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-/**
- * Copyright 2014-2023 JogAmp Community. All rights reserved.
- *
- * Redistribution and use in source and binary forms, with or without modification, are
- * permitted provided that the following conditions are met:
- *
- * 1. Redistributions of source code must retain the above copyright notice, this list of
- * conditions and the following disclaimer.
- *
- * 2. Redistributions in binary form must reproduce the above copyright notice, this list
- * of conditions and the following disclaimer in the documentation and/or other materials
- * provided with the distribution.
- *
- * THIS SOFTWARE IS PROVIDED BY JogAmp Community ``AS IS'' AND ANY EXPRESS OR IMPLIED
- * WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND
- * FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL JogAmp Community OR
- * CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
- * CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
- * SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON
- * ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
- * NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF
- * ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
- *
- * The views and conclusions contained in the software and documentation are those of the
- * authors and should not be interpreted as representing official policies, either expressed
- * or implied, of JogAmp Community.
- */
-
-package com.jogamp.opengl.math;
-
-import java.nio.FloatBuffer;
-
-import com.jogamp.opengl.math.geom.AABBox;
-import com.jogamp.opengl.math.geom.Frustum;
-import com.jogamp.opengl.math.geom.Frustum.Plane;
-
-/**
- * Basic 4x4 float matrix implementation using fields for intensive use-cases (host operations).
- * <p>
- * Implementation covers {@link FloatUtil} matrix functionality, exposed in an object oriented manner.
- * </p>
- * <p>
- * 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.
- * </p>
- * <p>
- * For array operations the layout is expected in column-major order
- * matching OpenGL's implementation, illustration:
- * <pre>
- 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;
-
- * </pre>
- * </p>
- * <p>
- * <ul>
- * <li><a href="http://web.archive.org/web/20041029003853/http://www.j3d.org/matrix_faq/matrfaq_latest.html">Matrix-FAQ</a></li>
- * <li><a href="https://en.wikipedia.org/wiki/Matrix_%28mathematics%29">Wikipedia-Matrix</a></li>
- * <li><a href="http://www.euclideanspace.com/maths/algebra/matrix/index.htm">euclideanspace.com-Matrix</a></li>
- * </ul>
- * </p>
- * <p>
- * Implementation utilizes unrolling of small vertices and matrices wherever possible
- * while trying to access memory in a linear fashion for performance reasons, see:
- * <ul>
- * <li><a href="https://lessthanoptimal.github.io/Java-Matrix-Benchmark/">java-matrix-benchmark</a></li>
- * <li><a href="https://github.com/lessthanoptimal/ejml">EJML Efficient Java Matrix Library</a></li>
- * </ul>
- * </p>
- * @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);
- }
-
- /**
- * Creates a new matrix based on given {@link FloatBuffer} 4x4 column major order.
- * @param m 4x4 matrix in column-major order
- */
- public Matrix4f(final FloatBuffer m) {
- load(m);
- }
-
- //
- // Write to Matrix via set(..) or load(..)
- //
-
- /** Sets the {@code i}th component with float {@code v} 0 <= i < 16 */
- public void set(final int i, final float v) {
- switch (i) {
- case 0+4*0: m00 = v; break;
- case 1+4*0: m10 = v; break;
- case 2+4*0: m20 = v; break;
- case 3+4*0: m30 = v; break;
-
- case 0+4*1: m01 = v; break;
- case 1+4*1: m11 = v; break;
- case 2+4*1: m21 = v; break;
- case 3+4*1: m31 = v; break;
-
- case 0+4*2: m02 = v; break;
- case 1+4*2: m12 = v; break;
- case 2+4*2: m22 = v; break;
- case 3+4*2: m32 = v; break;
-
- case 0+4*3: m03 = v; break;
- case 1+4*3: m13 = v; break;
- case 2+4*3: m23 = v; break;
- case 3+4*3: m33 = v; break;
- default: throw new IndexOutOfBoundsException();
- }
- }
-
- /**
- * Set this matrix to identity.
- * <pre>
- Translation matrix (Column Order):
- 1 0 0 0
- 0 1 0 0
- 0 0 1 0
- 0 0 0 1
- * </pre>
- * @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.
