android/android-9.0.0_r35 : android/opengl/Matrix.java

Matrix
https://source.android.com/
/*
 * Copyright (C) 2007 The Android Open Source Project
 *
 * 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 android.opengl;

Matrix math utilities. These methods operate on OpenGL ES format
matrices and vectors stored in float arrays.

Matrices are 4 x 4 column-vector matrices stored in column-major
order:
 m[offset +  0] m[offset +  4] m[offset +  8] m[offset + 12]
 m[offset +  1] m[offset +  5] m[offset +  9] m[offset + 13]
 m[offset +  2] m[offset +  6] m[offset + 10] m[offset + 14]
 m[offset +  3] m[offset +  7] m[offset + 11] m[offset + 15]
Vectors are 4 x 1 column vectors stored in order:
v[offset + 0]
v[offset + 1]
v[offset + 2]
v[offset + 3]
/**
 * Matrix math utilities. These methods operate on OpenGL ES format
 * matrices and vectors stored in float arrays.
 * <p>
 * Matrices are 4 x 4 column-vector matrices stored in column-major
 * order:
 * <pre>
 *  m[offset +  0] m[offset +  4] m[offset +  8] m[offset + 12]
 *  m[offset +  1] m[offset +  5] m[offset +  9] m[offset + 13]
 *  m[offset +  2] m[offset +  6] m[offset + 10] m[offset + 14]
 *  m[offset +  3] m[offset +  7] m[offset + 11] m[offset + 15]</pre>
 *
 * Vectors are 4 x 1 column vectors stored in order:
 * <pre>
 * v[offset + 0]
 * v[offset + 1]
 * v[offset + 2]
 * v[offset + 3]</pre>
 */
public class Matrix {

    Temporary memory for operations that need temporary matrix data. /** Temporary memory for operations that need temporary matrix data. */
    private final static float[] sTemp = new float[32];

    Deprecated: All methods are static, do not instantiate this class./**
     * @deprecated All methods are static, do not instantiate this class.
     */
    @Deprecated
    public Matrix() {}

    Multiplies two 4x4 matrices together and stores the result in a third 4x4
matrix. In matrix notation: result = lhs x rhs. Due to the way
matrix multiplication works, the result matrix will have the same
effect as first multiplying by the rhs matrix, then multiplying by
the lhs matrix. This is the opposite of what you might expect.

The same float array may be passed for result, lhs, and/or rhs. However,
the result element values are undefined if the result elements overlap
either the lhs or rhs elements.
Params: result – The float array that holds the result.
resultOffset – The offset into the result array where the result is
       stored.
lhs – The float array that holds the left-hand-side matrix.
lhsOffset – The offset into the lhs array where the lhs is stored
rhs – The float array that holds the right-hand-side matrix.
rhsOffset – The offset into the rhs array where the rhs is stored.
Throws: IllegalArgumentException – if result, lhs, or rhs are null, or if
resultOffset + 16 > result.length or lhsOffset + 16 > lhs.length or
rhsOffset + 16 > rhs.length./**
     * Multiplies two 4x4 matrices together and stores the result in a third 4x4
     * matrix. In matrix notation: result = lhs x rhs. Due to the way
     * matrix multiplication works, the result matrix will have the same
     * effect as first multiplying by the rhs matrix, then multiplying by
     * the lhs matrix. This is the opposite of what you might expect.
     * <p>
     * The same float array may be passed for result, lhs, and/or rhs. However,
     * the result element values are undefined if the result elements overlap
     * either the lhs or rhs elements.
     *
     * @param result The float array that holds the result.
     * @param resultOffset The offset into the result array where the result is
     *        stored.
     * @param lhs The float array that holds the left-hand-side matrix.
     * @param lhsOffset The offset into the lhs array where the lhs is stored
     * @param rhs The float array that holds the right-hand-side matrix.
     * @param rhsOffset The offset into the rhs array where the rhs is stored.
     *
     * @throws IllegalArgumentException if result, lhs, or rhs are null, or if
     * resultOffset + 16 > result.length or lhsOffset + 16 > lhs.length or
     * rhsOffset + 16 > rhs.length.
     */
    public static native void multiplyMM(float[] result, int resultOffset,
            float[] lhs, int lhsOffset, float[] rhs, int rhsOffset);

    Multiplies a 4 element vector by a 4x4 matrix and stores the result in a
4-element column vector. In matrix notation: result = lhs x rhs

