src.android.opengl.Matrix Maven / Gradle / Ivy
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/*
* 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]
*/
public class Matrix {
/** 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
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.
*
* @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.
*
* @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.
*
* @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.
*
* @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.
*
* @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.
*
* @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.
*
* @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.
*
* @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.
*
* 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.
*
* @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.
*
* @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).
*
* 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).
*
* @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).
*
* @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.
*
* @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.
*
* @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);
}
}