- * <p>
- * Implementation uses relative {@link FloatBuffer#get()},
- * hence caller may want to issue {@link FloatBuffer#reset()} thereafter.
- * </p>
- * @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 {@code i}th 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 <i>v_out</i> 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 <i>v_out</i> 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 <i>v_out</i> 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 <i>v_out</i> 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
- * @return {@code dst} for chaining
- */
- public float[] 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;
- return dst;
- }
-
- /**
- * Get this matrix into the given float[16] array in column major order.
- *
- * @param dst float[16] array storage in column major order
- * @return {@code dst} for chaining
- */
- public float[] 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;
- return dst;
- }
-
- /**
- * Get this matrix into the given {@link FloatBuffer} in column major order.
- * <p>
- * Implementation uses relative {@link FloatBuffer#put(float)},
- * hence caller may want to issue {@link FloatBuffer#reset()} thereafter.
- * </p>
- *
- * @param dst {@link FloatBuffer} array storage in column major order
- * @return {@code dst} for chaining
- */
- public FloatBuffer 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 );
- return dst;
- }
-
- //
- // 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;
- try {
- scale = mulScale();
- } catch(final ArithmeticException aex) {
- return false; // max was 0
- }
- 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;
- }
- final float invdet = 1.0f / det;
-
- m00 = b00 * invdet;
- m10 = b01 * invdet;
- m20 = b02 * invdet;
- m30 = b03 * invdet;
-
- m01 = b10 * invdet;
- m11 = b11 * invdet;
- m21 = b12 * invdet;
- m31 = b13 * invdet;
-
- m02 = b20 * invdet;
- m12 = b21 * invdet;
- m22 = b22 * invdet;
- m32 = b23 * invdet;
-
- m03 = b30 * invdet;
- m13 = b31 * invdet;
- m23 = b32 * invdet;
- m33 = b33 * invdet;
- 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) {
- final float scale;
- try {
- scale = src.mulScale();
- } catch(final ArithmeticException aex) {
- return false; // max was 0
- }
- final float a00 = src.m00*scale;
- final float a10 = src.m10*scale;
- final float a20 = src.m20*scale;
- final float a30 = src.m30*scale;
-
- final float a01 = src.m01*scale;
- final float a11 = src.m11*scale;
- final float a21 = src.m21*scale;
- final float a31 = src.m31*scale;
-
- final float a02 = src.m02*scale;
- final float a12 = src.m12*scale;
- final float a22 = src.m22*scale;
- final float a32 = src.m32*scale;
-
- final float a03 = src.m03*scale;
- final float a13 = src.m13*scale;
- final float a23 = src.m23*scale;
- final float a33 = src.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;
- }
- final float invdet = 1.0f / det;
-
- m00 = b00 * invdet;
- m10 = b01 * invdet;
- m20 = b02 * invdet;
- m30 = b03 * invdet;
-
- m01 = b10 * invdet;
- m11 = b11 * invdet;
- m21 = b12 * invdet;
- m31 = b13 * invdet;
-
- m02 = b20 * invdet;
- m12 = b21 * invdet;
- m22 = b22 * invdet;
- m32 = b23 * invdet;
-
- m03 = b30 * invdet;
- m13 = b31 * invdet;
- m23 = b32 * invdet;
- m33 = b33 * invdet;
- return true;
- }
-
- private final float mulScale() {
- /**
- // No Hotspot intrinsic Math.* optimization for at least Math.max(),
- // hence this chunk is slower.
