final long serialVersionUID = -2717655254359579617L;
/** XX: Typically the unrotated X component for scaling, also the cosine of the angle when rotated on the Y and/or Z axis. On
* Vector3 multiplication this value is multiplied with the source X component and added to the target X component. */
public static final int M00 = 0;
/** XY: Typically the negative sine of the angle when rotated on the Z axis. On Vector3 multiplication this value is multiplied
* with the source Y component and added to the target X component. */
public static final int M01 = 4;
/** XZ: Typically the sine of the angle when rotated on the Y axis. On Vector3 multiplication this value is multiplied with the
* source Z component and added to the target X component. */
public static final int M02 = 8;
/** XW: Typically the translation of the X component. On Vector3 multiplication this value is added to the target X component. */
public static final int M03 = 12;
/** YX: Typically the sine of the angle when rotated on the Z axis. On Vector3 multiplication this value is multiplied with the
* source X component and added to the target Y component. */
public static final int M10 = 1;
/** YY: Typically the unrotated Y component for scaling, also the cosine of the angle when rotated on the X and/or Z axis. On
* Vector3 multiplication this value is multiplied with the source Y component and added to the target Y component. */
public static final int M11 = 5;
/** YZ: Typically the negative sine of the angle when rotated on the X axis. On Vector3 multiplication this value is multiplied
* with the source Z component and added to the target Y component. */
public static final int M12 = 9;
/** YW: Typically the translation of the Y component. On Vector3 multiplication this value is added to the target Y component. */
public static final int M13 = 13;
/** ZX: Typically the negative sine of the angle when rotated on the Y axis. On Vector3 multiplication this value is multiplied
* with the source X component and added to the target Z component. */
public static final int M20 = 2;
/** ZY: Typical the sine of the angle when rotated on the X axis. On Vector3 multiplication this value is multiplied with the
* source Y component and added to the target Z component. */
public static final int M21 = 6;
/** ZZ: Typically the unrotated Z component for scaling, also the cosine of the angle when rotated on the X and/or Y axis. On
* Vector3 multiplication this value is multiplied with the source Z component and added to the target Z component. */
public static final int M22 = 10;
/** ZW: Typically the translation of the Z component. On Vector3 multiplication this value is added to the target Z component. */
public static final int M23 = 14;
/** WX: Typically the value zero. On Vector3 multiplication this value is ignored. */
public static final int M30 = 3;
/** WY: Typically the value zero. On Vector3 multiplication this value is ignored. */
public static final int M31 = 7;
/** WZ: Typically the value zero. On Vector3 multiplication this value is ignored. */
public static final int M32 = 11;
/** WW: Typically the value one. On Vector3 multiplication this value is ignored. */
public static final int M33 = 15;
private static final float tmp[] = new float[16];
public final float val[] = new float[16];
/** Constructs an identity matrix */
public Matrix4 () {
val[M00] = 1f;
val[M11] = 1f;
val[M22] = 1f;
val[M33] = 1f;
}
/** Constructs a matrix from the given matrix.
*
* @param matrix The matrix to copy. (This matrix is not modified) */
public Matrix4 (Matrix4 matrix) {
this.set(matrix);
}
/** Constructs a matrix from the given float array. The array must have at least 16 elements; the first 16 will be copied.
* @param values The float array to copy. Remember that this matrix is in <a
* href="http://en.wikipedia.org/wiki/Row-major_order">column major</a> order. (The float array is not modified) */
public Matrix4 (float[] values) {
this.set(values);
}
/** Constructs a rotation matrix from the given {@link Quaternion}.
* @param quaternion The quaternion to be copied. (The quaternion is not modified) */
public Matrix4 (Quaternion quaternion) {
this.set(quaternion);
}
/** Construct a matrix from the given translation, rotation and scale.
* @param position The translation
* @param rotation The rotation, must be normalized
* @param scale The scale */
public Matrix4 (Vector3 position, Quaternion rotation, Vector3 scale) {
set(position, rotation, scale);
}
/** Sets the matrix to the given matrix.
*
* @param matrix The matrix that is to be copied. (The given matrix is not modified)
* @return This matrix for the purpose of chaining methods together. */
public Matrix4 set (Matrix4 matrix) {
return this.set(matrix.val);
}
/** Sets the matrix to the given matrix as a float array. The float array must have at least 16 elements; the first 16 will be
* copied.
*
* @param values The matrix, in float form, that is to be copied. Remember that this matrix is in <a
* href="http://en.wikipedia.org/wiki/Row-major_order">column major</a> order.
* @return This matrix for the purpose of chaining methods together. */
public Matrix4 set (float[] values) {
System.arraycopy(values, 0, val, 0, val.length);
return this;
}
/** Sets the matrix to a rotation matrix representing the quaternion.
*
* @param quaternion The quaternion that is to be used to set this matrix.
* @return This matrix for the purpose of chaining methods together. */
public Matrix4 set (Quaternion quaternion) {
return set(quaternion.x, quaternion.y, quaternion.z, quaternion.w);
}
/** Sets the matrix to a rotation matrix representing the quaternion.
*
* @param quaternionX The X component of the quaternion that is to be used to set this matrix.
* @param quaternionY The Y component of the quaternion that is to be used to set this matrix.
* @param quaternionZ The Z component of the quaternion that is to be used to set this matrix.
* @param quaternionW The W component of the quaternion that is to be used to set this matrix.
* @return This matrix for the purpose of chaining methods together. */
public Matrix4 set (float quaternionX, float quaternionY, float quaternionZ, float quaternionW) {
return set(0f, 0f, 0f, quaternionX, quaternionY, quaternionZ, quaternionW);
}
/** Set this matrix to the specified translation and rotation.
* @param position The translation
* @param orientation The rotation, must be normalized
* @return This matrix for chaining */
public Matrix4 set (Vector3 position, Quaternion orientation) {
return set(position.x, position.y, position.z, orientation.x, orientation.y, orientation.z, orientation.w);
}
/** Sets the matrix to a rotation matrix representing the translation and quaternion.
*
* @param translationX The X component of the translation that is to be used to set this matrix.
* @param translationY The Y component of the translation that is to be used to set this matrix.
* @param translationZ The Z component of the translation that is to be used to set this matrix.
* @param quaternionX The X component of the quaternion that is to be used to set this matrix.
* @param quaternionY The Y component of the quaternion that is to be used to set this matrix.
* @param quaternionZ The Z component of the quaternion that is to be used to set this matrix.
* @param quaternionW The W component of the quaternion that is to be used to set this matrix.
* @return This matrix for the purpose of chaining methods together. */
public Matrix4 set (float translationX, float translationY, float translationZ, float quaternionX, float quaternionY,
float quaternionZ, float quaternionW) {
final float xs = quaternionX * 2f, ys = quaternionY * 2f, zs = quaternionZ * 2f;
final float wx = quaternionW * xs, wy = quaternionW * ys, wz = quaternionW * zs;
final float xx = quaternionX * xs, xy = quaternionX * ys, xz = quaternionX * zs;
final float yy = quaternionY * ys, yz = quaternionY * zs, zz = quaternionZ * zs;
val[M00] = (1.0f - (yy + zz));
val[M01] = (xy - wz);
val[M02] = (xz + wy);
val[M03] = translationX;
val[M10] = (xy + wz);
val[M11] = (1.0f - (xx + zz));
val[M12] = (yz - wx);
val[M13] = translationY;
val[M20] = (xz - wy);
val[M21] = (yz + wx);
val[M22] = (1.0f - (xx + yy));
val[M23] = translationZ;
val[M30] = 0.f;
val[M31] = 0.f;
val[M32] = 0.f;
val[M33] = 1.0f;
return this;
}
/** Set this matrix to the specified translation, rotation and scale.
* @param position The translation
* @param orientation The rotation, must be normalized
* @param scale The scale
* @return This matrix for chaining */
public Matrix4 set (Vector3 position, Quaternion orientation, Vector3 scale) {
return set(position.x, position.y, position.z, orientation.x, orientation.y, orientation.z, orientation.w, scale.x,
scale.y, scale.z);
}
/** Sets the matrix to a rotation matrix representing the translation and quaternion.
*
* @param translationX The X component of the translation that is to be used to set this matrix.
* @param translationY The Y component of the translation that is to be used to set this matrix.
* @param translationZ The Z component of the translation that is to be used to set this matrix.
* @param quaternionX The X component of the quaternion that is to be used to set this matrix.
* @param quaternionY The Y component of the quaternion that is to be used to set this matrix.
* @param quaternionZ The Z component of the quaternion that is to be used to set this matrix.
* @param quaternionW The W component of the quaternion that is to be used to set this matrix.
* @param scaleX The X component of the scaling that is to be used to set this matrix.
