Matrixpublic class Matrix extends Object | 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] |
| Fields Summary |
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| private static final float[] | sTempTemporary memory for operations that need temporary matrix data. |
| Constructors Summary |
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public Matrix()
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| Methods Summary |
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| public static void | frustumM(float[] m, int offset, float left, float right, float bottom, float top, float near, float far)Defines a projection matrix in terms of six clip planes.
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;
| | public static boolean | invertM(float[] mInv, int mInvOffset, float[] m, int mOffset)Inverts a 4 x 4 matrix.
mInv and m must not overlap.
// 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;
| | public static float | length(float x, float y, float z)Computes the length of a vector.
return (float) Math.sqrt(x * x + y * y + z * z);
| | public static native void | multiplyMM(float[] result, int resultOffset, float[] lhs, int lhsOffset, float[] rhs, int rhsOffset)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.
| | public static native void | multiplyMV(float[] resultVec, int resultVecOffset, float[] lhsMat, int lhsMatOffset, float[] rhsVec, int rhsVecOffset)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.
| | public static void | orthoM(float[] m, int mOffset, float left, float right, float bottom, float top, float near, float far)Computes an orthographic projection matrix.
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;
| | public static void | perspectiveM(float[] m, int offset, float fovy, float aspect, float zNear, float zFar)Defines a projection matrix in terms of a field of view angle, an
aspect ratio, and z clip planes.
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;
| | public static void | rotateM(float[] rm, int rmOffset, float[] m, int mOffset, float a, float x, float y, float z)Rotates matrix m by angle a (in degrees) around the axis (x, y, z).
m and rm must not overlap.
synchronized(sTemp) {
setRotateM(sTemp, 0, a, x, y, z);
multiplyMM(rm, rmOffset, m, mOffset, sTemp, 0);
}
| | public static void | rotateM(float[] m, int mOffset, float a, float x, float y, float z)Rotates matrix m in place by angle a (in degrees)
around the axis (x, y, z).
synchronized(sTemp) {
setRotateM(sTemp, 0, a, x, y, z);
multiplyMM(sTemp, 16, m, mOffset, sTemp, 0);
System.arraycopy(sTemp, 16, m, mOffset, 16);
}
| | public static void | scaleM(float[] sm, int smOffset, float[] m, int mOffset, float x, float y, float z)Scales matrix m by x, y, and z, putting the result in sm.
m and sm must not overlap.
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];
}
| | public static void | scaleM(float[] m, int mOffset, float x, float y, float z)Scales matrix m in place by sx, sy, and sz.
for (int i=0 ; i<4 ; i++) {
int mi = mOffset + i;
m[ mi] *= x;
m[ 4 + mi] *= y;
m[ 8 + mi] *= z;
}
| | public static void | setIdentityM(float[] sm, int smOffset)Sets matrix m to the identity matrix.
for (int i=0 ; i<16 ; i++) {
sm[smOffset + i] = 0;
}
for(int i = 0; i < 16; i += 5) {
sm[smOffset + i] = 1.0f;
}
| | 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)Defines a viewing transformation in terms of an eye point, a center of
view, and an up vector.
// 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);
| | public static void | setRotateEulerM(float[] rm, int rmOffset, float x, float y, float z)Converts Euler angles to a rotation matrix.
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;
| | public static void | setRotateM(float[] rm, int rmOffset, float a, float x, float y, float z)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).
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;
}
| | public static void | translateM(float[] tm, int tmOffset, float[] m, int mOffset, float x, float y, float z)Translates matrix m by x, y, and z, putting the result in tm.
m and tm must not overlap.
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];
}
| | public static void | translateM(float[] m, int mOffset, float x, float y, float z)Translates matrix m by x, y, and z in place.
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;
}
| | public static void | transposeM(float[] mTrans, int mTransOffset, float[] m, int mOffset)Transposes a 4 x 4 matrix.
mTrans and m must not overlap.
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];
}
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