The same float array may be passed for resultVec, lhsMat, and/or rhsVec.
However, the resultVec element values are undefined if the resultVec
elements overlap either the lhsMat or rhsVec elements.
Params: resultVec – The float array that holds the result vector.
resultVecOffset – The offset into the result array where the result
       vector is stored.
lhsMat – The float array that holds the left-hand-side matrix.
lhsMatOffset – The offset into the lhs array where the lhs is stored
rhsVec – The float array that holds the right-hand-side vector.
rhsVecOffset – The offset into the rhs vector where the rhs vector
       is stored.
Throws: IllegalArgumentException – if resultVec, lhsMat,
or rhsVec are null, or if resultVecOffset + 4 > resultVec.length
or lhsMatOffset + 16 > lhsMat.length or
rhsVecOffset + 4 > rhsVec.length./**
     * Multiplies a 4 element vector by a 4x4 matrix and stores the result in a
     * 4-element column vector. In matrix notation: result = lhs x rhs
     * <p>
     * The same float array may be passed for resultVec, lhsMat, and/or rhsVec.
     * However, the resultVec element values are undefined if the resultVec
     * elements overlap either the lhsMat or rhsVec elements.
     *
     * @param resultVec The float array that holds the result vector.
     * @param resultVecOffset The offset into the result array where the result
     *        vector is stored.
     * @param lhsMat The float array that holds the left-hand-side matrix.
     * @param lhsMatOffset The offset into the lhs array where the lhs is stored
     * @param rhsVec The float array that holds the right-hand-side vector.
     * @param rhsVecOffset The offset into the rhs vector where the rhs vector
     *        is stored.
     *
     * @throws IllegalArgumentException if resultVec, lhsMat,
     * or rhsVec are null, or if resultVecOffset + 4 > resultVec.length
     * or lhsMatOffset + 16 > lhsMat.length or
     * rhsVecOffset + 4 > rhsVec.length.
     */
    public static native void multiplyMV(float[] resultVec,
            int resultVecOffset, float[] lhsMat, int lhsMatOffset,
            float[] rhsVec, int rhsVecOffset);

    Transposes a 4 x 4 matrix.

mTrans and m must not overlap.
Params: mTrans – the array that holds the output transposed matrix
mTransOffset – an offset into mTrans where the transposed matrix is
       stored.
m – the input array
mOffset – an offset into m where the input matrix is stored./**
     * Transposes a 4 x 4 matrix.
     * <p>
     * mTrans and m must not overlap.
     *
     * @param mTrans the array that holds the output transposed matrix
     * @param mTransOffset an offset into mTrans where the transposed matrix is
     *        stored.
     * @param m the input array
     * @param mOffset an offset into m where the input matrix is stored.
     */
    public static void transposeM(float[] mTrans, int mTransOffset, float[] m,
            int mOffset) {
        for (int i = 0; i < 4; i++) {
            int mBase = i * 4 + mOffset;
            mTrans[i + mTransOffset] = m[mBase];
            mTrans[i + 4 + mTransOffset] = m[mBase + 1];
            mTrans[i + 8 + mTransOffset] = m[mBase + 2];
            mTrans[i + 12 + mTransOffset] = m[mBase + 3];
        }
    }

    Inverts a 4 x 4 matrix.

mInv and m must not overlap.
Params: mInv – the array that holds the output inverted matrix
mInvOffset – an offset into mInv where the inverted matrix is
       stored.
m – the input array
mOffset – an offset into m where the input matrix is stored.
Returns: true if the matrix could be inverted, false if it could not./**
     * Inverts a 4 x 4 matrix.
     * <p>
     * mInv and m must not overlap.
     *
     * @param mInv the array that holds the output inverted matrix
     * @param mInvOffset an offset into mInv where the inverted matrix is
     *        stored.
     * @param m the input array
     * @param mOffset an offset into m where the input matrix is stored.
     * @return true if the matrix could be inverted, false if it could not.
     */
    public static boolean invertM(float[] mInv, int mInvOffset, float[] m,
            int mOffset) {
        // Invert a 4 x 4 matrix using Cramer's Rule

        // transpose matrix
        final float src0  = m[mOffset +  0];
        final float src4  = m[mOffset +  1];
        final float src8  = m[mOffset +  2];
        final float src12 = m[mOffset +  3];

        final float src1  = m[mOffset +  4];
        final float src5  = m[mOffset +  5];
        final float src9  = m[mOffset +  6];
        final float src13 = m[mOffset +  7];

        final float src2  = m[mOffset +  8];
        final float src6  = m[mOffset +  9];
        final float src10 = m[mOffset + 10];
        final float src14 = m[mOffset + 11];

        final float src3  = m[mOffset + 12];
        final float src7  = m[mOffset + 13];
        final float src11 = m[mOffset + 14];
        final float src15 = m[mOffset + 15];