* @param scaleY The Y component of the scaling that is to be used to set this matrix.
* @param scaleZ The Z component of the scaling that is to be used to set this matrix.
* @return This matrix for the purpose of chaining methods together. */
public Matrix4 set (float translationX, float translationY, float translationZ, float quaternionX, float quaternionY,
float quaternionZ, float quaternionW, float scaleX, float scaleY, float scaleZ) {
final float xs = quaternionX * 2f, ys = quaternionY * 2f, zs = quaternionZ * 2f;
final float wx = quaternionW * xs, wy = quaternionW * ys, wz = quaternionW * zs;
final float xx = quaternionX * xs, xy = quaternionX * ys, xz = quaternionX * zs;
final float yy = quaternionY * ys, yz = quaternionY * zs, zz = quaternionZ * zs;
val[M00] = scaleX * (1.0f - (yy + zz));
val[M01] = scaleY * (xy - wz);
val[M02] = scaleZ * (xz + wy);
val[M03] = translationX;
val[M10] = scaleX * (xy + wz);
val[M11] = scaleY * (1.0f - (xx + zz));
val[M12] = scaleZ * (yz - wx);
val[M13] = translationY;
val[M20] = scaleX * (xz - wy);
val[M21] = scaleY * (yz + wx);
val[M22] = scaleZ * (1.0f - (xx + yy));
val[M23] = translationZ;
val[M30] = 0.f;
val[M31] = 0.f;
val[M32] = 0.f;
val[M33] = 1.0f;
return this;
}
/** Sets the four columns of the matrix which correspond to the x-, y- and z-axis of the vector space this matrix creates as
* well as the 4th column representing the translation of any point that is multiplied by this matrix.
*
* @param xAxis The x-axis.
* @param yAxis The y-axis.
* @param zAxis The z-axis.
* @param pos The translation vector. */
public Matrix4 set (Vector3 xAxis, Vector3 yAxis, Vector3 zAxis, Vector3 pos) {
val[M00] = xAxis.x;
val[M01] = xAxis.y;
val[M02] = xAxis.z;
val[M10] = yAxis.x;
val[M11] = yAxis.y;
val[M12] = yAxis.z;
val[M20] = zAxis.x;
val[M21] = zAxis.y;
val[M22] = zAxis.z;
val[M03] = pos.x;
val[M13] = pos.y;
val[M23] = pos.z;
val[M30] = 0;
val[M31] = 0;
val[M32] = 0;
val[M33] = 1;
return this;
}
/** @return a copy of this matrix */
public Matrix4 cpy () {
return new Matrix4(this);
}
/** Adds a translational component to the matrix in the 4th column. The other columns are untouched.
*
* @param vector The translation vector to add to the current matrix. (This vector is not modified)
* @return This matrix for the purpose of chaining methods together. */
public Matrix4 trn (Vector3 vector) {
val[M03] += vector.x;
val[M13] += vector.y;
val[M23] += vector.z;
return this;
}
/** Adds a translational component to the matrix in the 4th column. The other columns are untouched.
*
* @param x The x-component of the translation vector.
* @param y The y-component of the translation vector.
* @param z The z-component of the translation vector.
* @return This matrix for the purpose of chaining methods together. */
public Matrix4 trn (float x, float y, float z) {
val[M03] += x;
val[M13] += y;
val[M23] += z;
return this;
}
/** @return the backing float array */
public float[] getValues () {
return val;
}
/** Postmultiplies this matrix with the given matrix, storing the result in this matrix. For example:
*
* <pre>
* A.mul(B) results in A := AB.
* </pre>
*
* @param matrix The other matrix to multiply by.
* @return This matrix for the purpose of chaining operations together. */
public Matrix4 mul (Matrix4 matrix) {
mul(val, matrix.val);
return this;
}
/** Premultiplies this matrix with the given matrix, storing the result in this matrix. For example:
*
* <pre>
* A.mulLeft(B) results in A := BA.
* </pre>
*
* @param matrix The other matrix to multiply by.
* @return This matrix for the purpose of chaining operations together. */
public Matrix4 mulLeft (Matrix4 matrix) {
tmpMat.set(matrix);
mul(tmpMat.val, this.val);
return set(tmpMat);
}
/** Transposes the matrix.
*
* @return This matrix for the purpose of chaining methods together. */
public Matrix4 tra () {
tmp[M00] = val[M00];
tmp[M01] = val[M10];
tmp[M02] = val[M20];
tmp[M03] = val[M30];
tmp[M10] = val[M01];
tmp[M11] = val[M11];
tmp[M12] = val[M21];
tmp[M13] = val[M31];
tmp[M20] = val[M02];
tmp[M21] = val[M12];
tmp[M22] = val[M22];
tmp[M23] = val[M32];
tmp[M30] = val[M03];
tmp[M31] = val[M13];
tmp[M32] = val[M23];
tmp[M33] = val[M33];
return set(tmp);
}
/** Sets the matrix to an identity matrix.
*
* @return This matrix for the purpose of chaining methods together. */
public Matrix4 idt () {
val[M00] = 1;
val[M01] = 0;
val[M02] = 0;
val[M03] = 0;
val[M10] = 0;
val[M11] = 1;
val[M12] = 0;
val[M13] = 0;
val[M20] = 0;
val[M21] = 0;
val[M22] = 1;
val[M23] = 0;
val[M30] = 0;
val[M31] = 0;
val[M32] = 0;
val[M33] = 1;
return this;
}
/** Inverts the matrix. Stores the result in this matrix.
*
* @return This matrix for the purpose of chaining methods together.
* @throws RuntimeException if the matrix is singular (not invertible) */
public Matrix4 inv () {
float l_det = val[M30] * val[M21] * val[M12] * val[M03] - val[M20] * val[M31] * val[M12] * val[M03] - val[M30] * val[M11]
* val[M22] * val[M03] + val[M10] * val[M31] * val[M22] * val[M03] + val[M20] * val[M11] * val[M32] * val[M03] - val[M10]
* val[M21] * val[M32] * val[M03] - val[M30] * val[M21] * val[M02] * val[M13] + val[M20] * val[M31] * val[M02] * val[M13]
+ val[M30] * val[M01] * val[M22] * val[M13] - val[M00] * val[M31] * val[M22] * val[M13] - val[M20] * val[M01] * val[M32]
* val[M13] + val[M00] * val[M21] * val[M32] * val[M13] + val[M30] * val[M11] * val[M02] * val[M23] - val[M10] * val[M31]
* val[M02] * val[M23] - val[M30] * val[M01] * val[M12] * val[M23] + val[M00] * val[M31] * val[M12] * val[M23] + val[M10]
* val[M01] * val[M32] * val[M23] - val[M00] * val[M11] * val[M32] * val[M23] - val[M20] * val[M11] * val[M02] * val[M33]
+ val[M10] * val[M21] * val[M02] * val[M33] + val[M20] * val[M01] * val[M12] * val[M33] - val[M00] * val[M21] * val[M12]
* val[M33] - val[M10] * val[M01] * val[M22] * val[M33] + val[M00] * val[M11] * val[M22] * val[M33];
if (l_det == 0f) throw new RuntimeException("non-invertible matrix");
float inv_det = 1.0f / l_det;
tmp[M00] = val[M12] * val[M23] * val[M31] - val[M13] * val[M22] * val[M31] + val[M13] * val[M21] * val[M32] - val[M11]
* val[M23] * val[M32] - val[M12] * val[M21] * val[M33] + val[M11] * val[M22] * val[M33];
tmp[M01] = val[M03] * val[M22] * val[M31] - val[M02] * val[M23] * val[M31] - val[M03] * val[M21] * val[M32] + val[M01]
* val[M23] * val[M32] + val[M02] * val[M21] * val[M33] - val[M01] * val[M22] * val[M33];
tmp[M02] = val[M02] * val[M13] * val[M31] - val[M03] * val[M12] * val[M31] + val[M03] * val[M11] * val[M32] - val[M01]
* val[M13] * val[M32] - val[M02] * val[M11] * val[M33] + val[M01] * val[M12] * val[M33];
tmp[M03] = val[M03] * val[M12] * val[M21] - val[M02] * val[M13] * val[M21] - val[M03] * val[M11] * val[M22] + val[M01]
* val[M13] * val[M22] + val[M02] * val[M11] * val[M23] - val[M01] * val[M12] * val[M23];
tmp[M10] = val[M13] * val[M22] * val[M30] - val[M12] * val[M23] * val[M30] - val[M13] * val[M20] * val[M32] + val[M10]
* val[M23] * val[M32] + val[M12] * val[M20] * val[M33] - val[M10] * val[M22] * val[M33];
