* Implementation covers {@link FloatUtil} matrix functionality, exposed in an object oriented manner. *
** Unlike {@link com.jogamp.opengl.util.PMVMatrix PMVMatrix}, this class only represents one single matrix * without a complete {@link com.jogamp.opengl.fixedfunc.GLMatrixFunc GLMatrixFunc} implementation. *
** For array operations the layout is expected in column-major order * matching OpenGL's implementation, illustration: *
Row-Major Column-Major (OpenGL):
| 0 1 2 tx |
| |
| 4 5 6 ty |
M = | |
| 8 9 10 tz |
| |
| 12 13 14 15 |
R C R C
m[0*4+3] = tx; m[0+4*3] = tx;
m[1*4+3] = ty; m[1+4*3] = ty;
m[2*4+3] = tz; m[2+4*3] = tz;
RC (std subscript order) RC (std subscript order)
m03 = tx; m03 = tx;
m13 = ty; m13 = ty;
m23 = tz; m23 = tz;
*
*
* *
* ** Implementation utilizes unrolling of small vertices and matrices wherever possible * while trying to access memory in a linear fashion for performance reasons, see: *
* * @see com.jogamp.opengl.util.PMVMatrix * @see FloatUtil */ public class Matrix4f { /** * Creates a new identity matrix. */ public Matrix4f() { m00 = m11 = m22 = m33 = 1.0f; // remaining fields have default init to zero } /** * Creates a new matrix copying the values of the given {@code src} matrix. */ public Matrix4f(final Matrix4f src) { load(src); } /** * Creates a new matrix based on given float[4*4] column major order. * @param m 4x4 matrix in column-major order */ public Matrix4f(final float[] m) { load(m); } /** * Creates a new matrix based on given float[4*4] column major order. * @param m 4x4 matrix in column-major order * @param m_off offset for matrix {@code m} */ public Matrix4f(final float[] m, final int m_off) { load(m, m_off); } // // Write to Matrix via load(..) // /** * Set this matrix to identity. *
Translation matrix (Column Order):
1 0 0 0
0 1 0 0
0 0 1 0
0 0 0 1
*
* @return this matrix for chaining
*/
public final Matrix4f loadIdentity() {
m00 = m11 = m22 = m33 = 1.0f;
m01 = m02 = m03 =
m10 = m12 = m13 =
m20 = m21 = m23 =
m30 = m31 = m32 = 0.0f;
return this;
}
/**
* Load the values of the given matrix {@code b} to this matrix.
* @param src the source values
* @return this matrix for chaining
*/
public Matrix4f load(final Matrix4f src) {
m00 = src.m00; m10 = src.m10; m20 = src.m20; m30 = src.m30;
m01 = src.m01; m11 = src.m11; m21 = src.m21; m31 = src.m31;
m02 = src.m02; m12 = src.m12; m22 = src.m22; m32 = src.m32;
m03 = src.m03; m13 = src.m13; m23 = src.m23; m33 = src.m33;
return this;
}
/**
* Load the values of the given matrix {@code src} to this matrix.
* @param src 4x4 matrix float[16] in column-major order
* @return this matrix for chaining
*/
public Matrix4f load(final float[] src) {
m00 = src[0+0*4]; // column 0
m10 = src[1+0*4];
m20 = src[2+0*4];
m30 = src[3+0*4];
m01 = src[0+1*4]; // column 1
m11 = src[1+1*4];
m21 = src[2+1*4];
m31 = src[3+1*4];
m02 = src[0+2*4]; // column 2
m12 = src[1+2*4];
m22 = src[2+2*4];
m32 = src[3+2*4];
m03 = src[0+3*4]; // column 3
m13 = src[1+3*4];
m23 = src[2+3*4];
m33 = src[3+3*4];
return this;
}
/**
* Load the values of the given matrix {@code src} to this matrix.
* @param src 4x4 matrix float[16] in column-major order
* @param src_off offset for matrix {@code src}
* @return this matrix for chaining
*/
public Matrix4f load(final float[] src, final int src_off) {
m00 = src[src_off+0+0*4];
m10 = src[src_off+1+0*4];
m20 = src[src_off+2+0*4];
m30 = src[src_off+3+0*4];
m01 = src[src_off+0+1*4];
m11 = src[src_off+1+1*4];
m21 = src[src_off+2+1*4];
m31 = src[src_off+3+1*4];
m02 = src[src_off+0+2*4];
m12 = src[src_off+1+2*4];
m22 = src[src_off+2+2*4];
m32 = src[src_off+3+2*4];
m03 = src[src_off+0+3*4];
m13 = src[src_off+1+3*4];
m23 = src[src_off+2+3*4];
m33 = src[src_off+3+3*4];
return this;
}
/**
* Load the values of the given matrix {@code src} to this matrix.