        // calculate pairs for first 8 elements (cofactors)
        final float atmp0  = src10 * src15;
        final float atmp1  = src11 * src14;
        final float atmp2  = src9  * src15;
        final float atmp3  = src11 * src13;
        final float atmp4  = src9  * src14;
        final float atmp5  = src10 * src13;
        final float atmp6  = src8  * src15;
        final float atmp7  = src11 * src12;
        final float atmp8  = src8  * src14;
        final float atmp9  = src10 * src12;
        final float atmp10 = src8  * src13;
        final float atmp11 = src9  * src12;

        // calculate first 8 elements (cofactors)
        final float dst0  = (atmp0 * src5 + atmp3 * src6 + atmp4  * src7)
                          - (atmp1 * src5 + atmp2 * src6 + atmp5  * src7);
        final float dst1  = (atmp1 * src4 + atmp6 * src6 + atmp9  * src7)
                          - (atmp0 * src4 + atmp7 * src6 + atmp8  * src7);
        final float dst2  = (atmp2 * src4 + atmp7 * src5 + atmp10 * src7)
                          - (atmp3 * src4 + atmp6 * src5 + atmp11 * src7);
        final float dst3  = (atmp5 * src4 + atmp8 * src5 + atmp11 * src6)
                          - (atmp4 * src4 + atmp9 * src5 + atmp10 * src6);
        final float dst4  = (atmp1 * src1 + atmp2 * src2 + atmp5  * src3)
                          - (atmp0 * src1 + atmp3 * src2 + atmp4  * src3);
        final float dst5  = (atmp0 * src0 + atmp7 * src2 + atmp8  * src3)
                          - (atmp1 * src0 + atmp6 * src2 + atmp9  * src3);
        final float dst6  = (atmp3 * src0 + atmp6 * src1 + atmp11 * src3)
                          - (atmp2 * src0 + atmp7 * src1 + atmp10 * src3);
        final float dst7  = (atmp4 * src0 + atmp9 * src1 + atmp10 * src2)
                          - (atmp5 * src0 + atmp8 * src1 + atmp11 * src2);

        // calculate pairs for second 8 elements (cofactors)
        final float btmp0  = src2 * src7;
        final float btmp1  = src3 * src6;
        final float btmp2  = src1 * src7;
        final float btmp3  = src3 * src5;
        final float btmp4  = src1 * src6;
        final float btmp5  = src2 * src5;
        final float btmp6  = src0 * src7;
        final float btmp7  = src3 * src4;
        final float btmp8  = src0 * src6;
        final float btmp9  = src2 * src4;
        final float btmp10 = src0 * src5;
        final float btmp11 = src1 * src4;

        // calculate second 8 elements (cofactors)
        final float dst8  = (btmp0  * src13 + btmp3  * src14 + btmp4  * src15)
                          - (btmp1  * src13 + btmp2  * src14 + btmp5  * src15);
        final float dst9  = (btmp1  * src12 + btmp6  * src14 + btmp9  * src15)
                          - (btmp0  * src12 + btmp7  * src14 + btmp8  * src15);
        final float dst10 = (btmp2  * src12 + btmp7  * src13 + btmp10 * src15)
                          - (btmp3  * src12 + btmp6  * src13 + btmp11 * src15);
        final float dst11 = (btmp5  * src12 + btmp8  * src13 + btmp11 * src14)
                          - (btmp4  * src12 + btmp9  * src13 + btmp10 * src14);
        final float dst12 = (btmp2  * src10 + btmp5  * src11 + btmp1  * src9 )
                          - (btmp4  * src11 + btmp0  * src9  + btmp3  * src10);
        final float dst13 = (btmp8  * src11 + btmp0  * src8  + btmp7  * src10)
                          - (btmp6  * src10 + btmp9  * src11 + btmp1  * src8 );
        final float dst14 = (btmp6  * src9  + btmp11 * src11 + btmp3  * src8 )
                          - (btmp10 * src11 + btmp2  * src8  + btmp7  * src9 );
        final float dst15 = (btmp10 * src10 + btmp4  * src8  + btmp9  * src9 )
                          - (btmp8  * src9  + btmp11 * src10 + btmp5  * src8 );