tmp[M11] = val[M02] * val[M23] * val[M30] - val[M03] * val[M22] * val[M30] + val[M03] * val[M20] * val[M32] - val[M00]
* val[M23] * val[M32] - val[M02] * val[M20] * val[M33] + val[M00] * val[M22] * val[M33];
tmp[M12] = val[M03] * val[M12] * val[M30] - val[M02] * val[M13] * val[M30] - val[M03] * val[M10] * val[M32] + val[M00]
* val[M13] * val[M32] + val[M02] * val[M10] * val[M33] - val[M00] * val[M12] * val[M33];
tmp[M13] = val[M02] * val[M13] * val[M20] - val[M03] * val[M12] * val[M20] + val[M03] * val[M10] * val[M22] - val[M00]
* val[M13] * val[M22] - val[M02] * val[M10] * val[M23] + val[M00] * val[M12] * val[M23];
tmp[M20] = val[M11] * val[M23] * val[M30] - val[M13] * val[M21] * val[M30] + val[M13] * val[M20] * val[M31] - val[M10]
* val[M23] * val[M31] - val[M11] * val[M20] * val[M33] + val[M10] * val[M21] * val[M33];
tmp[M21] = val[M03] * val[M21] * val[M30] - val[M01] * val[M23] * val[M30] - val[M03] * val[M20] * val[M31] + val[M00]
* val[M23] * val[M31] + val[M01] * val[M20] * val[M33] - val[M00] * val[M21] * val[M33];
tmp[M22] = val[M01] * val[M13] * val[M30] - val[M03] * val[M11] * val[M30] + val[M03] * val[M10] * val[M31] - val[M00]
* val[M13] * val[M31] - val[M01] * val[M10] * val[M33] + val[M00] * val[M11] * val[M33];
tmp[M23] = val[M03] * val[M11] * val[M20] - val[M01] * val[M13] * val[M20] - val[M03] * val[M10] * val[M21] + val[M00]
* val[M13] * val[M21] + val[M01] * val[M10] * val[M23] - val[M00] * val[M11] * val[M23];
tmp[M30] = val[M12] * val[M21] * val[M30] - val[M11] * val[M22] * val[M30] - val[M12] * val[M20] * val[M31] + val[M10]
* val[M22] * val[M31] + val[M11] * val[M20] * val[M32] - val[M10] * val[M21] * val[M32];
tmp[M31] = val[M01] * val[M22] * val[M30] - val[M02] * val[M21] * val[M30] + val[M02] * val[M20] * val[M31] - val[M00]
* val[M22] * val[M31] - val[M01] * val[M20] * val[M32] + val[M00] * val[M21] * val[M32];
tmp[M32] = val[M02] * val[M11] * val[M30] - val[M01] * val[M12] * val[M30] - val[M02] * val[M10] * val[M31] + val[M00]
* val[M12] * val[M31] + val[M01] * val[M10] * val[M32] - val[M00] * val[M11] * val[M32];
tmp[M33] = val[M01] * val[M12] * val[M20] - val[M02] * val[M11] * val[M20] + val[M02] * val[M10] * val[M21] - val[M00]
* val[M12] * val[M21] - val[M01] * val[M10] * val[M22] + val[M00] * val[M11] * val[M22];
val[M00] = tmp[M00] * inv_det;
val[M01] = tmp[M01] * inv_det;
val[M02] = tmp[M02] * inv_det;
val[M03] = tmp[M03] * inv_det;
val[M10] = tmp[M10] * inv_det;
val[M11] = tmp[M11] * inv_det;
val[M12] = tmp[M12] * inv_det;
val[M13] = tmp[M13] * inv_det;
val[M20] = tmp[M20] * inv_det;
val[M21] = tmp[M21] * inv_det;
val[M22] = tmp[M22] * inv_det;
val[M23] = tmp[M23] * inv_det;
val[M30] = tmp[M30] * inv_det;
val[M31] = tmp[M31] * inv_det;
val[M32] = tmp[M32] * inv_det;
val[M33] = tmp[M33] * inv_det;
return this;
}
/** @return The determinant of this matrix */
public float det () {
return val[M30] * val[M21] * val[M12] * val[M03] - val[M20] * val[M31] * val[M12] * val[M03] - val[M30] * val[M11]
* val[M22] * val[M03] + val[M10] * val[M31] * val[M22] * val[M03] + val[M20] * val[M11] * val[M32] * val[M03] - val[M10]
* val[M21] * val[M32] * val[M03] - val[M30] * val[M21] * val[M02] * val[M13] + val[M20] * val[M31] * val[M02] * val[M13]
+ val[M30] * val[M01] * val[M22] * val[M13] - val[M00] * val[M31] * val[M22] * val[M13] - val[M20] * val[M01] * val[M32]
* val[M13] + val[M00] * val[M21] * val[M32] * val[M13] + val[M30] * val[M11] * val[M02] * val[M23] - val[M10] * val[M31]
* val[M02] * val[M23] - val[M30] * val[M01] * val[M12] * val[M23] + val[M00] * val[M31] * val[M12] * val[M23] + val[M10]
* val[M01] * val[M32] * val[M23] - val[M00] * val[M11] * val[M32] * val[M23] - val[M20] * val[M11] * val[M02] * val[M33]
+ val[M10] * val[M21] * val[M02] * val[M33] + val[M20] * val[M01] * val[M12] * val[M33] - val[M00] * val[M21] * val[M12]
* val[M33] - val[M10] * val[M01] * val[M22] * val[M33] + val[M00] * val[M11] * val[M22] * val[M33];
}
/** @return The determinant of the 3x3 upper left matrix */
public float det3x3 () {
return val[M00] * val[M11] * val[M22] + val[M01] * val[M12] * val[M20] + val[M02] * val[M10] * val[M21] - val[M00]
* val[M12] * val[M21] - val[M01] * val[M10] * val[M22] - val[M02] * val[M11] * val[M20];
}
/** Sets the matrix to a projection matrix with a near- and far plane, a field of view in degrees and an aspect ratio. Note that
* the field of view specified is the angle in degrees for the height, the field of view for the width will be calculated
* according to the aspect ratio.
*
* @param near The near plane
* @param far The far plane
* @param fovy The field of view of the height in degrees
* @param aspectRatio The "width over height" aspect ratio
* @return This matrix for the purpose of chaining methods together. */
public Matrix4 setToProjection (float near, float far, float fovy, float aspectRatio) {
idt();
float l_fd = (float)(1.0 / Math.tan((fovy * (Math.PI / 180)) / 2.0));
float l_a1 = (far + near) / (near - far);
float l_a2 = (2 * far * near) / (near - far);
val[M00] = l_fd / aspectRatio;
val[M10] = 0;
val[M20] = 0;
val[M30] = 0;
val[M01] = 0;
val[M11] = l_fd;
val[M21] = 0;
val[M31] = 0;
val[M02] = 0;
val[M12] = 0;
val[M22] = l_a1;
val[M32] = -1;
val[M03] = 0;
val[M13] = 0;
val[M23] = l_a2;
val[M33] = 0;
return this;
}
/** Sets the matrix to a projection matrix with a near/far plane, and left, bottom, right and top specifying the points on the
* near plane that are mapped to the lower left and upper right corners of the viewport. This allows to create projection
* matrix with off-center vanishing point.
*
* @param left
* @param right
* @param bottom
* @param top
* @param near The near plane
* @param far The far plane
* @return This matrix for the purpose of chaining methods together. */
public Matrix4 setToProjection (float left, float right, float bottom, float top, float near, float far) {
float x = 2.0f * near / (right - left);
float y = 2.0f * near / (top - bottom);
float a = (right + left) / (right - left);
float b = (top + bottom) / (top - bottom);
float l_a1 = (far + near) / (near - far);
float l_a2 = (2 * far * near) / (near - far);
val[M00] = x;
val[M10] = 0;
val[M20] = 0;
val[M30] = 0;
val[M01] = 0;
val[M11] = y;
val[M21] = 0;
val[M31] = 0;
val[M02] = a;
val[M12] = b;
val[M22] = l_a1;
val[M32] = -1;
val[M03] = 0;
val[M13] = 0;
val[M23] = l_a2;
val[M33] = 0;
return this;
}
/** Sets this matrix to an orthographic projection matrix with the origin at (x,y) extending by width and height. The near plane
* is set to 0, the far plane is set to 1.
*
* @param x The x-coordinate of the origin
* @param y The y-coordinate of the origin
* @param width The width
* @param height The height
* @return This matrix for the purpose of chaining methods together. */
public Matrix4 setToOrtho2D (float x, float y, float width, float height) {
setToOrtho(x, x + width, y, y + height, 0, 1);
return this;
}
/** Sets this matrix to an orthographic projection matrix with the origin at (x,y) extending by width and height, having a near
* and far plane.