* * Implementation uses relative {@link FloatBuffer#get()}, * hence caller may want to issue {@link FloatBuffer#reset()} thereafter. *
* @param src 4x4 matrix {@link FloatBuffer} in column-major order * @return this matrix for chaining */ public Matrix4f load(final FloatBuffer src) { m00 = src.get(); m10 = src.get(); m20 = src.get(); m30 = src.get(); m01 = src.get(); m11 = src.get(); m21 = src.get(); m31 = src.get(); m02 = src.get(); m12 = src.get(); m22 = src.get(); m32 = src.get(); m03 = src.get(); m13 = src.get(); m23 = src.get(); m33 = src.get(); return this; } // // Read out Matrix via get(..) // /** Gets the ith component, 0 <= i < 16 */ public float get(final int i) { switch (i) { case 0+4*0: return m00; case 1+4*0: return m10; case 2+4*0: return m20; case 3+4*0: return m30; case 0+4*1: return m01; case 1+4*1: return m11; case 2+4*1: return m21; case 3+4*1: return m31; case 0+4*2: return m02; case 1+4*2: return m12; case 2+4*2: return m22; case 3+4*2: return m32; case 0+4*3: return m03; case 1+4*3: return m13; case 2+4*3: return m23; case 3+4*3: return m33; default: throw new IndexOutOfBoundsException(); } } /** * Get the named column of the given column-major matrix to v_out. * @param column named column to copy * @param v_out the column-vector storage * @return given result vector v_out for chaining */ public Vec4f getColumn(final int column, final Vec4f v_out) { v_out.set( get(0+column*4), get(1+column*4), get(2+column*4), get(3+column*4) ); return v_out; } /** * Get the named column of the given column-major matrix to v_out. * @param column named column to copy * @param v_out the column-vector storage * @return given result vector v_out for chaining */ public Vec3f getColumn(final int column, final Vec3f v_out) { v_out.set( get(0+column*4), get(1+column*4), get(2+column*4) ); return v_out; } /** * Get the named row of the given column-major matrix to v_out. * @param row named row to copy * @param v_out the row-vector storage * @return given result vector v_out for chaining */ public Vec4f getRow(final int row, final Vec4f v_out) { v_out.set( get(row+0*4), get(row+1*4), get(row+2*4), get(row+3*4) ); return v_out; } /** * Get the named row of the given column-major matrix to v_out. * @param row named row to copy * @param v_out the row-vector storage * @return given result vector v_out for chaining */ public Vec3f getRow(final int row, final Vec3f v_out) { v_out.set( get(row+0*4), get(row+1*4), get(row+2*4) ); return v_out; } /** * Get this matrix into the given float[16] array at {@code dst_off} in column major order. * * @param dst float[16] array storage in column major order * @param dst_off offset */ public void get(final float[] dst, final int dst_off) { dst[dst_off+0+0*4] = m00; dst[dst_off+1+0*4] = m10; dst[dst_off+2+0*4] = m20; dst[dst_off+3+0*4] = m30; dst[dst_off+0+1*4] = m01; dst[dst_off+1+1*4] = m11; dst[dst_off+2+1*4] = m21; dst[dst_off+3+1*4] = m31; dst[dst_off+0+2*4] = m02; dst[dst_off+1+2*4] = m12; dst[dst_off+2+2*4] = m22; dst[dst_off+3+2*4] = m32; dst[dst_off+0+3*4] = m03; dst[dst_off+1+3*4] = m13; dst[dst_off+2+3*4] = m23; dst[dst_off+3+3*4] = m33; } /** * Get this matrix into the given float[16] array in column major order. * * @param dst float[16] array storage in column major order */ public void get(final float[] dst) { dst[0+0*4] = m00; dst[1+0*4] = m10; dst[2+0*4] = m20; dst[3+0*4] = m30; dst[0+1*4] = m01; dst[1+1*4] = m11; dst[2+1*4] = m21; dst[3+1*4] = m31; dst[0+2*4] = m02; dst[1+2*4] = m12; dst[2+2*4] = m22; dst[3+2*4] = m32; dst[0+3*4] = m03; dst[1+3*4] = m13; dst[2+3*4] = m23; dst[3+3*4] = m33; } /** * Get this matrix into the given {@link FloatBuffer} in column major order. ** Implementation uses relative {@link FloatBuffer#put(float)}, * hence caller may want to issue {@link FloatBuffer#reset()} thereafter. *