        // calculate determinant
        final float det =
                src0 * dst0 + src1 * dst1 + src2 * dst2 + src3 * dst3;

        if (det == 0.0f) {
            return false;
        }

        // calculate matrix inverse
        final float invdet = 1.0f / det;
        mInv[     mInvOffset] = dst0  * invdet;
        mInv[ 1 + mInvOffset] = dst1  * invdet;
        mInv[ 2 + mInvOffset] = dst2  * invdet;
        mInv[ 3 + mInvOffset] = dst3  * invdet;

        mInv[ 4 + mInvOffset] = dst4  * invdet;
        mInv[ 5 + mInvOffset] = dst5  * invdet;
        mInv[ 6 + mInvOffset] = dst6  * invdet;
        mInv[ 7 + mInvOffset] = dst7  * invdet;

        mInv[ 8 + mInvOffset] = dst8  * invdet;
        mInv[ 9 + mInvOffset] = dst9  * invdet;
        mInv[10 + mInvOffset] = dst10 * invdet;
        mInv[11 + mInvOffset] = dst11 * invdet;

        mInv[12 + mInvOffset] = dst12 * invdet;
        mInv[13 + mInvOffset] = dst13 * invdet;
        mInv[14 + mInvOffset] = dst14 * invdet;
        mInv[15 + mInvOffset] = dst15 * invdet;

        return true;
    }

    Computes an orthographic projection matrix.
Params: m – returns the result
mOffset – 
left – 
right – 
bottom – 
top – 
near – 
far – /**
     * Computes an orthographic projection matrix.
     *
     * @param m returns the result
     * @param mOffset
     * @param left
     * @param right
     * @param bottom
     * @param top
     * @param near
     * @param far
     */
    public static void orthoM(float[] m, int mOffset,
        float left, float right, float bottom, float top,
        float near, float far) {
        if (left == right) {
            throw new IllegalArgumentException("left == right");
        }
        if (bottom == top) {
            throw new IllegalArgumentException("bottom == top");
        }
        if (near == far) {
            throw new IllegalArgumentException("near == far");
        }

        final float r_width  = 1.0f / (right - left);
        final float r_height = 1.0f / (top - bottom);
        final float r_depth  = 1.0f / (far - near);
        final float x =  2.0f * (r_width);
        final float y =  2.0f * (r_height);
        final float z = -2.0f * (r_depth);
        final float tx = -(right + left) * r_width;
        final float ty = -(top + bottom) * r_height;
        final float tz = -(far + near) * r_depth;
        m[mOffset + 0] = x;
        m[mOffset + 5] = y;
        m[mOffset +10] = z;
        m[mOffset +12] = tx;
        m[mOffset +13] = ty;
        m[mOffset +14] = tz;
        m[mOffset +15] = 1.0f;
        m[mOffset + 1] = 0.0f;
        m[mOffset + 2] = 0.0f;
        m[mOffset + 3] = 0.0f;
        m[mOffset + 4] = 0.0f;
        m[mOffset + 6] = 0.0f;
        m[mOffset + 7] = 0.0f;
        m[mOffset + 8] = 0.0f;
        m[mOffset + 9] = 0.0f;
        m[mOffset + 11] = 0.0f;
    }


    Defines a projection matrix in terms of six clip planes.
Params: m – the float array that holds the output perspective matrix
offset – the offset into float array m where the perspective
       matrix data is written
left – 
right – 
bottom – 
top – 
near – 
far – /**
     * Defines a projection matrix in terms of six clip planes.
     *
     * @param m the float array that holds the output perspective matrix
     * @param offset the offset into float array m where the perspective
     *        matrix data is written
     * @param left
     * @param right
     * @param bottom
     * @param top
     * @param near
     * @param far
     */
    public static void frustumM(float[] m, int offset,
            float left, float right, float bottom, float top,
            float near, float far) {
        if (left == right) {
            throw new IllegalArgumentException("left == right");
        }
        if (top == bottom) {
            throw new IllegalArgumentException("top == bottom");
        }
        if (near == far) {
            throw new IllegalArgumentException("near == far");
        }
        if (near <= 0.0f) {
            throw new IllegalArgumentException("near <= 0.0f");
        }
        if (far <= 0.0f) {
            throw new IllegalArgumentException("far <= 0.0f");
        }
        final float r_width  = 1.0f / (right - left);
        final float r_height = 1.0f / (top - bottom);
        final float r_depth  = 1.0f / (near - far);
        final float x = 2.0f * (near * r_width);
        final float y = 2.0f * (near * r_height);
        final float A = (right + left) * r_width;
        final float B = (top + bottom) * r_height;
        final float C = (far + near) * r_depth;
        final float D = 2.0f * (far * near * r_depth);
        m[offset + 0] = x;
        m[offset + 5] = y;
        m[offset + 8] = A;
        m[offset +  9] = B;
        m[offset + 10] = C;
        m[offset + 14] = D;
        m[offset + 11] = -1.0f;
        m[offset +  1] = 0.0f;
        m[offset +  2] = 0.0f;
        m[offset +  3] = 0.0f;
        m[offset +  4] = 0.0f;
        m[offset +  6] = 0.0f;
        m[offset +  7] = 0.0f;
        m[offset + 12] = 0.0f;
        m[offset + 13] = 0.0f;
        m[offset + 15] = 0.0f;
    }