*
* @param x The x-coordinate of the origin
* @param y The y-coordinate of the origin
* @param width The width
* @param height The height
* @param near The near plane
* @param far The far plane
* @return This matrix for the purpose of chaining methods together. */
public Matrix4 setToOrtho2D (float x, float y, float width, float height, float near, float far) {
setToOrtho(x, x + width, y, y + height, near, far);
return this;
}
/** Sets the matrix to an orthographic projection like glOrtho (http://www.opengl.org/sdk/docs/man/xhtml/glOrtho.xml) following
* the OpenGL equivalent
*
* @param left The left clipping plane
* @param right The right clipping plane
* @param bottom The bottom clipping plane
* @param top The top clipping plane
* @param near The near clipping plane
* @param far The far clipping plane
* @return This matrix for the purpose of chaining methods together. */
public Matrix4 setToOrtho (float left, float right, float bottom, float top, float near, float far) {
this.idt();
float x_orth = 2 / (right - left);
float y_orth = 2 / (top - bottom);
float z_orth = -2 / (far - near);
float tx = -(right + left) / (right - left);
float ty = -(top + bottom) / (top - bottom);
float tz = -(far + near) / (far - near);
val[M00] = x_orth;
val[M10] = 0;
val[M20] = 0;
val[M30] = 0;
val[M01] = 0;
val[M11] = y_orth;
val[M21] = 0;
val[M31] = 0;
val[M02] = 0;
val[M12] = 0;
val[M22] = z_orth;
val[M32] = 0;
val[M03] = tx;
val[M13] = ty;
val[M23] = tz;
val[M33] = 1;
return this;
}
/** Sets the 4th column to the translation vector.
*
* @param vector The translation vector
* @return This matrix for the purpose of chaining methods together. */
public Matrix4 setTranslation (Vector3 vector) {
val[M03] = vector.x;
val[M13] = vector.y;
val[M23] = vector.z;
return this;
}
/** Sets the 4th column to the translation vector.
*
* @param x The X coordinate of the translation vector
* @param y The Y coordinate of the translation vector
* @param z The Z coordinate of the translation vector
* @return This matrix for the purpose of chaining methods together. */
public Matrix4 setTranslation (float x, float y, float z) {
val[M03] = x;
val[M13] = y;
val[M23] = z;
return this;
}
/** Sets this matrix to a translation matrix, overwriting it first by an identity matrix and then setting the 4th column to the
* translation vector.
*
* @param vector The translation vector
* @return This matrix for the purpose of chaining methods together. */
public Matrix4 setToTranslation (Vector3 vector) {
idt();
val[M03] = vector.x;
val[M13] = vector.y;
val[M23] = vector.z;
return this;
}
/** Sets this matrix to a translation matrix, overwriting it first by an identity matrix and then setting the 4th column to the
* translation vector.
*
* @param x The x-component of the translation vector.
* @param y The y-component of the translation vector.
* @param z The z-component of the translation vector.
* @return This matrix for the purpose of chaining methods together. */
public Matrix4 setToTranslation (float x, float y, float z) {
idt();
val[M03] = x;
val[M13] = y;
val[M23] = z;
return this;
}
/** Sets this matrix to a translation and scaling matrix by first overwriting it with an identity and then setting the
* translation vector in the 4th column and the scaling vector in the diagonal.
*
* @param translation The translation vector
* @param scaling The scaling vector
* @return This matrix for the purpose of chaining methods together. */
public Matrix4 setToTranslationAndScaling (Vector3 translation, Vector3 scaling) {
idt();
val[M03] = translation.x;
val[M13] = translation.y;
val[M23] = translation.z;
val[M00] = scaling.x;
val[M11] = scaling.y;
val[M22] = scaling.z;
return this;
}
/** Sets this matrix to a translation and scaling matrix by first overwriting it with an identity and then setting the
* translation vector in the 4th column and the scaling vector in the diagonal.
*
* @param translationX The x-component of the translation vector
* @param translationY The y-component of the translation vector
* @param translationZ The z-component of the translation vector
* @param scalingX The x-component of the scaling vector
* @param scalingY The x-component of the scaling vector
* @param scalingZ The x-component of the scaling vector
* @return This matrix for the purpose of chaining methods together. */
public Matrix4 setToTranslationAndScaling (float translationX, float translationY, float translationZ, float scalingX,
float scalingY, float scalingZ) {
idt();
val[M03] = translationX;
val[M13] = translationY;
val[M23] = translationZ;
val[M00] = scalingX;
val[M11] = scalingY;
val[M22] = scalingZ;
return this;
}
static Quaternion quat = new Quaternion();
static Quaternion quat2 = new Quaternion();
/** Sets the matrix to a rotation matrix around the given axis.
*
* @param axis The axis
* @param degrees The angle in degrees
* @return This matrix for the purpose of chaining methods together. */
public Matrix4 setToRotation (Vector3 axis, float degrees) {
if (degrees == 0) {
idt();
return this;
}
return set(quat.set(axis, degrees));
}
/** Sets the matrix to a rotation matrix around the given axis.
*
* @param axis The axis
* @param radians The angle in radians
* @return This matrix for the purpose of chaining methods together. */
public Matrix4 setToRotationRad (Vector3 axis, float radians) {
if (radians == 0) {
idt();
return this;
}
return set(quat.setFromAxisRad(axis, radians));
}
/** Sets the matrix to a rotation matrix around the given axis.
*
* @param axisX The x-component of the axis
* @param axisY The y-component of the axis
* @param axisZ The z-component of the axis
* @param degrees The angle in degrees
* @return This matrix for the purpose of chaining methods together. */
public Matrix4 setToRotation (float axisX, float axisY, float axisZ, float degrees) {
if (degrees == 0) {
idt();
return this;
}
return set(quat.setFromAxis(axisX, axisY, axisZ, degrees));
}
/** Sets the matrix to a rotation matrix around the given axis.
*
* @param axisX The x-component of the axis
* @param axisY The y-component of the axis
* @param axisZ The z-component of the axis
* @param radians The angle in radians
* @return This matrix for the purpose of chaining methods together. */
public Matrix4 setToRotationRad (float axisX, float axisY, float axisZ, float radians) {
if (radians == 0) {
idt();
return this;
}
return set(quat.setFromAxisRad(axisX, axisY, axisZ, radians));
}
/** Set the matrix to a rotation matrix between two vectors.
* @param v1 The base vector
* @param v2 The target vector
* @return This matrix for the purpose of chaining methods together */
public Matrix4 setToRotation (final Vector3 v1, final Vector3 v2) {
return set(quat.setFromCross(v1, v2));
}
/** Set the matrix to a rotation matrix between two vectors.
* @param x1 The base vectors x value
* @param y1 The base vectors y value
* @param z1 The base vectors z value
* @param x2 The target vector x value
* @param y2 The target vector y value
* @param z2 The target vector z value
* @return This matrix for the purpose of chaining methods together */
public Matrix4 setToRotation (final float x1, final float y1, final float z1, final float x2, final float y2, final float z2) {
return set(quat.setFromCross(x1, y1, z1, x2, y2, z2));
}
/** Sets this matrix to a rotation matrix from the given euler angles.
* @param yaw the yaw in degrees
* @param pitch the pitch in degrees
* @param roll the roll in degrees
* @return This matrix */
public Matrix4 setFromEulerAngles (float yaw, float pitch, float roll) {
quat.setEulerAngles(yaw, pitch, roll);
return set(quat);
}
/** Sets this matrix to a rotation matrix from the given euler angles.
* @param yaw the yaw in radians
* @param pitch the pitch in radians
* @param roll the roll in radians
* @return This matrix */
public Matrix4 setFromEulerAnglesRad (float yaw, float pitch, float roll) {
quat.setEulerAnglesRad(yaw, pitch, roll);
return set(quat);
}
/** Sets this matrix to a scaling matrix
*
* @param vector The scaling vector
* @return This matrix for chaining. */
public Matrix4 setToScaling (Vector3 vector) {
idt();
val[M00] = vector.x;
val[M11] = vector.y;
val[M22] = vector.z;
return this;
}
/** Sets this matrix to a scaling matrix
*
* @param x The x-component of the scaling vector
* @param y The y-component of the scaling vector
* @param z The z-component of the scaling vector
* @return This matrix for chaining. */
public Matrix4 setToScaling (float x, float y, float z) {
idt();
val[M00] = x;
val[M11] = y;
val[M22] = z;
return this;
}
static final Vector3 l_vez = new Vector3();
static final Vector3 l_vex = new Vector3();
static final Vector3 l_vey = new Vector3();
/** Sets the matrix to a look at matrix with a direction and an up vector. Multiply with a translation matrix to get a camera
* model view matrix.