* * @param dst {@link FloatBuffer} array storage in column major order */ public void get(final FloatBuffer dst) { dst.put( m00 ); dst.put( m10 ); dst.put( m20 ); dst.put( m30 ); dst.put( m01 ); dst.put( m11 ); dst.put( m21 ); dst.put( m31 ); dst.put( m02 ); dst.put( m12 ); dst.put( m22 ); dst.put( m32 ); dst.put( m03 ); dst.put( m13 ); dst.put( m23 ); dst.put( m33 ); } // // Basic matrix operations // /** * Returns the determinant of this matrix * @return the matrix determinant */ public float determinant() { float ret = 0; ret += m00 * ( + m11*(m22*m33 - m23*m32) - m12*(m21*m33 - m23*m31) + m13*(m21*m32 - m22*m31)); ret -= m01 * ( + m10*(m22*m33 - m23*m32) - m12*(m20*m33 - m23*m30) + m13*(m20*m32 - m22*m30)); ret += m02 * ( + m10*(m21*m33 - m23*m31) - m11*(m20*m33 - m23*m30) + m13*(m20*m31 - m21*m30)); ret -= m03 * ( + m10*(m21*m32 - m22*m31) - m11*(m20*m32 - m22*m30) + m12*(m20*m31 - m21*m30)); return ret; } /** * Transpose this matrix. * * @return this matrix for chaining */ public final Matrix4f transpose() { float tmp; tmp = m10; m10 = m01; m01 = tmp; tmp = m20; m20 = m02; m02 = tmp; tmp = m30; m30 = m03; m03 = tmp; tmp = m21; m21 = m12; m12 = tmp; tmp = m31; m31 = m13; m13 = tmp; tmp = m32; m32 = m23; m23 = tmp; return this; } /** * Transpose the given {@code src} matrix into this matrix. * * @param src source 4x4 matrix * @return this matrix (result) for chaining */ public final Matrix4f transpose(final Matrix4f src) { if( src == this ) { return transpose(); } m00 = src.m00; m10 = src.m01; m20 = src.m02; m30 = src.m03; m01 = src.m10; m11 = src.m11; m21 = src.m12; m31 = src.m13; m02 = src.m20; m12 = src.m21; m22 = src.m22; m32 = src.m23; m03 = src.m30; m13 = src.m31; m23 = src.m32; m33 = src.m33; return this; } /** * Invert this matrix. * @return false if this matrix is singular and inversion not possible, otherwise true */ public boolean invert() { final float scale; { float a = Math.abs(m00); float max = a; a = Math.abs(m01); if( a > max ) max = a; a = Math.abs(m02); if( a > max ) max = a; a = Math.abs(m03); if( a > max ) max = a; a = Math.abs(m10); if( a > max ) max = a; a = Math.abs(m11); if( a > max ) max = a; a = Math.abs(m12); if( a > max ) max = a; a = Math.abs(m13); if( a > max ) max = a; a = Math.abs(m20); if( a > max ) max = a; a = Math.abs(m21); if( a > max ) max = a; a = Math.abs(m22); if( a > max ) max = a; a = Math.abs(m23); if( a > max ) max = a; a = Math.abs(m30); if( a > max ) max = a; a = Math.abs(m31); if( a > max ) max = a; a = Math.abs(m32); if( a > max ) max = a; a = Math.abs(m33); if( a > max ) max = a; if( 0 == max ) { return false; } scale = 1.0f/max; } final float a00 = m00*scale; final float a10 = m10*scale; final float a20 = m20*scale; final float a30 = m30*scale; final float a01 = m01*scale; final float a11 = m11*scale; final float a21 = m21*scale; final float a31 = m31*scale; final float a02 = m02*scale; final float a12 = m12*scale; final float a22 = m22*scale; final float a32 = m32*scale; final float a03 = m03*scale; final float a13 = m13*scale; final float a23 = m23*scale; final float a33 = m33*scale; final float b00 = + a11*(a22*a33 - a23*a32) - a12*(a21*a33 - a23*a31) + a13*(a21*a32 - a22*a31); final float b01 = -( + a10*(a22*a33 - a23*a32) - a12*(a20*a33 - a23*a30) + a13*(a20*a32 - a22*a30)); final float b02 = + a10*(a21*a33 - a23*a31) - a11*(a20*a33 - a23*a30) + a13*(a20*a31 - a21*a30); final float b03 = -( + a10*(a21*a32 - a22*a31) - a11*(a20*a32 - a22*a30) + a12*(a20*a31 - a21*a30)); final float b10 = -( + a01*(a22*a33 - a23*a32) - a02*(a21*a33 - a23*a31) + a03*(a21*a32 - a22*a31)); final float b11 = + a00*(a22*a33 - a23*a32) - a02*(a20*a33 - a23*a30) + a03*(a20*a32 - a22*a30); final float b12 = -( + a00*(a21*a33 - a23*a31) - a01*(a20*a33 - a23*a30) + a03*(a20*a31 - a21*a30)); final float b13 = + a00*(a21*a32 - a22*a31) - a01*(a20*a32 - a22*a30) + a02*(a20*a31 - a21*a30); final float b20 = + a01*(a12*a33 - a13*a32) - a02*(a11*a33 - a13*a31) + a03*(a11*a32 - a12*a31); final float b21 = -( + a00*(a12*a33 - a13*a32) - a02*(a10*a33 - a13*a30) + a03*(a10*a32 - a12*a30)); final float b22 = + a00*(a11*a33 - a13*a31) - a01*(a10*a33 - a13*a30) + a03*(a10*a31 - a11*a30); final float b23 = -( + a00*(a11*a32 - a12*a31) - a01*(a10*a32 - a12*a30) + a02*(a10*a31 - a11*a30)); final float b30 = -( + a01*(a12*a23 - a13*a22) - a02*(a11*a23 - a13*a21) + a03*(a11*a22 - a12*a21)); final float b31 = + a00*(a12*a23 - a13*a22) - a02*(a10*a23 - a13*a20) + a03*(a10*a22 - a12*a20); final float b32 = -( + a00*(a11*a23 - a13*a21) - a01*(a10*a23 - a13*a20) + a03*(a10*a21 - a11*a20)); final float b33 = + a00*(a11*a22 - a12*a21) - a01*(a10*a22 - a12*a20) + a02*(a10*a21 - a11*a20); final float det = (a00*b00 + a01*b01 + a02*b02 + a03*b03) / scale; if( 0 == det ) { return false; } m00 = b00 / det; m10 = b01 / det; m20 = b02 / det; m30 = b03 / det; m01 = b10 / det; m11 = b11 / det; m21 = b12 / det; m31 = b13 / det; m02 = b20 / det; m12 = b21 / det; m22 = b22 / det; m32 = b23 / det; m03 = b30 / det; m13 = b31 / det; m23 = b32 / det; m33 = b33 / det; return true; } /** * Invert the {@code src} matrix values into this matrix * @param src the source matrix, which values are to be inverted * @return false if {@code src} matrix is singular and inversion not possible, otherwise true */ public boolean invert(final Matrix4f src) { return load(src).invert(); } /** * Multiply matrix: [this] = [this] x [b] ** Roughly 15% slower than {@link #mul(Matrix4f, Matrix4f)} * Roughly 3% slower than {@link FloatUtil#multMatrix(float[], float[])} *
* @param b 4x4 matrix * @return this matrix for chaining * @see #mul(Matrix4f, Matrix4f) */ public final Matrix4f mul(final Matrix4f b) { // return mul(new Matrix4f(this), b); // <- roughly half speed float ai0=m00; // row-0, m[0+0*4] float ai1=m01; float ai2=m02; float ai3=m03; m00 = ai0 * b.m00 + ai1 * b.m10 + ai2 * b.m20 + ai3 * b.m30 ; m01 = ai0 * b.m01 + ai1 * b.m11 + ai2 * b.m21 + ai3 * b.m31 ; m02 = ai0 * b.m02 + ai1 * b.m12 + ai2 * b.m22 + ai3 * b.m32 ; m03 = ai0 * b.m03 + ai1 * b.m13 + ai2 * b.m23 + ai3 * b.m33 ; ai0=m10; //row-1, m[1+0*4] ai1=m11; ai2=m12; ai3=m13; m10 = ai0 * b.m00 + ai1 * b.m10 + ai2 * b.m20 + ai3 * b.m30 ; m11 = ai0 * b.m01 + ai1 * b.m11 + ai2 * b.m21 + ai3 * b.m31 ; m12 = ai0 * b.m02 + ai1 * b.m12 + ai2 * b.m22 + ai3 * b.m32 ; m13 = ai0 * b.m03 + ai1 * b.m13 + ai2 * b.m23 + ai3 * b.m33 ; ai0=m20; // row-2, m[2+0*4] ai1=m21; ai2=m22; ai3=m23; m20 = ai0 * b.m00 + ai1 * b.m10 + ai2 * b.m20 + ai3 * b.m30 ; m21 = ai0 * b.m01 + ai1 * b.m11 + ai2 * b.m21 + ai3 * b.m31 ; m22 = ai0 * b.m02 + ai1 * b.m12 + ai2 * b.m22 + ai3 * b.m32 ; m23 = ai0 * b.m03 + ai1 * b.m13 + ai2 * b.m23 + ai3 * b.m33 ; ai0=m30; // row-3, m[3+0*4] ai1=m31; ai2=m32; ai3=m33; m30 = ai0 * b.m00 + ai1 * b.m10 + ai2 * b.m20 + ai3 * b.m30 ; m31 = ai0 * b.m01 + ai1 * b.m11 + ai2 * b.m21 + ai3 * b.m31 ; m32 = ai0 * b.m02 + ai1 * b.m12 + ai2 * b.m22 + ai3 * b.m32 ; m33 = ai0 * b.m03 + ai1 * b.m13 + ai2 * b.m23 + ai3 * b.m33 ; return this; } /** * Multiply matrix: [this] = [a] x [b] ** Roughly 13% faster than {@link #mul(Matrix4f)} * Roughly 11% faster than {@link FloatUtil#multMatrix(float[], float[])} *
* @param a 4x4 matrix, can't be this matrix * @param b 4x4 matrix, can't be this matrix * @return this matrix for chaining * @see #mul(Matrix4f) */ public final Matrix4f mul(final Matrix4f a, final Matrix4f b) { // row-0, m[0+0*4] m00 = a.m00 * b.m00 + a.m01 * b.m10 + a.m02 * b.m20 + a.m03 * b.m30 ; m01 = a.m00 * b.m01 + a.m01 * b.m11 + a.m02 * b.m21 + a.m03 * b.m31 ; m02 = a.m00 * b.m02 + a.m01 * b.m12 + a.m02 * b.m22 + a.m03 * b.m32 ; m03 = a.m00 * b.m03 + a.m01 * b.m13 + a.m02 * b.m23 + a.m03 * b.m33 ; //row-1, m[1+0*4] m10 = a.m10 * b.m00 + a.m11 * b.m10 + a.m12 * b.m20 + a.m13 * b.m30 ; m11 = a.m10 * b.m01 + a.m11 * b.m11 + a.m12 * b.m21 + a.m13 * b.m31 ; m12 = a.m10 * b.m02 + a.m11 * b.m12 + a.m12 * b.m22 + a.m13 * b.m32 ; m13 = a.m10 * b.m03 + a.m11 * b.m13 + a.m12 * b.m23 + a.m13 * b.m33 ; // row-2, m[2+0*4] m20 = a.m20 * b.m00 + a.m21 * b.m10 + a.m22 * b.m20 + a.m23 * b.m30 ; m21 = a.m20 * b.m01 + a.m21 * b.m11 + a.m22 * b.m21 + a.m23 * b.m31 ; m22 = a.m20 * b.m02 + a.m21 * b.m12 + a.m22 * b.m22 + a.m23 * b.m32 ; m23 = a.m20 * b.m03 + a.m21 * b.m13 + a.m22 * b.m23 + a.m23 * b.m33 ; // row-3, m[3+0*4] m30 = a.m30 * b.m00 + a.m31 * b.m10 + a.m32 * b.m20 + a.m33 * b.m30 ; m31 = a.m30 * b.m01 + a.m31 * b.m11 + a.m32 * b.m21 + a.m33 * b.m31 ; m32 = a.m30 * b.m02 + a.m31 * b.m12 + a.m32 * b.m22 + a.m33 * b.m32 ; m33 = a.m30 * b.m03 + a.m31 * b.m13 + a.m32 * b.m23 + a.m33 * b.m33 ; return this; } /** * @param v_in 4-component column-vector * @param v_out this * v_in * @returns v_out for chaining */ public final float[] mulVec4f(final float[/*4*/] v_in, final float[/*4*/] v_out) { // (one matrix row in column-major order) X (column vector) final float x = v_in[0], y = v_in[1], z = v_in[2], w = v_in[3]; v_out[0] = x * m00 + y * m01 + z * m02 + w * m03; v_out[1] = x * m10 + y * m11 + z * m12 + w * m13; v_out[2] = x * m20 + y * m21 + z * m22 + w * m23; v_out[3] = x * m30 + y * m31 + z * m32 + w * m33; return v_out; } /** * @param v_in 4-component column-vector * @param v_out this * v_in * @returns v_out for chaining */ public final Vec4f mulVec4f(final Vec4f v_in, final Vec4f v_out) { // (one matrix row in column-major order) X (column vector) final float x = v_in.x(), y = v_in.y(), z = v_in.z(), w = v_in.w(); v_out.set( x * m00 + y * m01 + z * m02 + w * m03, x * m10 + y * m11 + z * m12 + w * m13, x * m20 + y * m21 + z * m22 + w * m23, x * m30 + y * m31 + z * m32 + w * m33 ); return v_out; } /** * Affine 3f-vector transformation by 4x4 matrix * * 4x4 matrix multiplication with 3-component vector, * using {@code 1} for for {@code v_in[3]} and dropping {@code v_out[3]}, * which shall be {@code 1}. * * @param v_in 3-component column-vector * @param v_out m_in * v_in, 3-component column-vector * @returns v_out for chaining */ public final float[] mulVec3f(final float[/*3*/] v_in, final float[/*3*/] v_out) { // (one matrix row in column-major order) X (column vector) final float x = v_in[0], y = v_in[1], z = v_in[2]; v_out[0] = x * m00 + y * m01 + z * m02 + 1f * m03; v_out[1] = x * m10 + y * m11 + z * m12 + 1f * m13; v_out[2] = x * m20 + y * m21 + z * m22 + 1f * m23; return v_out; } /** * Affine 3f-vector transformation by 4x4 matrix * * 4x4 matrix multiplication with 3-component vector, * using {@code 1} for for {@code v_in.w()} and dropping {@code v_out.w()}, * which shall be {@code 1}. * * @param v_in 3-component column-vector {@link Vec3f} * @param v_out m_in * v_in, 3-component column-vector {@link Vec3f} * @returns v_out for chaining */ public final Vec3f mulVec3f(final Vec3f v_in, final Vec3f v_out) { // (one matrix row in column-major order) X (column vector) final float x = v_in.x(), y = v_in.y(), z = v_in.z(); v_out.set( x * m00 + y * m01 + z * m02 + 1f * m03, x * m10 + y * m11 + z * m12 + 1f * m13, x * m20 + y * m21 + z * m22 + 1f * m23 ); return v_out; } // // Matrix setTo...(), affine + basic // /** * Set this matrix to translation. *
Translation matrix (Column Order):
1 0 0 0
0 1 0 0
0 0 1 0
x y z 1
*
* @param x x-axis translate
* @param y y-axis translate
* @param z z-axis translate
* @return this matrix for chaining
*/
public final Matrix4f setToTranslation(final float x, final float y, final float z) {
m00 = m11 = m22 = m33 = 1.0f;
m03 = x;
m13 = y;
m23 = z;
m01 = m02 =
m10 = m12 =
m20 = m21 =
m30 = m31 = m32 = 0.0f;
return this;
}
/**
* Set this matrix to translation.
*
Translation matrix (Column Order):
1 0 0 0
0 1 0 0
0 0 1 0
x y z 1
*
* @param t translate Vec3f
* @return this matrix for chaining
*/
public final Matrix4f setToTranslation(final Vec3f t) {
return setToTranslation(t.x(), t.y(), t.z());
}
/**
* Set this matrix to scale.
*
Scale matrix (Any Order):
x 0 0 0
0 y 0 0
0 0 z 0
0 0 0 1
*
* @param x x-axis scale
* @param y y-axis scale
* @param z z-axis scale
* @return this matrix for chaining
*/
public final Matrix4f setToScale(final float x, final float y, final float z) {
m33 = 1.0f;
m00 = x;
m11 = y;
m22 = z;
m01 = m02 = m03 =
m10 = m12 = m13 =
m20 = m21 = m23 =
m30 = m31 = m32 = 0.0f;
return this;
}
/**
* Set this matrix to rotation from the given axis and angle in radians.
*
Rotation matrix (Column Order):
xx(1-c)+c xy(1-c)+zs xz(1-c)-ys 0
xy(1-c)-zs yy(1-c)+c yz(1-c)+xs 0
xz(1-c)+ys yz(1-c)-xs zz(1-c)+c 0
0 0 0 1
*
* @see Matrix-FAQ Q38
* @param ang_rad angle in radians
* @param x x of rotation axis
* @param y y of rotation axis
* @param z z of rotation axis
* @return this matrix for chaining
*/
public final Matrix4f setToRotationAxis(final float ang_rad, float x, float y, float z) {
final float c = FloatUtil.cos(ang_rad);
final float ic= 1.0f - c;
final float s = FloatUtil.sin(ang_rad);
final float[] tmpVec3f = { x, y, z };
VectorUtil.normalizeVec3(tmpVec3f);
x = tmpVec3f[0]; y = tmpVec3f[1]; z = tmpVec3f[2];
final float xy = x*y;
final float xz = x*z;
final float xs = x*s;
final float ys = y*s;
final float yz = y*z;
final float zs = z*s;
m00 = x*x*ic+c;
m10 = xy*ic+zs;
m20 = xz*ic-ys;
m30 = 0;
m01 = xy*ic-zs;
m11 = y*y*ic+c;
m21 = yz*ic+xs;
m31 = 0;
m02 = xz*ic+ys;
m12 = yz*ic-xs;
m22 = z*z*ic+c;
m32 = 0;
m03 = 0f;
m13 = 0f;
m23 = 0f;
m33 = 1f;
return this;
}
/**
* Set this matrix to rotation from the given axis and angle in radians.