    Defines a projection matrix in terms of a field of view angle, an
aspect ratio, and z clip planes.
Params: m – the float array that holds the perspective matrix
offset – the offset into float array m where the perspective
       matrix data is written
fovy – field of view in y direction, in degrees
aspect – width to height aspect ratio of the viewport
zNear – 
zFar – /**
     * Defines a projection matrix in terms of a field of view angle, an
     * aspect ratio, and z clip planes.
     *
     * @param m the float array that holds the perspective matrix
     * @param offset the offset into float array m where the perspective
     *        matrix data is written
     * @param fovy field of view in y direction, in degrees
     * @param aspect width to height aspect ratio of the viewport
     * @param zNear
     * @param zFar
     */
    public static void perspectiveM(float[] m, int offset,
          float fovy, float aspect, float zNear, float zFar) {
        float f = 1.0f / (float) Math.tan(fovy * (Math.PI / 360.0));
        float rangeReciprocal = 1.0f / (zNear - zFar);

        m[offset + 0] = f / aspect;
        m[offset + 1] = 0.0f;
        m[offset + 2] = 0.0f;
        m[offset + 3] = 0.0f;

        m[offset + 4] = 0.0f;
        m[offset + 5] = f;
        m[offset + 6] = 0.0f;
        m[offset + 7] = 0.0f;

        m[offset + 8] = 0.0f;
        m[offset + 9] = 0.0f;
        m[offset + 10] = (zFar + zNear) * rangeReciprocal;
        m[offset + 11] = -1.0f;

        m[offset + 12] = 0.0f;
        m[offset + 13] = 0.0f;
        m[offset + 14] = 2.0f * zFar * zNear * rangeReciprocal;
        m[offset + 15] = 0.0f;
    }

    Computes the length of a vector.
Params: x – x coordinate of a vector
y – y coordinate of a vector
z – z coordinate of a vector
Returns: the length of a vector/**
     * Computes the length of a vector.
     *
     * @param x x coordinate of a vector
     * @param y y coordinate of a vector
     * @param z z coordinate of a vector
     * @return the length of a vector
     */
    public static float length(float x, float y, float z) {
        return (float) Math.sqrt(x * x + y * y + z * z);
    }

    Sets matrix m to the identity matrix.
Params: sm – returns the result
smOffset – index into sm where the result matrix starts/**
     * Sets matrix m to the identity matrix.
     *
     * @param sm returns the result
     * @param smOffset index into sm where the result matrix starts
     */
    public static void setIdentityM(float[] sm, int smOffset) {
        for (int i=0 ; i<16 ; i++) {
            sm[smOffset + i] = 0;
        }
        for(int i = 0; i < 16; i += 5) {
            sm[smOffset + i] = 1.0f;
        }
    }

    Scales matrix m by x, y, and z, putting the result in sm.

m and sm must not overlap.
Params: sm – returns the result
smOffset – index into sm where the result matrix starts
m – source matrix
mOffset – index into m where the source matrix starts
x – scale factor x
y – scale factor y
z – scale factor z/**
     * Scales matrix m by x, y, and z, putting the result in sm.
     * <p>
     * m and sm must not overlap.
     *
     * @param sm returns the result
     * @param smOffset index into sm where the result matrix starts
     * @param m source matrix
     * @param mOffset index into m where the source matrix starts
     * @param x scale factor x
     * @param y scale factor y
     * @param z scale factor z
     */
    public static void scaleM(float[] sm, int smOffset,
            float[] m, int mOffset,
            float x, float y, float z) {
        for (int i=0 ; i<4 ; i++) {
            int smi = smOffset + i;
            int mi = mOffset + i;
            sm[     smi] = m[     mi] * x;
            sm[ 4 + smi] = m[ 4 + mi] * y;
            sm[ 8 + smi] = m[ 8 + mi] * z;
            sm[12 + smi] = m[12 + mi];
        }
    }