*
* @param direction The direction vector
* @param up The up vector
* @return This matrix for the purpose of chaining methods together. */
public Matrix4 setToLookAt (Vector3 direction, Vector3 up) {
l_vez.set(direction).nor();
l_vex.set(direction).nor();
l_vex.crs(up).nor();
l_vey.set(l_vex).crs(l_vez).nor();
idt();
val[M00] = l_vex.x;
val[M01] = l_vex.y;
val[M02] = l_vex.z;
val[M10] = l_vey.x;
val[M11] = l_vey.y;
val[M12] = l_vey.z;
val[M20] = -l_vez.x;
val[M21] = -l_vez.y;
val[M22] = -l_vez.z;
return this;
}
static final Vector3 tmpVec = new Vector3();
static final Matrix4 tmpMat = new Matrix4();
/** Sets this matrix to a look at matrix with the given position, target and up vector.
*
* @param position the position
* @param target the target
* @param up the up vector
* @return This matrix */
public Matrix4 setToLookAt (Vector3 position, Vector3 target, Vector3 up) {
tmpVec.set(target).sub(position);
setToLookAt(tmpVec, up);
this.mul(tmpMat.setToTranslation(-position.x, -position.y, -position.z));
return this;
}
static final Vector3 right = new Vector3();
static final Vector3 tmpForward = new Vector3();
static final Vector3 tmpUp = new Vector3();
public Matrix4 setToWorld (Vector3 position, Vector3 forward, Vector3 up) {
tmpForward.set(forward).nor();
right.set(tmpForward).crs(up).nor();
tmpUp.set(right).crs(tmpForward).nor();
this.set(right, tmpUp, tmpForward.scl(-1), position);
return this;
}
public String toString () {
return "[" + val[M00] + "|" + val[M01] + "|" + val[M02] + "|" + val[M03] + "]\n" + "[" + val[M10] + "|" + val[M11] + "|"
+ val[M12] + "|" + val[M13] + "]\n" + "[" + val[M20] + "|" + val[M21] + "|" + val[M22] + "|" + val[M23] + "]\n" + "["
+ val[M30] + "|" + val[M31] + "|" + val[M32] + "|" + val[M33] + "]\n";
}
/** Linearly interpolates between this matrix and the given matrix mixing by alpha
* @param matrix the matrix
* @param alpha the alpha value in the range [0,1]
* @return This matrix for the purpose of chaining methods together. */
public Matrix4 lerp (Matrix4 matrix, float alpha) {
for (int i = 0; i < 16; i++)
this.val[i] = this.val[i] * (1 - alpha) + matrix.val[i] * alpha;
return this;
}
/** Averages the given transform with this one and stores the result in this matrix. Translations and scales are lerped while
* rotations are slerped.
* @param other The other transform
* @param w Weight of this transform; weight of the other transform is (1 - w)
* @return This matrix for chaining */
public Matrix4 avg (Matrix4 other, float w) {
getScale(tmpVec);
other.getScale(tmpForward);
getRotation(quat);
other.getRotation(quat2);
getTranslation(tmpUp);
other.getTranslation(right);
setToScaling(tmpVec.scl(w).add(tmpForward.scl(1 - w)));
rotate(quat.slerp(quat2, 1 - w));
setTranslation(tmpUp.scl(w).add(right.scl(1 - w)));
return this;
}
/** Averages the given transforms and stores the result in this matrix. Translations and scales are lerped while rotations are
* slerped. Does not destroy the data contained in t.
* @param t List of transforms
* @return This matrix for chaining */
public Matrix4 avg (Matrix4[] t) {
final float w = 1.0f / t.length;
tmpVec.set(t[0].getScale(tmpUp).scl(w));
quat.set(t[0].getRotation(quat2).exp(w));
tmpForward.set(t[0].getTranslation(tmpUp).scl(w));
for (int i = 1; i < t.length; i++) {
tmpVec.add(t[i].getScale(tmpUp).scl(w));
quat.mul(t[i].getRotation(quat2).exp(w));
tmpForward.add(t[i].getTranslation(tmpUp).scl(w));
}
quat.nor();
setToScaling(tmpVec);
rotate(quat);
setTranslation(tmpForward);
return this;
}
/** Averages the given transforms with the given weights and stores the result in this matrix. Translations and scales are
* lerped while rotations are slerped. Does not destroy the data contained in t or w; Sum of w_i must be equal to 1, or
* unexpected results will occur.
* @param t List of transforms
* @param w List of weights
* @return This matrix for chaining */
public Matrix4 avg (Matrix4[] t, float[] w) {
tmpVec.set(t[0].getScale(tmpUp).scl(w[0]));
quat.set(t[0].getRotation(quat2).exp(w[0]));
tmpForward.set(t[0].getTranslation(tmpUp).scl(w[0]));
for (int i = 1; i < t.length; i++) {
tmpVec.add(t[i].getScale(tmpUp).scl(w[i]));
quat.mul(t[i].getRotation(quat2).exp(w[i]));
tmpForward.add(t[i].getTranslation(tmpUp).scl(w[i]));
}
quat.nor();
setToScaling(tmpVec);
rotate(quat);
setTranslation(tmpForward);
return this;
}
/** Sets this matrix to the given 3x3 matrix. The third column of this matrix is set to (0,0,1,0).
* @param mat the matrix */
public Matrix4 set (Matrix3 mat) {
val[0] = mat.val[0];
val[1] = mat.val[1];
val[2] = mat.val[2];
val[3] = 0;
val[4] = mat.val[3];
val[5] = mat.val[4];
val[6] = mat.val[5];
val[7] = 0;
val[8] = 0;
val[9] = 0;
val[10] = 1;
val[11] = 0;
val[12] = mat.val[6];
val[13] = mat.val[7];
val[14] = 0;
val[15] = mat.val[8];
return this;
}
/** Sets this matrix to the given affine matrix. The values are mapped as follows:
*
* <pre>
* [ M00 M01 0 M02 ]
* [ M10 M11 0 M12 ]
* [ 0 0 1 0 ]
* [ 0 0 0 1 ]
* </pre>
* @param affine the affine matrix
* @return This matrix for chaining */
public Matrix4 set (Affine2 affine) {
val[M00] = affine.m00;
val[M10] = affine.m10;
val[M20] = 0;
val[M30] = 0;
val[M01] = affine.m01;
val[M11] = affine.m11;
val[M21] = 0;
val[M31] = 0;
val[M02] = 0;
val[M12] = 0;
val[M22] = 1;
val[M32] = 0;
val[M03] = affine.m02;
val[M13] = affine.m12;
val[M23] = 0;
val[M33] = 1;
return this;
}
/** Assumes that this matrix is a 2D affine transformation, copying only the relevant components. The values are mapped as
* follows:
*
* <pre>
* [ M00 M01 _ M02 ]
* [ M10 M11 _ M12 ]
* [ _ _ _ _ ]
* [ _ _ _ _ ]
* </pre>
* @param affine the source matrix
* @return This matrix for chaining */
public Matrix4 setAsAffine (Affine2 affine) {
val[M00] = affine.m00;
val[M10] = affine.m10;
val[M01] = affine.m01;
val[M11] = affine.m11;
val[M03] = affine.m02;
val[M13] = affine.m12;
return this;
}
/** Assumes that both matrices are 2D affine transformations, copying only the relevant components. The copied values are:
*
* <pre>
* [ M00 M01 _ M03 ]
* [ M10 M11 _ M13 ]
* [ _ _ _ _ ]
* [ _ _ _ _ ]
* </pre>
* @param mat the source matrix
* @return This matrix for chaining */
public Matrix4 setAsAffine (Matrix4 mat) {
val[M00] = mat.val[M00];
val[M10] = mat.val[M10];
val[M01] = mat.val[M01];
val[M11] = mat.val[M11];
val[M03] = mat.val[M03];
val[M13] = mat.val[M13];
return this;
}
public Matrix4 scl (Vector3 scale) {
val[M00] *= scale.x;
val[M11] *= scale.y;
val[M22] *= scale.z;
return this;
}
public Matrix4 scl (float x, float y, float z) {
val[M00] *= x;
val[M11] *= y;
val[M22] *= z;
return this;
}
public Matrix4 scl (float scale) {
val[M00] *= scale;
val[M11] *= scale;
val[M22] *= scale;
return this;
}
public Vector3 getTranslation (Vector3 position) {
position.x = val[M03];
position.y = val[M13];
position.z = val[M23];
return position;
}
/** Gets the rotation of this matrix.
* @param rotation The {@link Quaternion} to receive the rotation
* @param normalizeAxes True to normalize the axes, necessary when the matrix might also include scaling.