*
Rotation matrix (Column Order):
xx(1-c)+c xy(1-c)+zs xz(1-c)-ys 0
xy(1-c)-zs yy(1-c)+c yz(1-c)+xs 0
xz(1-c)+ys yz(1-c)-xs zz(1-c)+c 0
0 0 0 1
*
* @see Matrix-FAQ Q38
* @param ang_rad angle in radians
* @param axis rotation axis
* @return this matrix for chaining
*/
public final Matrix4f setToRotationAxis(final float ang_rad, final Vec3f axis) {
return setToRotationAxis(ang_rad, axis.x(), axis.y(), axis.z());
}
/**
* Set this matrix to rotation from the given Euler rotation angles in radians.
* * The rotations are applied in the given order: *
* Implementation does not use Quaternion and hence is exposed to * Gimbal-Lock, * consider using {@link #setToRotation(Quaternion)}. *
* @see Matrix-FAQ Q36 * @see euclideanspace.com-eulerToMatrix * @see #setToRotation(Quaternion) */ public Matrix4f setToRotationEuler(final float bankX, final float headingY, final float attitudeZ) { // Assuming the angles are in radians. final float ch = FloatUtil.cos(headingY); final float sh = FloatUtil.sin(headingY); final float ca = FloatUtil.cos(attitudeZ); final float sa = FloatUtil.sin(attitudeZ); final float cb = FloatUtil.cos(bankX); final float sb = FloatUtil.sin(bankX); m00 = ch*ca; m10 = sa; m20 = -sh*ca; m30 = 0; m01 = sh*sb - ch*sa*cb; m11 = ca*cb; m21 = sh*sa*cb + ch*sb; m31 = 0; m02 = ch*sa*sb + sh*cb; m12 = -ca*sb; m22 = -sh*sa*sb + ch*cb; m32 = 0; m03 = 0; m13 = 0; m23 = 0; m33 = 1; return this; } /** * Set this matrix to rotation using the given Quaternion. ** Implementation Details: *
Ortho matrix (Column Order):
2/dx 0 0 0
0 2/dy 0 0
0 0 2/dz 0
tx ty tz 1
*
* @param left
* @param right
* @param bottom
* @param top
* @param zNear
* @param zFar
* @return this matrix for chaining
*/
public Matrix4f setToOrtho(final float left, final float right,
final float bottom, final float top,
final float zNear, final float zFar) {
{
// m00 = m11 = m22 = m33 = 1f;
m10 = m20 = m30 = 0f;
m01 = m21 = m31 = 0f;
m02 = m12 = m32 = 0f;
// m03 = m13 = m23 = 0f;
}
final float dx=right-left;
final float dy=top-bottom;
final float dz=zFar-zNear;
final float tx=-1.0f*(right+left)/dx;
final float ty=-1.0f*(top+bottom)/dy;
final float tz=-1.0f*(zFar+zNear)/dz;
m00 = 2.0f/dx;
m11 = 2.0f/dy;
m22 = -2.0f/dz;
m03 = tx;
m13 = ty;
m23 = tz;
m33 = 1f;
return this;
}
/**
* Set this matrix to frustum.
*
Frustum matrix (Column Order):
2*zNear/dx 0 0 0
0 2*zNear/dy 0 0
A B C -1
0 0 D 0
*
* @param left
* @param right
* @param bottom
* @param top
* @param zNear
* @param zFar
* @return this matrix for chaining
* @throws IllegalArgumentException if {@code zNear <= 0} or {@code zFar <= zNear}
* or {@code left == right}, or {@code bottom == top}.
*/
public Matrix4f setToFrustum(final float left, final float right,
final float bottom, final float top,
final float zNear, final float zFar) throws IllegalArgumentException {
if( zNear <= 0.0f || zFar <= zNear ) {
throw new IllegalArgumentException("Requirements zNear > 0 and zFar > zNear, but zNear "+zNear+", zFar "+zFar);
}
if( left == right || top == bottom) {
throw new IllegalArgumentException("GL_INVALID_VALUE: top,bottom and left,right must not be equal");
}
{
// m00 = m11 = m22 = m33 = 1f;
m10 = m20 = m30 = 0f;
m01 = m21 = m31 = 0f;
m03 = m13 = 0f;
}
final float zNear2 = 2.0f*zNear;
final float dx=right-left;
final float dy=top-bottom;
final float dz=zFar-zNear;
final float A=(right+left)/dx;
final float B=(top+bottom)/dy;
final float C=-1.0f*(zFar+zNear)/dz;
final float D=-2.0f*(zFar*zNear)/dz;
m00 = zNear2/dx;
m11 = zNear2/dy;
m02 = A;
m12 = B;
m22 = C;
m32 = -1.0f;
m23 = D;
m33 = 0f;
return this;
}
/**
* Set this matrix to perspective {@link #setToFrustum(float, float, float, float, float, float) frustum} projection.