    Scales matrix m in place by sx, sy, and sz.
Params: m – matrix to scale
mOffset – index into m where the matrix starts
x – scale factor x
y – scale factor y
z – scale factor z/**
     * Scales matrix m in place by sx, sy, and sz.
     *
     * @param m matrix to scale
     * @param mOffset index into m where the matrix starts
     * @param x scale factor x
     * @param y scale factor y
     * @param z scale factor z
     */
    public static void scaleM(float[] m, int mOffset,
            float x, float y, float z) {
        for (int i=0 ; i<4 ; i++) {
            int mi = mOffset + i;
            m[     mi] *= x;
            m[ 4 + mi] *= y;
            m[ 8 + mi] *= z;
        }
    }

    Translates matrix m by x, y, and z, putting the result in tm.

m and tm must not overlap.
Params: tm – returns the result
tmOffset – index into sm where the result matrix starts
m – source matrix
mOffset – index into m where the source matrix starts
x – translation factor x
y – translation factor y
z – translation factor z/**
     * Translates matrix m by x, y, and z, putting the result in tm.
     * <p>
     * m and tm must not overlap.
     *
     * @param tm returns the result
     * @param tmOffset index into sm where the result matrix starts
     * @param m source matrix
     * @param mOffset index into m where the source matrix starts
     * @param x translation factor x
     * @param y translation factor y
     * @param z translation factor z
     */
    public static void translateM(float[] tm, int tmOffset,
            float[] m, int mOffset,
            float x, float y, float z) {
        for (int i=0 ; i<12 ; i++) {
            tm[tmOffset + i] = m[mOffset + i];
        }
        for (int i=0 ; i<4 ; i++) {
            int tmi = tmOffset + i;
            int mi = mOffset + i;
            tm[12 + tmi] = m[mi] * x + m[4 + mi] * y + m[8 + mi] * z +
                m[12 + mi];
        }
    }

    Translates matrix m by x, y, and z in place.
Params: m – matrix
mOffset – index into m where the matrix starts
x – translation factor x
y – translation factor y
z – translation factor z/**
     * Translates matrix m by x, y, and z in place.
     *
     * @param m matrix
     * @param mOffset index into m where the matrix starts
     * @param x translation factor x
     * @param y translation factor y
     * @param z translation factor z
     */
    public static void translateM(
            float[] m, int mOffset,
            float x, float y, float z) {
        for (int i=0 ; i<4 ; i++) {
            int mi = mOffset + i;
            m[12 + mi] += m[mi] * x + m[4 + mi] * y + m[8 + mi] * z;
        }
    }

    Rotates matrix m by angle a (in degrees) around the axis (x, y, z).

m and rm must not overlap.
Params: rm – returns the result
rmOffset – index into rm where the result matrix starts
m – source matrix
mOffset – index into m where the source matrix starts
a – angle to rotate in degrees
x – X axis component
y – Y axis component
z – Z axis component/**
     * Rotates matrix m by angle a (in degrees) around the axis (x, y, z).
     * <p>
     * m and rm must not overlap.
     *
     * @param rm returns the result
     * @param rmOffset index into rm where the result matrix starts
     * @param m source matrix
     * @param mOffset index into m where the source matrix starts
     * @param a angle to rotate in degrees
     * @param x X axis component
     * @param y Y axis component
     * @param z Z axis component
     */
    public static void rotateM(float[] rm, int rmOffset,
            float[] m, int mOffset,
            float a, float x, float y, float z) {
        synchronized(sTemp) {
            setRotateM(sTemp, 0, a, x, y, z);
            multiplyMM(rm, rmOffset, m, mOffset, sTemp, 0);
        }
    }

    Rotates matrix m in place by angle a (in degrees)
around the axis (x, y, z).
Params: m – source matrix
mOffset – index into m where the matrix starts
a – angle to rotate in degrees
x – X axis component
y – Y axis component
z – Z axis component/**
     * Rotates matrix m in place by angle a (in degrees)
     * around the axis (x, y, z).
     *
     * @param m source matrix
     * @param mOffset index into m where the matrix starts
     * @param a angle to rotate in degrees
     * @param x X axis component
     * @param y Y axis component
     * @param z Z axis component
     */
    public static void rotateM(float[] m, int mOffset,
            float a, float x, float y, float z) {
        synchronized(sTemp) {
            setRotateM(sTemp, 0, a, x, y, z);
            multiplyMM(sTemp, 16, m, mOffset, sTemp, 0);
            System.arraycopy(sTemp, 16, m, mOffset, 16);
        }
    }

    Creates a matrix for rotation by angle a (in degrees)
around the axis (x, y, z).