* @return The provided {@link Quaternion} for chaining. */
public Quaternion getRotation (Quaternion rotation, boolean normalizeAxes) {
return rotation.setFromMatrix(normalizeAxes, this);
}
/** Gets the rotation of this matrix.
* @param rotation The {@link Quaternion} to receive the rotation
* @return The provided {@link Quaternion} for chaining. */
public Quaternion getRotation (Quaternion rotation) {
return rotation.setFromMatrix(this);
}
/** @return the squared scale factor on the X axis */
public float getScaleXSquared () {
return val[Matrix4.M00] * val[Matrix4.M00] + val[Matrix4.M01] * val[Matrix4.M01] + val[Matrix4.M02] * val[Matrix4.M02];
}
/** @return the squared scale factor on the Y axis */
public float getScaleYSquared () {
return val[Matrix4.M10] * val[Matrix4.M10] + val[Matrix4.M11] * val[Matrix4.M11] + val[Matrix4.M12] * val[Matrix4.M12];
}
/** @return the squared scale factor on the Z axis */
public float getScaleZSquared () {
return val[Matrix4.M20] * val[Matrix4.M20] + val[Matrix4.M21] * val[Matrix4.M21] + val[Matrix4.M22] * val[Matrix4.M22];
}
/** @return the scale factor on the X axis (non-negative) */
public float getScaleX () {
return (MathUtils.isZero(val[Matrix4.M01]) && MathUtils.isZero(val[Matrix4.M02])) ? Math.abs(val[Matrix4.M00])
: (float)Math.sqrt(getScaleXSquared());
}
/** @return the scale factor on the Y axis (non-negative) */
public float getScaleY () {
return (MathUtils.isZero(val[Matrix4.M10]) && MathUtils.isZero(val[Matrix4.M12])) ? Math.abs(val[Matrix4.M11])
: (float)Math.sqrt(getScaleYSquared());
}
/** @return the scale factor on the X axis (non-negative) */
public float getScaleZ () {
return (MathUtils.isZero(val[Matrix4.M20]) && MathUtils.isZero(val[Matrix4.M21])) ? Math.abs(val[Matrix4.M22])
: (float)Math.sqrt(getScaleZSquared());
}
/** @param scale The vector which will receive the (non-negative) scale components on each axis.
* @return The provided vector for chaining. */
public Vector3 getScale (Vector3 scale) {
return scale.set(getScaleX(), getScaleY(), getScaleZ());
}
/** removes the translational part and transposes the matrix. */
public Matrix4 toNormalMatrix () {
val[M03] = 0;
val[M13] = 0;
val[M23] = 0;
return inv().tra();
}
// @off
/*JNI
#include <memory.h>
#include <stdio.h>
#include <string.h>
#define M00 0
#define M01 4
#define M02 8
#define M03 12
#define M10 1
#define M11 5
#define M12 9
#define M13 13
#define M20 2
#define M21 6
#define M22 10
#define M23 14
#define M30 3
#define M31 7
#define M32 11
#define M33 15
static inline void matrix4_mul(float* mata, float* matb) {
float tmp[16];
tmp[M00] = mata[M00] * matb[M00] + mata[M01] * matb[M10] + mata[M02] * matb[M20] + mata[M03] * matb[M30];
tmp[M01] = mata[M00] * matb[M01] + mata[M01] * matb[M11] + mata[M02] * matb[M21] + mata[M03] * matb[M31];
tmp[M02] = mata[M00] * matb[M02] + mata[M01] * matb[M12] + mata[M02] * matb[M22] + mata[M03] * matb[M32];
tmp[M03] = mata[M00] * matb[M03] + mata[M01] * matb[M13] + mata[M02] * matb[M23] + mata[M03] * matb[M33];
tmp[M10] = mata[M10] * matb[M00] + mata[M11] * matb[M10] + mata[M12] * matb[M20] + mata[M13] * matb[M30];
tmp[M11] = mata[M10] * matb[M01] + mata[M11] * matb[M11] + mata[M12] * matb[M21] + mata[M13] * matb[M31];
tmp[M12] = mata[M10] * matb[M02] + mata[M11] * matb[M12] + mata[M12] * matb[M22] + mata[M13] * matb[M32];
tmp[M13] = mata[M10] * matb[M03] + mata[M11] * matb[M13] + mata[M12] * matb[M23] + mata[M13] * matb[M33];
tmp[M20] = mata[M20] * matb[M00] + mata[M21] * matb[M10] + mata[M22] * matb[M20] + mata[M23] * matb[M30];
tmp[M21] = mata[M20] * matb[M01] + mata[M21] * matb[M11] + mata[M22] * matb[M21] + mata[M23] * matb[M31];
tmp[M22] = mata[M20] * matb[M02] + mata[M21] * matb[M12] + mata[M22] * matb[M22] + mata[M23] * matb[M32];
tmp[M23] = mata[M20] * matb[M03] + mata[M21] * matb[M13] + mata[M22] * matb[M23] + mata[M23] * matb[M33];
tmp[M30] = mata[M30] * matb[M00] + mata[M31] * matb[M10] + mata[M32] * matb[M20] + mata[M33] * matb[M30];
tmp[M31] = mata[M30] * matb[M01] + mata[M31] * matb[M11] + mata[M32] * matb[M21] + mata[M33] * matb[M31];
tmp[M32] = mata[M30] * matb[M02] + mata[M31] * matb[M12] + mata[M32] * matb[M22] + mata[M33] * matb[M32];
tmp[M33] = mata[M30] * matb[M03] + mata[M31] * matb[M13] + mata[M32] * matb[M23] + mata[M33] * matb[M33];
memcpy(mata, tmp, sizeof(float) * 16);
}
static inline float matrix4_det(float* val) {
return val[M30] * val[M21] * val[M12] * val[M03] - val[M20] * val[M31] * val[M12] * val[M03] - val[M30] * val[M11]
* val[M22] * val[M03] + val[M10] * val[M31] * val[M22] * val[M03] + val[M20] * val[M11] * val[M32] * val[M03] - val[M10]
* val[M21] * val[M32] * val[M03] - val[M30] * val[M21] * val[M02] * val[M13] + val[M20] * val[M31] * val[M02] * val[M13]
+ val[M30] * val[M01] * val[M22] * val[M13] - val[M00] * val[M31] * val[M22] * val[M13] - val[M20] * val[M01] * val[M32]
* val[M13] + val[M00] * val[M21] * val[M32] * val[M13] + val[M30] * val[M11] * val[M02] * val[M23] - val[M10] * val[M31]
* val[M02] * val[M23] - val[M30] * val[M01] * val[M12] * val[M23] + val[M00] * val[M31] * val[M12] * val[M23] + val[M10]
* val[M01] * val[M32] * val[M23] - val[M00] * val[M11] * val[M32] * val[M23] - val[M20] * val[M11] * val[M02] * val[M33]
+ val[M10] * val[M21] * val[M02] * val[M33] + val[M20] * val[M01] * val[M12] * val[M33] - val[M00] * val[M21] * val[M12]
* val[M33] - val[M10] * val[M01] * val[M22] * val[M33] + val[M00] * val[M11] * val[M22] * val[M33];
}
static inline bool matrix4_inv(float* val) {
float tmp[16];
float l_det = matrix4_det(val);
if (l_det == 0) return false;
tmp[M00] = val[M12] * val[M23] * val[M31] - val[M13] * val[M22] * val[M31] + val[M13] * val[M21] * val[M32] - val[M11]
* val[M23] * val[M32] - val[M12] * val[M21] * val[M33] + val[M11] * val[M22] * val[M33];
tmp[M01] = val[M03] * val[M22] * val[M31] - val[M02] * val[M23] * val[M31] - val[M03] * val[M21] * val[M32] + val[M01]
* val[M23] * val[M32] + val[M02] * val[M21] * val[M33] - val[M01] * val[M22] * val[M33];
tmp[M02] = val[M02] * val[M13] * val[M31] - val[M03] * val[M12] * val[M31] + val[M03] * val[M11] * val[M32] - val[M01]
* val[M13] * val[M32] - val[M02] * val[M11] * val[M33] + val[M01] * val[M12] * val[M33];
tmp[M03] = val[M03] * val[M12] * val[M21] - val[M02] * val[M13] * val[M21] - val[M03] * val[M11] * val[M22] + val[M01]
* val[M13] * val[M22] + val[M02] * val[M11] * val[M23] - val[M01] * val[M12] * val[M23];
tmp[M10] = val[M13] * val[M22] * val[M30] - val[M12] * val[M23] * val[M30] - val[M13] * val[M20] * val[M32] + val[M10]
* val[M23] * val[M32] + val[M12] * val[M20] * val[M33] - val[M10] * val[M22] * val[M33];
tmp[M11] = val[M02] * val[M23] * val[M30] - val[M03] * val[M22] * val[M30] + val[M03] * val[M20] * val[M32] - val[M00]
* val[M23] * val[M32] - val[M02] * val[M20] * val[M33] + val[M00] * val[M22] * val[M33];