*
* @param fovy_rad angle in radians
* @param aspect aspect ratio width / height
* @param zNear
* @param zFar
* @return this matrix for chaining
* @throws IllegalArgumentException if {@code zNear <= 0} or {@code zFar <= zNear}
* @see #setToFrustum(float, float, float, float, float, float)
*/
public Matrix4f setToPerspective(final float fovy_rad, final float aspect, final float zNear, final float zFar) throws IllegalArgumentException {
final float top = FloatUtil.tan(fovy_rad/2f) * zNear; // use tangent of half-fov !
final float bottom = -1.0f * top; // -1f * fovhvTan.top * zNear
final float left = aspect * bottom; // aspect * -1f * fovhvTan.top * zNear
final float right = aspect * top; // aspect * fovhvTan.top * zNear
return setToFrustum(left, right, bottom, top, zNear, zFar);
}
/**
* Set this matrix to perspective {@link #setToFrustum(float, float, float, float, float, float) frustum} projection.
*
* @param fovhv {@link FovHVHalves} field of view in both directions, may not be centered, either in radians or tangent
* @param zNear
* @param zFar
* @return this matrix for chaining
* @throws IllegalArgumentException if {@code zNear <= 0} or {@code zFar <= zNear}
* @see #setToFrustum(float, float, float, float, float, float)
* @see Frustum#updateByFovDesc(float[], int, boolean, Frustum.FovDesc)
*/
public Matrix4f setToPerspective(final FovHVHalves fovhv, final float zNear, final float zFar) throws IllegalArgumentException {
final FovHVHalves fovhvTan = fovhv.toTangents(); // use tangent of half-fov !
final float top = fovhvTan.top * zNear;
final float bottom = -1.0f * fovhvTan.bottom * zNear;
final float left = -1.0f * fovhvTan.left * zNear;
final float right = fovhvTan.right * zNear;
return setToFrustum(left, right, bottom, top, zNear, zFar);
}
/**
* Calculate the frustum planes in world coordinates
* using the passed float[16] as premultiplied P*MV (column major order).
* * Frustum plane's normals will point to the inside of the viewing frustum, * as required by this class. *
*/ public void updateFrustumPlanes(final Frustum frustum) { // Left: a = m41 + m11, b = m42 + m12, c = m43 + m13, d = m44 + m14 - [1..4] column-major // Left: a = m30 + m00, b = m31 + m01, c = m32 + m02, d = m33 + m03 - [0..3] column-major { final Frustum.Plane p = frustum.getPlanes()[Frustum.LEFT]; final Vec3f p_n = p.n; p_n.set( m30 + m00, m31 + m01, m32 + m02 ); p.d = m33 + m03; } // Right: a = m41 - m11, b = m42 - m12, c = m43 - m13, d = m44 - m14 - [1..4] column-major // Right: a = m30 - m00, b = m31 - m01, c = m32 - m02, d = m33 - m03 - [0..3] column-major { final Frustum.Plane p = frustum.getPlanes()[Frustum.RIGHT]; final Vec3f p_n = p.n; p_n.set( m30 - m00, m31 - m01, m32 - m02 ); p.d = m33 - m03; } // Bottom: a = m41m21, b = m42m22, c = m43m23, d = m44m24 - [1..4] column-major // Bottom: a = m30m10, b = m31m11, c = m32m12, d = m33m13 - [0..3] column-major { final Frustum.Plane p = frustum.getPlanes()[Frustum.BOTTOM]; final Vec3f p_n = p.n; p_n.set( m30 + m10, m31 + m11, m32 + m12 ); p.d = m33 + m13; } // Top: a = m41 - m21, b = m42 - m22, c = m43 - m23, d = m44 - m24 - [1..4] column-major // Top: a = m30 - m10, b = m31 - m11, c = m32 - m12, d = m33 - m13 - [0..3] column-major { final Frustum.Plane p = frustum.getPlanes()[Frustum.TOP]; final Vec3f p_n = p.n; p_n.set( m30 - m10, m31 - m11, m32 - m12 ); p.d = m33 - m13; } // Near: a = m41m31, b = m42m32, c = m43m33, d = m44m34 - [1..4] column-major // Near: a = m30m20, b = m31m21, c = m32m22, d = m33m23 - [0..3] column-major { final Frustum.Plane p = frustum.getPlanes()[Frustum.NEAR]; final Vec3f p_n = p.n; p_n.set( m30 + m20, m31 + m21, m32 + m22 ); p.d = m33 + m23; } // Far: a = m41 - m31, b = m42 - m32, c = m43 - m33, d = m44 - m34 - [1..4] column-major // Far: a = m30 - m20, b = m31 - m21, c = m32m22, d = m33m23 - [0..3] column-major { final Frustum.Plane p = frustum.getPlanes()[Frustum.FAR]; final Vec3f p_n = p.n; p_n.set( m30 - m20, m31 - m21, m32 - m22 ); p.d = m33 - m23; } // Normalize all planes for (int i = 0; i < 6; ++i) { final Plane p = frustum.getPlanes()[i]; final Vec3f p_n = p.n; final float invLen = 1f / p_n.length(); p_n.scale(invLen); p.d *= invLen; } } /** * Make given matrix the look-at matrix based on given parameters. ** Consist out of two matrix multiplications: *
* R = L x T,
* with L for look-at matrix and
* T for eye translation.
*
* Result R can be utilized for projection or modelview multiplication, i.e.
* M = M x R,
* with M being the projection or modelview matrix.