- float max = Math.abs(m00);
-
- max = Math.max(max, Math.abs(m01));
- max = Math.max(max, Math.abs(m02));
- ... etc
- */
- 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;
-
- return 1.0f/max;
- }
-
- /**
- * Multiply matrix: [this] = [this] x [b]
- * @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]
- * @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, can be v_out for in-place transformation
- * @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;
- }
-
- /**
- * @param v_inout 4-component column-vector input and output, i.e. in-place transformation
- * @returns v_inout for chaining
- */
- public final Vec4f mulVec4f(final Vec4f v_inout) {
- // (one matrix row in column-major order) X (column vector)
- final float x = v_inout.x(), y = v_inout.y(), z = v_inout.z(), w = v_inout.w();
- v_inout.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_inout;
- }
-
- /**
- * 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}, can be v_out for in-place transformation
- * @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;
- }
-
- /**
- * Affine 3f-vector transformation by 4x4 matrix
- *
- * 4x4 matrix multiplication with 3-component vector,
- * using {@code 1} for for {@code v_inout.w()} and dropping {@code v_inout.w()},
- * which shall be {@code 1}.
- *
- * @param v_inout 3-component column-vector {@link Vec3f} input and output, i.e. in-place transformation
- * @returns v_inout for chaining
- */
- public final Vec3f mulVec3f(final Vec3f v_inout) {
- // (one matrix row in column-major order) X (column vector)
- final float x = v_inout.x(), y = v_inout.y(), z = v_inout.z();
- v_inout.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_inout;
- }
-
- //
- // Matrix setTo...(), affine + basic
- //
-
- /**
- * Set this matrix to translation.
- * <pre>
- Translation matrix (Column Order):
- 1 0 0 0
- 0 1 0 0
- 0 0 1 0
- x y z 1
- * </pre>
- * @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.
- * <pre>
- Translation matrix (Column Order):
- 1 0 0 0
- 0 1 0 0
- 0 0 1 0
- x y z 1
- * </pre>
- * @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.
- * <pre>
- Scale matrix (Any Order):
- x 0 0 0
- 0 y 0 0
- 0 0 z 0
- 0 0 0 1
- * </pre>
- * @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 scale.
- * <pre>
- Scale matrix (Any Order):
- x 0 0 0
- 0 y 0 0
- 0 0 z 0
- 0 0 0 1
- * </pre>
- * @param s scale Vec3f
- * @return this matrix for chaining
- */
- public final Matrix4f setToScale(final Vec3f s) {
- return setToScale(s.x(), s.y(), s.z());
- }
-
- /**
- * Set this matrix to rotation from the given axis and angle in radians.
- * <pre>
- 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
- * </pre>
- * @see <a href="http://web.archive.org/web/20041029003853/http://www.j3d.org/matrix_faq/matrfaq_latest.html#Q38">Matrix-FAQ Q38</a>
- * @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 Vec3f tmp = new Vec3f(x, y, z).normalize();
- x = tmp.x(); y = tmp.y(); z = tmp.z();
-
- 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.
- * <pre>
- 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
- * </pre>
- * @see <a href="http://web.archive.org/web/20041029003853/http://www.j3d.org/matrix_faq/matrfaq_latest.html#Q38">Matrix-FAQ Q38</a>
- * @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.
- * <p>
- * The rotations are applied in the given order:
- * <ul>
- * <li>y - heading</li>
- * <li>z - attitude</li>
- * <li>x - bank</li>
- * </ul>
- * </p>
- * @param bankX the Euler pitch angle in radians. (rotation about the X axis)
- * @param headingY the Euler yaw angle in radians. (rotation about the Y axis)
- * @param attitudeZ the Euler roll angle in radians. (rotation about the Z axis)
- * @return this matrix for chaining
- * <p>
- * Implementation does not use Quaternion and hence is exposed to
- * <a href="http://web.archive.org/web/20041029003853/http://www.j3d.org/matrix_faq/matrfaq_latest.html#Q34">Gimbal-Lock</a>,
- * consider using {@link #setToRotation(Quaternion)}.
- * </p>
- * @see <a href="http://web.archive.org/web/20041029003853/http://www.j3d.org/matrix_faq/matrfaq_latest.html#Q36">Matrix-FAQ Q36</a>
- * @see <a href="http://www.euclideanspace.com/maths/geometry/rotations/conversions/eulerToMatrix/index.htm">euclideanspace.com-eulerToMatrix</a>
- * @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 from the given Euler rotation angles in radians.