An optimized path will be used for rotation about a major axis
(e.g. x=1.0f y=0.0f z=0.0f).
Params: rm – returns the result
rmOffset – index into rm where the result matrix starts
a – angle to rotate in degrees
x – X axis component
y – Y axis component
z – Z axis component/**
     * Creates a matrix for rotation by angle a (in degrees)
     * around the axis (x, y, z).
     * <p>
     * An optimized path will be used for rotation about a major axis
     * (e.g. x=1.0f y=0.0f z=0.0f).
     *
     * @param rm returns the result
     * @param rmOffset index into rm where the result matrix starts
     * @param a angle to rotate in degrees
     * @param x X axis component
     * @param y Y axis component
     * @param z Z axis component
     */
    public static void setRotateM(float[] rm, int rmOffset,
            float a, float x, float y, float z) {
        rm[rmOffset + 3] = 0;
        rm[rmOffset + 7] = 0;
        rm[rmOffset + 11]= 0;
        rm[rmOffset + 12]= 0;
        rm[rmOffset + 13]= 0;
        rm[rmOffset + 14]= 0;
        rm[rmOffset + 15]= 1;
        a *= (float) (Math.PI / 180.0f);
        float s = (float) Math.sin(a);
        float c = (float) Math.cos(a);
        if (1.0f == x && 0.0f == y && 0.0f == z) {
            rm[rmOffset + 5] = c;   rm[rmOffset + 10]= c;
            rm[rmOffset + 6] = s;   rm[rmOffset + 9] = -s;
            rm[rmOffset + 1] = 0;   rm[rmOffset + 2] = 0;
            rm[rmOffset + 4] = 0;   rm[rmOffset + 8] = 0;
            rm[rmOffset + 0] = 1;
        } else if (0.0f == x && 1.0f == y && 0.0f == z) {
            rm[rmOffset + 0] = c;   rm[rmOffset + 10]= c;
            rm[rmOffset + 8] = s;   rm[rmOffset + 2] = -s;
            rm[rmOffset + 1] = 0;   rm[rmOffset + 4] = 0;
            rm[rmOffset + 6] = 0;   rm[rmOffset + 9] = 0;
            rm[rmOffset + 5] = 1;
        } else if (0.0f == x && 0.0f == y && 1.0f == z) {
            rm[rmOffset + 0] = c;   rm[rmOffset + 5] = c;
            rm[rmOffset + 1] = s;   rm[rmOffset + 4] = -s;
            rm[rmOffset + 2] = 0;   rm[rmOffset + 6] = 0;
            rm[rmOffset + 8] = 0;   rm[rmOffset + 9] = 0;
            rm[rmOffset + 10]= 1;
        } else {
            float len = length(x, y, z);
            if (1.0f != len) {
                float recipLen = 1.0f / len;
                x *= recipLen;
                y *= recipLen;
                z *= recipLen;
            }
            float nc = 1.0f - c;
            float xy = x * y;
            float yz = y * z;
            float zx = z * x;
            float xs = x * s;
            float ys = y * s;
            float zs = z * s;
            rm[rmOffset +  0] = x*x*nc +  c;
            rm[rmOffset +  4] =  xy*nc - zs;
            rm[rmOffset +  8] =  zx*nc + ys;
            rm[rmOffset +  1] =  xy*nc + zs;
            rm[rmOffset +  5] = y*y*nc +  c;
            rm[rmOffset +  9] =  yz*nc - xs;
            rm[rmOffset +  2] =  zx*nc - ys;
            rm[rmOffset +  6] =  yz*nc + xs;
            rm[rmOffset + 10] = z*z*nc +  c;
        }
    }

    Converts Euler angles to a rotation matrix.
Params: rm – returns the result
rmOffset – index into rm where the result matrix starts
x – angle of rotation, in degrees
y – angle of rotation, in degrees
z – angle of rotation, in degrees/**
     * Converts Euler angles to a rotation matrix.
     *
     * @param rm returns the result
     * @param rmOffset index into rm where the result matrix starts
     * @param x angle of rotation, in degrees
     * @param y angle of rotation, in degrees
     * @param z angle of rotation, in degrees
     */
    public static void setRotateEulerM(float[] rm, int rmOffset,
            float x, float y, float z) {
        x *= (float) (Math.PI / 180.0f);
        y *= (float) (Math.PI / 180.0f);
        z *= (float) (Math.PI / 180.0f);
        float cx = (float) Math.cos(x);
        float sx = (float) Math.sin(x);
        float cy = (float) Math.cos(y);
        float sy = (float) Math.sin(y);
        float cz = (float) Math.cos(z);
        float sz = (float) Math.sin(z);
        float cxsy = cx * sy;
        float sxsy = sx * sy;

        rm[rmOffset + 0]  =   cy * cz;
        rm[rmOffset + 1]  =  -cy * sz;
        rm[rmOffset + 2]  =   sy;
        rm[rmOffset + 3]  =  0.0f;