*
*
* @param eye 3 component eye vector
* @param center 3 component center vector
* @param up 3 component up vector
* @param tmp temporary Matrix4f used for multiplication
* @return this matrix for chaining
*/
public Matrix4f setToLookAt(final Vec3f eye, final Vec3f center, final Vec3f up, final Matrix4f tmp) {
// normalized forward!
final Vec3f fwd = new Vec3f( center.x() - eye.x(),
center.y() - eye.y(),
center.z() - eye.z() ).normalize();
/* Side = forward x up, normalized */
final Vec3f side = fwd.cross(up).normalize();
/* Recompute up as: up = side x forward */
final Vec3f up2 = side.cross(fwd);
m00 = side.x();
m10 = up2.x();
m20 = -fwd.x();
m30 = 0;
m01 = side.y();
m11 = up2.y();
m21 = -fwd.y();
m31 = 0;
m02 = side.z();
m12 = up2.z();
m22 = -fwd.z();
m32 = 0;
m03 = 0;
m13 = 0;
m23 = 0;
m33 = 1;
return mul( tmp.setToTranslation( -eye.x(), -eye.y(), -eye.z() ) );
}
//
// Matrix affine operations using setTo..()
//
/**
* Rotate this matrix about give axis and angle in radians, i.e. multiply by {@link #setToRotationAxis(float, float, float, float) axis-rotation matrix}.
* @see Matrix-FAQ Q38
* @param angrad angle in radians
* @param x x of rotation axis
* @param y y of rotation axis
* @param z z of rotation axis
* @param tmp temporary Matrix4f used for multiplication
* @return this matrix for chaining
*/
public final Matrix4f rotate(final float ang_rad, final float x, final float y, final float z, final Matrix4f tmp) {
return mul( tmp.setToRotationAxis(ang_rad, x, y, z) );
}
/**
* Rotate this matrix about give axis and angle in radians, i.e. multiply by {@link #setToRotationAxis(float, Vec3f) axis-rotation matrix}.
* @see Matrix-FAQ Q38
* @param angrad angle in radians
* @param axis rotation axis
* @param tmp temporary Matrix4f used for multiplication
* @return this matrix for chaining
*/
public final Matrix4f rotate(final float ang_rad, final Vec3f axis, final Matrix4f tmp) {
return mul( tmp.setToRotationAxis(ang_rad, axis) );
}
/**
* Rotate this matrix with the given {@link Quaternion}, i.e. multiply by {@link #setToRotation(Quaternion) Quaternion's rotation matrix}.
* @param tmp temporary Matrix4f used for multiplication
* @return this matrix for chaining
*/
public final Matrix4f rotate(final Quaternion quat, final Matrix4f tmp) {
return mul( tmp.setToRotation(quat) );
}
/**
* Translate this matrix, i.e. multiply by {@link #setToTranslation(float, float, float) translation matrix}.
* @param x x translation
* @param y y translation
* @param z z translation
* @param tmp temporary Matrix4f used for multiplication
* @return this matrix for chaining
*/
public final Matrix4f translate(final float x, final float y, final float z, final Matrix4f tmp) {
return mul( tmp.setToTranslation(x, y, z) );
}
/**
* Translate this matrix, i.e. multiply by {@link #setToTranslation(Vec3f) translation matrix}.
* @param t translation Vec3f
* @param tmp temporary Matrix4f used for multiplication
* @return this matrix for chaining
*/
public final Matrix4f translate(final Vec3f t, final Matrix4f tmp) {
return mul( tmp.setToTranslation(t) );
}
/**
* Scale this matrix, i.e. multiply by {@link #setToScale(float, float, float) scale matrix}.
* @param x x scale
* @param y y scale
* @param z z scale
* @param tmp temporary Matrix4f used for multiplication
* @return this matrix for chaining
*/
public final Matrix4f scale(final float x, final float y, final float z, final Matrix4f tmp) {
return mul( tmp.setToScale(x, y, z) );
}
/**
* Scale this matrix, i.e. multiply by {@link #setToScale(float, float, float) scale matrix}.
* @param s scale for x-, y- and z-axis
* @param tmp temporary Matrix4f used for multiplication
* @return this matrix for chaining
*/
public final Matrix4f scale(final float s, final Matrix4f tmp) {
return mul( tmp.setToScale(s, s, s) );
}
//
// Matrix Stack
//
/**
* Push the matrix to it's stack, while preserving this matrix values.
* @see #pop()
*/
public final void push() {
stack.push(this);
}
/**
* Pop the current matrix from it's stack, replacing this matrix values.
* @see #push()
*/
public final void pop() {
stack.pop(this);
}
//
// equals
//
/**
* Equals check using a given {@link FloatUtil#EPSILON} value and {@link FloatUtil#isEqual(float, float, float)}.
* * Implementation considers following corner cases: *
* Implementation considers following corner cases: *
* Traditional gluProject implementation.
*
* Traditional gluProject implementation.
*
* Traditional gluUnProject implementation.
*
* Traditional gluUnProject implementation.
*
* Traditional gluUnProject implementation.
*
* Traditional gluUnProject4 implementation.
*
* Notes for picking winz0 and winz1: *
0
* in which case an {@link IndexOutOfBoundsException} is thrown.
*/
public Stack(final int initialSize, final int growSize) {
this.position = 0;
this.growSize = growSize;
this.buffer = new float[initialSize];
}
private final void growIfNecessary(final int length) throws IndexOutOfBoundsException {
if( position + length > buffer.length ) {
if( 0 >= growSize ) {
throw new IndexOutOfBoundsException("Out of fixed stack size: "+this);
}
final float[] newBuffer =
new float[buffer.length + growSize];
System.arraycopy(buffer, 0, newBuffer, 0, position);
buffer = newBuffer;
}
}
public final Matrix4f push(final Matrix4f src) throws IndexOutOfBoundsException {
growIfNecessary(16);
src.get(buffer, position);
position += 16;
return src;
}
public final Matrix4f pop(final Matrix4f dest) throws IndexOutOfBoundsException {
position -= 16;
dest.load(buffer, position);
return dest;
}
}
}