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 row x 1 column column-vectors stored in order:
v[offset + 0]
v[offset + 1]
v[offset + 2]
v[offset + 3]
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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)Define 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 = 2.0f * ((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.
// Invert a 4 x 4 matrix using Cramer's Rule
// array of transpose source matrix
float[] src = new float[16];
// transpose matrix
transposeM(src, 0, m, mOffset);
// temp array for pairs
float[] tmp = new float[12];
// calculate pairs for first 8 elements (cofactors)
tmp[0] = src[10] * src[15];
tmp[1] = src[11] * src[14];
tmp[2] = src[9] * src[15];
tmp[3] = src[11] * src[13];
tmp[4] = src[9] * src[14];
tmp[5] = src[10] * src[13];
tmp[6] = src[8] * src[15];
tmp[7] = src[11] * src[12];
tmp[8] = src[8] * src[14];
tmp[9] = src[10] * src[12];
tmp[10] = src[8] * src[13];
tmp[11] = src[9] * src[12];
// Holds the destination matrix while we're building it up.
float[] dst = new float[16];
// calculate first 8 elements (cofactors)
dst[0] = tmp[0] * src[5] + tmp[3] * src[6] + tmp[4] * src[7];
dst[0] -= tmp[1] * src[5] + tmp[2] * src[6] + tmp[5] * src[7];
dst[1] = tmp[1] * src[4] + tmp[6] * src[6] + tmp[9] * src[7];
dst[1] -= tmp[0] * src[4] + tmp[7] * src[6] + tmp[8] * src[7];
dst[2] = tmp[2] * src[4] + tmp[7] * src[5] + tmp[10] * src[7];
dst[2] -= tmp[3] * src[4] + tmp[6] * src[5] + tmp[11] * src[7];
dst[3] = tmp[5] * src[4] + tmp[8] * src[5] + tmp[11] * src[6];
dst[3] -= tmp[4] * src[4] + tmp[9] * src[5] + tmp[10] * src[6];
dst[4] = tmp[1] * src[1] + tmp[2] * src[2] + tmp[5] * src[3];
dst[4] -= tmp[0] * src[1] + tmp[3] * src[2] + tmp[4] * src[3];
dst[5] = tmp[0] * src[0] + tmp[7] * src[2] + tmp[8] * src[3];
dst[5] -= tmp[1] * src[0] + tmp[6] * src[2] + tmp[9] * src[3];
dst[6] = tmp[3] * src[0] + tmp[6] * src[1] + tmp[11] * src[3];
dst[6] -= tmp[2] * src[0] + tmp[7] * src[1] + tmp[10] * src[3];
dst[7] = tmp[4] * src[0] + tmp[9] * src[1] + tmp[10] * src[2];
dst[7] -= tmp[5] * src[0] + tmp[8] * src[1] + tmp[11] * src[2];
// calculate pairs for second 8 elements (cofactors)
tmp[0] = src[2] * src[7];
tmp[1] = src[3] * src[6];
tmp[2] = src[1] * src[7];
tmp[3] = src[3] * src[5];
tmp[4] = src[1] * src[6];
tmp[5] = src[2] * src[5];
tmp[6] = src[0] * src[7];
tmp[7] = src[3] * src[4];
tmp[8] = src[0] * src[6];
tmp[9] = src[2] * src[4];
tmp[10] = src[0] * src[5];
tmp[11] = src[1] * src[4];
// calculate second 8 elements (cofactors)
dst[8] = tmp[0] * src[13] + tmp[3] * src[14] + tmp[4] * src[15];
dst[8] -= tmp[1] * src[13] + tmp[2] * src[14] + tmp[5] * src[15];
dst[9] = tmp[1] * src[12] + tmp[6] * src[14] + tmp[9] * src[15];
dst[9] -= tmp[0] * src[12] + tmp[7] * src[14] + tmp[8] * src[15];
dst[10] = tmp[2] * src[12] + tmp[7] * src[13] + tmp[10] * src[15];
dst[10] -= tmp[3] * src[12] + tmp[6] * src[13] + tmp[11] * src[15];
dst[11] = tmp[5] * src[12] + tmp[8] * src[13] + tmp[11] * src[14];
dst[11] -= tmp[4] * src[12] + tmp[9] * src[13] + tmp[10] * src[14];
dst[12] = tmp[2] * src[10] + tmp[5] * src[11] + tmp[1] * src[9];
dst[12] -= tmp[4] * src[11] + tmp[0] * src[9] + tmp[3] * src[10];
dst[13] = tmp[8] * src[11] + tmp[0] * src[8] + tmp[7] * src[10];
dst[13] -= tmp[6] * src[10] + tmp[9] * src[11] + tmp[1] * src[8];
dst[14] = tmp[6] * src[9] + tmp[11] * src[11] + tmp[3] * src[8];
dst[14] -= tmp[10] * src[11] + tmp[2] * src[8] + tmp[7] * src[9];
dst[15] = tmp[10] * src[10] + tmp[4] * src[8] + tmp[9] * src[9];
dst[15] -= tmp[8] * src[9] + tmp[11] * src[10] + tmp[5] * src[8];
// calculate determinant
float det =
src[0] * dst[0] + src[1] * dst[1] + src[2] * dst[2] + src[3]
* dst[3];
if (det == 0.0f) {
}
// calculate matrix inverse
det = 1 / det;
for (int j = 0; j < 16; j++)
mInv[j + mInvOffset] = dst[j] * det;
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)Multiply two 4x4 matrices together and store 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)Multiply a 4 element vector by a 4x4 matrix and store 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 | 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)
float[] r = new float[16];
setRotateM(r, 0, a, x, y, z);
multiplyMM(rm, rmOffset, m, mOffset, r, 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)
float[] temp = new float[32];
setRotateM(temp, 0, a, x, y, z);
multiplyMM(temp, 16, m, mOffset, temp, 0);
System.arraycopy(temp, 16, m, mOffset, 16);
| | 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 | 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
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 | 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 | 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)Rotates matrix m by angle a (in degrees) around the axis (x, y, 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;
}
| | 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
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.
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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