- * <p>
- * The rotations are applied in the given order:
- * <ul>
- * <li>y - heading</li>
- * <li>z - attitude</li>
- * <li>x - bank</li>
- * </ul>
- * </p>
- * @param angradXYZ euler angle vector in radians holding x-bank, y-heading and z-attitude
- * @return this quaternion for chaining.
- * <p>
- * Implementation does not use Quaternion and hence is exposed to
- * <a href="http://web.archive.org/web/20041029003853/http://www.j3d.org/matrix_faq/matrfaq_latest.html#Q34">Gimbal-Lock</a>,
- * consider using {@link #setToRotation(Quaternion)}.
- * </p>
- * @see <a href="http://web.archive.org/web/20041029003853/http://www.j3d.org/matrix_faq/matrfaq_latest.html#Q36">Matrix-FAQ Q36</a>
- * @see <a href="http://www.euclideanspace.com/maths/geometry/rotations/conversions/eulerToMatrix/index.htm">euclideanspace.com-eulerToMatrix</a>
- * @see #setToRotation(Quaternion)
- */
- public Matrix4f setToRotationEuler(final Vec3f angradXYZ) {
- return setToRotationEuler(angradXYZ.x(), angradXYZ.y(), angradXYZ.z());
- }
-
- /**
- * Set this matrix to rotation using the given Quaternion.
- * <p>
- * Implementation Details:
- * <ul>
- * <li> makes identity matrix if {@link #magnitudeSquared()} is {@link FloatUtil#isZero(float, float) is zero} using {@link FloatUtil#EPSILON epsilon}</li>
- * <li> The fields [m00 .. m22] define the rotation</li>
- * </ul>
- * </p>
- *
- * @param q the Quaternion representing the rotation
- * @return this matrix for chaining
- * @see <a href="http://web.archive.org/web/20041029003853/http://www.j3d.org/matrix_faq/matrfaq_latest.html#Q54">Matrix-FAQ Q54</a>
- * @see Quaternion#toMatrix(float[])
- * @see #getRotation()
- */
- public final Matrix4f setToRotation(final Quaternion q) {
- // pre-multiply scaled-reciprocal-magnitude to reduce multiplications
- final float norm = q.magnitudeSquared();
- if ( FloatUtil.isZero(norm) ) {
- // identity matrix -> srecip = 0f
- loadIdentity();
- return this;
- }
- final float srecip;
- if ( FloatUtil.isEqual(1f, norm) ) {
- srecip = 2f;
- } else {
- srecip = 2.0f / norm;
- }
-
- final float x = q.x();
- final float y = q.y();
- final float z = q.z();
- final float w = q.w();
-
- final float xs = srecip * x;
- final float ys = srecip * y;
- final float zs = srecip * z;
-
- final float xx = x * xs;
- final float xy = x * ys;
- final float xz = x * zs;
- final float xw = xs * w;
- final float yy = y * ys;
- final float yz = y * zs;
- final float yw = ys * w;
- final float zz = z * zs;
- final float zw = zs * w;
-
- m00 = 1f - ( yy + zz );
- m01 = ( xy - zw );
- m02 = ( xz + yw );
- m03 = 0f;
-
- m10 = ( xy + zw );
- m11 = 1f - ( xx + zz );
- m12 = ( yz - xw );
- m13 = 0f;
-
- m20 = ( xz - yw );
- m21 = ( yz + xw );
- m22 = 1f - ( xx + yy );
- m23 = 0f;
-
- m30 = m31 = m32 = 0f;
- m33 = 1f;
- return this;
- }
-
- /**
- * Returns the rotation [m00 .. m22] fields converted to a Quaternion.
- * @param res resulting Quaternion
- * @return the resulting Quaternion for chaining.
- * @see Quaternion#setFromMatrix(float, float, float, float, float, float, float, float, float)
- * @see #setToRotation(Quaternion)
- */
- public final Quaternion getRotation(final Quaternion res) {
- res.setFromMatrix(m00, m01, m02, m10, m11, m12, m20, m21, m22);
- return res;
- }
-
- /**
- * Set this matrix to orthogonal projection.