tmp[M12] = val[M03] * val[M12] * val[M30] - val[M02] * val[M13] * val[M30] - val[M03] * val[M10] * val[M32] + val[M00]
* val[M13] * val[M32] + val[M02] * val[M10] * val[M33] - val[M00] * val[M12] * val[M33];
tmp[M13] = val[M02] * val[M13] * val[M20] - val[M03] * val[M12] * val[M20] + val[M03] * val[M10] * val[M22] - val[M00]
* val[M13] * val[M22] - val[M02] * val[M10] * val[M23] + val[M00] * val[M12] * val[M23];
tmp[M20] = val[M11] * val[M23] * val[M30] - val[M13] * val[M21] * val[M30] + val[M13] * val[M20] * val[M31] - val[M10]
* val[M23] * val[M31] - val[M11] * val[M20] * val[M33] + val[M10] * val[M21] * val[M33];
tmp[M21] = val[M03] * val[M21] * val[M30] - val[M01] * val[M23] * val[M30] - val[M03] * val[M20] * val[M31] + val[M00]
* val[M23] * val[M31] + val[M01] * val[M20] * val[M33] - val[M00] * val[M21] * val[M33];
tmp[M22] = val[M01] * val[M13] * val[M30] - val[M03] * val[M11] * val[M30] + val[M03] * val[M10] * val[M31] - val[M00]
* val[M13] * val[M31] - val[M01] * val[M10] * val[M33] + val[M00] * val[M11] * val[M33];
tmp[M23] = val[M03] * val[M11] * val[M20] - val[M01] * val[M13] * val[M20] - val[M03] * val[M10] * val[M21] + val[M00]
* val[M13] * val[M21] + val[M01] * val[M10] * val[M23] - val[M00] * val[M11] * val[M23];
tmp[M30] = val[M12] * val[M21] * val[M30] - val[M11] * val[M22] * val[M30] - val[M12] * val[M20] * val[M31] + val[M10]
* val[M22] * val[M31] + val[M11] * val[M20] * val[M32] - val[M10] * val[M21] * val[M32];
tmp[M31] = val[M01] * val[M22] * val[M30] - val[M02] * val[M21] * val[M30] + val[M02] * val[M20] * val[M31] - val[M00]
* val[M22] * val[M31] - val[M01] * val[M20] * val[M32] + val[M00] * val[M21] * val[M32];
tmp[M32] = val[M02] * val[M11] * val[M30] - val[M01] * val[M12] * val[M30] - val[M02] * val[M10] * val[M31] + val[M00]
* val[M12] * val[M31] + val[M01] * val[M10] * val[M32] - val[M00] * val[M11] * val[M32];
tmp[M33] = val[M01] * val[M12] * val[M20] - val[M02] * val[M11] * val[M20] + val[M02] * val[M10] * val[M21] - val[M00]
* val[M12] * val[M21] - val[M01] * val[M10] * val[M22] + val[M00] * val[M11] * val[M22];
float inv_det = 1.0f / l_det;
val[M00] = tmp[M00] * inv_det;
val[M01] = tmp[M01] * inv_det;
val[M02] = tmp[M02] * inv_det;
val[M03] = tmp[M03] * inv_det;
val[M10] = tmp[M10] * inv_det;
val[M11] = tmp[M11] * inv_det;
val[M12] = tmp[M12] * inv_det;
val[M13] = tmp[M13] * inv_det;
val[M20] = tmp[M20] * inv_det;
val[M21] = tmp[M21] * inv_det;
val[M22] = tmp[M22] * inv_det;
val[M23] = tmp[M23] * inv_det;
val[M30] = tmp[M30] * inv_det;
val[M31] = tmp[M31] * inv_det;
val[M32] = tmp[M32] * inv_det;
val[M33] = tmp[M33] * inv_det;
return true;
}
static inline void matrix4_mulVec(float* mat, float* vec) {
float x = vec[0] * mat[M00] + vec[1] * mat[M01] + vec[2] * mat[M02] + mat[M03];
float y = vec[0] * mat[M10] + vec[1] * mat[M11] + vec[2] * mat[M12] + mat[M13];
float z = vec[0] * mat[M20] + vec[1] * mat[M21] + vec[2] * mat[M22] + mat[M23];
vec[0] = x;
vec[1] = y;
vec[2] = z;
}
static inline void matrix4_proj(float* mat, float* vec) {
float inv_w = 1.0f / (vec[0] * mat[M30] + vec[1] * mat[M31] + vec[2] * mat[M32] + mat[M33]);
float x = (vec[0] * mat[M00] + vec[1] * mat[M01] + vec[2] * mat[M02] + mat[M03]) * inv_w;
float y = (vec[0] * mat[M10] + vec[1] * mat[M11] + vec[2] * mat[M12] + mat[M13]) * inv_w;
float z = (vec[0] * mat[M20] + vec[1] * mat[M21] + vec[2] * mat[M22] + mat[M23]) * inv_w;
vec[0] = x;
vec[1] = y;
vec[2] = z;
}
static inline void matrix4_rot(float* mat, float* vec) {
float x = vec[0] * mat[M00] + vec[1] * mat[M01] + vec[2] * mat[M02];
float y = vec[0] * mat[M10] + vec[1] * mat[M11] + vec[2] * mat[M12];
float z = vec[0] * mat[M20] + vec[1] * mat[M21] + vec[2] * mat[M22];
vec[0] = x;
vec[1] = y;
vec[2] = z;
}
*/
/** Multiplies the matrix mata with matrix matb, storing the result in mata. The arrays are assumed to hold 4x4 column major
* matrices as you can get from {@link Matrix4#val}. This is the same as {@link Matrix4#mul(Matrix4)}.
*
* @param mata the first matrix.
* @param matb the second matrix. */
public static native void mul (float[] mata, float[] matb) /*-{ }-*/; /*
matrix4_mul(mata, matb);
*/
/** Multiplies the vector with the given matrix. The matrix array is assumed to hold a 4x4 column major matrix as you can get
* from {@link Matrix4#val}. The vector array is assumed to hold a 3-component vector, with x being the first element, y being
* the second and z being the last component. The result is stored in the vector array. This is the same as
* {@link Vector3#mul(Matrix4)}.
* @param mat the matrix
* @param vec the vector. */
public static native void mulVec (float[] mat, float[] vec) /*-{ }-*/; /*
matrix4_mulVec(mat, vec);
*/
/** Multiplies the vectors with the given matrix. The matrix array is assumed to hold a 4x4 column major matrix as you can get
* from {@link Matrix4#val}. The vectors array is assumed to hold 3-component vectors. Offset specifies the offset into the
* array where the x-component of the first vector is located. The numVecs parameter specifies the number of vectors stored in
* the vectors array. The stride parameter specifies the number of floats between subsequent vectors and must be >= 3. This is
* the same as {@link Vector3#mul(Matrix4)} applied to multiple vectors.
*
* @param mat the matrix
* @param vecs the vectors
* @param offset the offset into the vectors array
* @param numVecs the number of vectors
* @param stride the stride between vectors in floats */
public static native void mulVec (float[] mat, float[] vecs, int offset, int numVecs, int stride) /*-{ }-*/; /*
float* vecPtr = vecs + offset;
for(int i = 0; i < numVecs; i++) {
matrix4_mulVec(mat, vecPtr);
vecPtr += stride;
}
*/
/** Multiplies the vector with the given matrix, performing a division by w. The matrix array is assumed to hold a 4x4 column
* major matrix as you can get from {@link Matrix4#val}. The vector array is assumed to hold a 3-component vector, with x being
* the first element, y being the second and z being the last component. The result is stored in the vector array. This is the
* same as {@link Vector3#prj(Matrix4)}.
* @param mat the matrix
* @param vec the vector. */
public static native void prj (float[] mat, float[] vec) /*-{ }-*/; /*
matrix4_proj(mat, vec);
*/
/** Multiplies the vectors with the given matrix, , performing a division by w. The matrix array is assumed to hold a 4x4 column
* major matrix as you can get from {@link Matrix4#val}. The vectors array is assumed to hold 3-component vectors. Offset
* specifies the offset into the array where the x-component of the first vector is located. The numVecs parameter specifies
* the number of vectors stored in the vectors array. The stride parameter specifies the number of floats between subsequent
* vectors and must be >= 3. This is the same as {@link Vector3#prj(Matrix4)} applied to multiple vectors.
