Android example source code file (Matrix.java)
The Matrix.java Android example source code/*
* 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;
import javax.microedition.khronos.opengles.GL10;
/**
* 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:
* <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 row x 1 column column-vectors stored in order:
* <pre>
* v[offset + 0]
* v[offset + 1]
* v[offset + 2]
* v[offset + 3]
* </pre>
*
*/
public class Matrix {
/**
* 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.
*
* @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);
/**
* 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.
*
* @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.
*
* @param mTrans the array that holds the output inverted matrix
* @param mTransOffset an offset into mInv where the inverted matrix is
* stored.
* @param m the input array
* @param mOffset an offset into m where the 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.
*
* @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 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
// 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;
}
/**
* 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;
}
/**
* Define a projection matrix in terms of six 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 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 = 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;
}
/**
* 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.
* @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
* @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
* @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
* @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.
* @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)
* @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 scale factor x
* @param y scale factor y
* @param z scale factor z
*/
public static void rotateM(float[] rm, int rmOffset,
float[] m, int mOffset,
float a, float x, float y, float z) {
float[] r = new float[16];
setRotateM(r, 0, a, x, y, z);
multiplyMM(rm, rmOffset, m, mOffset, r, 0);
}
/**
* 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 scale factor x
* @param y scale factor y
* @param z scale factor z
*/
public static void rotateM(float[] m, int mOffset,
float a, float x, float y, float 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);
}
/**
* Rotates matrix m by angle a (in degrees) around the axis (x, y, z)
* @param rm returns the result
* @param rmOffset index into rm where the result matrix starts
* @param a angle to rotate in degrees
* @param x scale factor x
* @param y scale factor y
* @param z scale factor z
*/
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
* @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;
}
/**
* Define 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);
}
}
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