        rm[rmOffset + 4]  =  cxsy * cz + cx * sz;
        rm[rmOffset + 5]  = -cxsy * sz + cx * cz;
        rm[rmOffset + 6]  =  -sx * cy;
        rm[rmOffset + 7]  =  0.0f;

        rm[rmOffset + 8]  = -sxsy * cz + sx * sz;
        rm[rmOffset + 9]  =  sxsy * sz + sx * cz;
        rm[rmOffset + 10] =  cx * cy;
        rm[rmOffset + 11] =  0.0f;

        rm[rmOffset + 12] =  0.0f;
        rm[rmOffset + 13] =  0.0f;
        rm[rmOffset + 14] =  0.0f;
        rm[rmOffset + 15] =  1.0f;
    }

    Defines a viewing transformation in terms of an eye point, a center of
view, and an up vector.
Params: rm – returns the result
rmOffset – index into rm where the result matrix starts
eyeX – eye point X
eyeY – eye point Y
eyeZ – eye point Z
centerX – center of view X
centerY – center of view Y
centerZ – center of view Z
upX – up vector X
upY – up vector Y
upZ – up vector Z/**
     * Defines a viewing transformation in terms of an eye point, a center of
     * view, and an up vector.
     *
     * @param rm returns the result
     * @param rmOffset index into rm where the result matrix starts
     * @param eyeX eye point X
     * @param eyeY eye point Y
     * @param eyeZ eye point Z
     * @param centerX center of view X
     * @param centerY center of view Y
     * @param centerZ center of view Z
     * @param upX up vector X
     * @param upY up vector Y
     * @param upZ up vector Z
     */
    public static void setLookAtM(float[] rm, int rmOffset,
            float eyeX, float eyeY, float eyeZ,
            float centerX, float centerY, float centerZ, float upX, float upY,
            float upZ) {

        // See the OpenGL GLUT documentation for gluLookAt for a description
        // of the algorithm. We implement it in a straightforward way:

        float fx = centerX - eyeX;
        float fy = centerY - eyeY;
        float fz = centerZ - eyeZ;

        // Normalize f
        float rlf = 1.0f / Matrix.length(fx, fy, fz);
        fx *= rlf;
        fy *= rlf;
        fz *= rlf;

        // compute s = f x up (x means "cross product")
        float sx = fy * upZ - fz * upY;
        float sy = fz * upX - fx * upZ;
        float sz = fx * upY - fy * upX;

        // and normalize s
        float rls = 1.0f / Matrix.length(sx, sy, sz);
        sx *= rls;
        sy *= rls;
        sz *= rls;

        // compute u = s x f
        float ux = sy * fz - sz * fy;
        float uy = sz * fx - sx * fz;
        float uz = sx * fy - sy * fx;

        rm[rmOffset + 0] = sx;
        rm[rmOffset + 1] = ux;
        rm[rmOffset + 2] = -fx;
        rm[rmOffset + 3] = 0.0f;

        rm[rmOffset + 4] = sy;
        rm[rmOffset + 5] = uy;
        rm[rmOffset + 6] = -fy;
        rm[rmOffset + 7] = 0.0f;

        rm[rmOffset + 8] = sz;
        rm[rmOffset + 9] = uz;
        rm[rmOffset + 10] = -fz;
        rm[rmOffset + 11] = 0.0f;

        rm[rmOffset + 12] = 0.0f;
        rm[rmOffset + 13] = 0.0f;
        rm[rmOffset + 14] = 0.0f;
        rm[rmOffset + 15] = 1.0f;

        translateM(rm, rmOffset, -eyeX, -eyeY, -eyeZ);
    }
}
Params:	result – The float array that holds the result. resultOffset – The offset into the result array where the result is stored. lhs – The float array that holds the left-hand-side matrix. lhsOffset – The offset into the lhs array where the lhs is stored rhs – The float array that holds the right-hand-side matrix. rhsOffset – The offset into the rhs array where the rhs is stored.
Throws:	IllegalArgumentException – if result, lhs, or rhs are null, or if resultOffset + 16 > result.length or lhsOffset + 16 > lhs.length or rhsOffset + 16 > rhs.length.
Params:	mInv – the array that holds the output inverted matrix mInvOffset – an offset into mInv where the inverted matrix is stored. m – the input array mOffset – an offset into m where the input matrix is stored.
Returns:	true if the matrix could be inverted, false if it could not.
Params:	x – x coordinate of a vector y – y coordinate of a vector z – z coordinate of a vector
Returns:	the length of a vector
/

android/ android-9.0.0_r35/ android/opengl/Matrix.java