*
* @param mat the matrix
* @param vecs the vectors
* @param offset the offset into the vectors array
* @param numVecs the number of vectors
* @param stride the stride between vectors in floats */
public static native void prj (float[] mat, float[] vecs, int offset, int numVecs, int stride) /*-{ }-*/; /*
float* vecPtr = vecs + offset;
for(int i = 0; i < numVecs; i++) {
matrix4_proj(mat, vecPtr);
vecPtr += stride;
}
*/
/** Multiplies the vector with the top most 3x3 sub-matrix of the given matrix. The matrix array is assumed to hold a 4x4 column
* major matrix as you can get from {@link Matrix4#val}. The vector array is assumed to hold a 3-component vector, with x being
* the first element, y being the second and z being the last component. The result is stored in the vector array. This is the
* same as {@link Vector3#rot(Matrix4)}.
* @param mat the matrix
* @param vec the vector. */
public static native void rot (float[] mat, float[] vec) /*-{ }-*/; /*
matrix4_rot(mat, vec);
*/
/** Multiplies the vectors with the top most 3x3 sub-matrix of the given matrix. The matrix array is assumed to hold a 4x4
* column major matrix as you can get from {@link Matrix4#val}. The vectors array is assumed to hold 3-component vectors.
* Offset specifies the offset into the array where the x-component of the first vector is located. The numVecs parameter
* specifies the number of vectors stored in the vectors array. The stride parameter specifies the number of floats between
* subsequent vectors and must be >= 3. This is the same as {@link Vector3#rot(Matrix4)} applied to multiple vectors.
*
* @param mat the matrix
* @param vecs the vectors
* @param offset the offset into the vectors array
* @param numVecs the number of vectors
* @param stride the stride between vectors in floats */
public static native void rot (float[] mat, float[] vecs, int offset, int numVecs, int stride) /*-{ }-*/; /*
float* vecPtr = vecs + offset;
for(int i = 0; i < numVecs; i++) {
matrix4_rot(mat, vecPtr);
vecPtr += stride;
}
*/
/** Computes the inverse of the given matrix. The matrix array is assumed to hold a 4x4 column major matrix as you can get from
* {@link Matrix4#val}.
* @param values the matrix values.
* @return false in case the inverse could not be calculated, true otherwise. */
public static native boolean inv (float[] values) /*-{ }-*/; /*
return matrix4_inv(values);
*/
/** Computes the determinante of the given matrix. The matrix array is assumed to hold a 4x4 column major matrix as you can get
* from {@link Matrix4#val}.
* @param values the matrix values.
* @return the determinante. */
public static native float det (float[] values) /*-{ }-*/; /*
return matrix4_det(values);
*/
// @on
/** Postmultiplies this matrix by a translation matrix. Postmultiplication is also used by OpenGL ES'
* glTranslate/glRotate/glScale
* @param translation
* @return This matrix for the purpose of chaining methods together. */
public Matrix4 translate (Vector3 translation) {
return translate(translation.x, translation.y, translation.z);
}
/** Postmultiplies this matrix by a translation matrix. Postmultiplication is also used by OpenGL ES' 1.x
* glTranslate/glRotate/glScale.
* @param x Translation in the x-axis.
* @param y Translation in the y-axis.
* @param z Translation in the z-axis.
* @return This matrix for the purpose of chaining methods together. */
public Matrix4 translate (float x, float y, float z) {
tmp[M00] = 1;
tmp[M01] = 0;
tmp[M02] = 0;
tmp[M03] = x;
tmp[M10] = 0;
tmp[M11] = 1;
tmp[M12] = 0;
tmp[M13] = y;
tmp[M20] = 0;
tmp[M21] = 0;
tmp[M22] = 1;
tmp[M23] = z;
tmp[M30] = 0;
tmp[M31] = 0;
tmp[M32] = 0;
tmp[M33] = 1;
mul(val, tmp);
return this;
}
/** Postmultiplies this matrix with a (counter-clockwise) rotation matrix. Postmultiplication is also used by OpenGL ES' 1.x
* glTranslate/glRotate/glScale.
*
* @param axis The vector axis to rotate around.
* @param degrees The angle in degrees.
* @return This matrix for the purpose of chaining methods together. */
public Matrix4 rotate (Vector3 axis, float degrees) {
if (degrees == 0) return this;
quat.set(axis, degrees);
return rotate(quat);
}
/** Postmultiplies this matrix with a (counter-clockwise) rotation matrix. Postmultiplication is also used by OpenGL ES' 1.x
* glTranslate/glRotate/glScale.
*
* @param axis The vector axis to rotate around.
* @param radians The angle in radians.
* @return This matrix for the purpose of chaining methods together. */
public Matrix4 rotateRad (Vector3 axis, float radians) {
if (radians == 0) return this;
quat.setFromAxisRad(axis, radians);
return rotate(quat);
}
/** Postmultiplies this matrix with a (counter-clockwise) rotation matrix. Postmultiplication is also used by OpenGL ES' 1.x
* glTranslate/glRotate/glScale
* @param axisX The x-axis component of the vector to rotate around.
* @param axisY The y-axis component of the vector to rotate around.
* @param axisZ The z-axis component of the vector to rotate around.
* @param degrees The angle in degrees
* @return This matrix for the purpose of chaining methods together. */
public Matrix4 rotate (float axisX, float axisY, float axisZ, float degrees) {
if (degrees == 0) return this;
quat.setFromAxis(axisX, axisY, axisZ, degrees);
return rotate(quat);
}
/** Postmultiplies this matrix with a (counter-clockwise) rotation matrix. Postmultiplication is also used by OpenGL ES' 1.x
* glTranslate/glRotate/glScale
* @param axisX The x-axis component of the vector to rotate around.
* @param axisY The y-axis component of the vector to rotate around.
* @param axisZ The z-axis component of the vector to rotate around.
* @param radians The angle in radians
* @return This matrix for the purpose of chaining methods together. */
public Matrix4 rotateRad (float axisX, float axisY, float axisZ, float radians) {
if (radians == 0) return this;
quat.setFromAxisRad(axisX, axisY, axisZ, radians);
return rotate(quat);
}
/** Postmultiplies this matrix with a (counter-clockwise) rotation matrix. Postmultiplication is also used by OpenGL ES' 1.x
* glTranslate/glRotate/glScale.
*
* @param rotation
* @return This matrix for the purpose of chaining methods together. */
public Matrix4 rotate (Quaternion rotation) {
rotation.toMatrix(tmp);
mul(val, tmp);
return this;
}
/** Postmultiplies this matrix by the rotation between two vectors.
* @param v1 The base vector
* @param v2 The target vector
* @return This matrix for the purpose of chaining methods together */
public Matrix4 rotate (final Vector3 v1, final Vector3 v2) {
return rotate(quat.setFromCross(v1, v2));
}
/** Postmultiplies this matrix with a scale matrix. Postmultiplication is also used by OpenGL ES' 1.x
* glTranslate/glRotate/glScale.
* @param scaleX The scale in the x-axis.
* @param scaleY The scale in the y-axis.
* @param scaleZ The scale in the z-axis.
* @return This matrix for the purpose of chaining methods together. */
public Matrix4 scale (float scaleX, float scaleY, float scaleZ) {
tmp[M00] = scaleX;
tmp[M01] = 0;
tmp[M02] = 0;
tmp[M03] = 0;
tmp[M10] = 0;
tmp[M11] = scaleY;
tmp[M12] = 0;
tmp[M13] = 0;
tmp[M20] = 0;
tmp[M21] = 0;
tmp[M22] = scaleZ;
tmp[M23] = 0;
tmp[M30] = 0;
tmp[M31] = 0;
tmp[M32] = 0;
tmp[M33] = 1;
mul(val, tmp);
return this;
}
/** Copies the 4x3 upper-left sub-matrix into float array. The destination array is supposed to be a column major matrix.
* @param dst the destination matrix */
public void extract4x3Matrix (float[] dst) {
dst[0] = val[M00];
dst[1] = val[M10];
dst[2] = val[M20];
dst[3] = val[M01];
dst[4] = val[M11];
dst[5] = val[M21];
dst[6] = val[M02];
dst[7] = val[M12];
dst[8] = val[M22];
dst[9] = val[M03];
dst[10] = val[M13];
dst[11] = val[M23];
}
/** @return True if this matrix has any rotation or scaling, false otherwise */
public boolean hasRotationOrScaling () {
return !(MathUtils.isEqual(val[M00], 1) && MathUtils.isEqual(val[M11], 1) && MathUtils.isEqual(val[M22], 1)
&& MathUtils.isZero(val[M01]) && MathUtils.isZero(val[M02]) && MathUtils.isZero(val[M10]) && MathUtils.isZero(val[M12])
&& MathUtils.isZero(val[M20]) && MathUtils.isZero(val[M21]));
}
}