- * <pre>
- Ortho matrix (Column Order):
- 2/dx 0 0 0
- 0 2/dy 0 0
- 0 0 2/dz 0
- tx ty tz 1
- * </pre>
- * @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.
- * <pre>
- Frustum matrix (Column Order):
- 2*zNear/dx 0 0 0
- 0 2*zNear/dy 0 0
- A B C -1
- 0 0 D 0
- * </pre>
- * @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(Matrix4f, com.jogamp.opengl.math.geom.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 this premultiplied P*MV (column major order) matrix.
- * <p>
- * Frustum plane's normals will point to the inside of the viewing frustum,
- * as required by this class.
- * </p>
- * <p>
- * Usually called by {@link Frustum#updateFrustumPlanes(Matrix4f)}.
- * </p>
- */
- 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;
- }
- }
-
- /**
- * Set this matrix to the <i>look-at</i> matrix based on given parameters.
- * <p>
- * Consist out of two matrix multiplications:
- * <pre>
- * <b>R</b> = <b>L</b> x <b>T</b>,
- * with <b>L</b> for <i>look-at</i> matrix and
- * <b>T</b> for eye translation.
- *
- * Result <b>R</b> can be utilized for <i>projection or modelview</i> multiplication, i.e.
- * <b>M</b> = <b>M</b> x <b>R</b>,
- * with <b>M</b> being the <i>projection or modelview</i> matrix.
- * </pre>
- * </p>
- * @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() ) );
- }
-
- /**
- * Set this matrix to the <i>pick</i> matrix based on given parameters.
- * <p>
- * Traditional <code>gluPickMatrix</code> implementation.
- * </p>
- * <p>
- * Consist out of two matrix multiplications:
- * <pre>
- * <b>R</b> = <b>T</b> x <b>S</b>,
- * with <b>T</b> for viewport translation matrix and
- * <b>S</b> for viewport scale matrix.
- *
- * Result <b>R</b> can be utilized for <i>projection</i> multiplication, i.e.
- * <b>P</b> = <b>P</b> x <b>R</b>,
- * with <b>P</b> being the <i>projection</i> matrix.
- * </pre>
- * </p>
- * <p>
- * To effectively use the generated pick matrix for picking,
- * call {@link #setToPick(float, float, float, float, Recti, Matrix4f) setToPick(..)}
- * and multiply a {@link #setToPerspective(float, float, float, float) custom perspective matrix}
- * by this pick matrix. Then you may load the result onto the perspective matrix stack.
- * </p>
- * @param x the center x-component of a picking region in window coordinates
- * @param y the center y-component of a picking region in window coordinates
- * @param deltaX the width of the picking region in window coordinates.
- * @param deltaY the height of the picking region in window coordinates.
- * @param viewport Rect4i viewport
- * @param mat4Tmp temp storage
- * @return this matrix for chaining or {@code null} if either delta value is <= zero.
- */
- public Matrix4f setToPick(final float x, final float y, final float deltaX, final float deltaY,
- final Recti viewport, final Matrix4f mat4Tmp) {
- if (deltaX <= 0 || deltaY <= 0) {
- return null;
- }
- /* Translate and scale the picked region to the entire window */
- setToTranslation( ( viewport.width() - 2 * ( x - viewport.x() ) ) / deltaX,
- ( viewport.height() - 2 * ( y - viewport.y() ) ) / deltaY,
- 0);
- mat4Tmp.setToScale( viewport.width() / deltaX, viewport.height() / deltaY, 1.0f );
- return mul(mat4Tmp);
- }
-
- //
- // 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 <a href="http://web.archive.org/web/20041029003853/http://www.j3d.org/matrix_faq/matrfaq_latest.html#Q38">Matrix-FAQ Q38</a>
- * @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 <a href="http://web.archive.org/web/20041029003853/http://www.j3d.org/matrix_faq/matrfaq_latest.html#Q38">Matrix-FAQ Q38</a>
- * @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)}.
- * <p>
- * Implementation considers following corner cases:
- * <ul>
- * <li>NaN == NaN</li>
- * <li>+Inf == +Inf</li>
- * <li>-Inf == -Inf</li>
- * </ul>
- * @param o comparison value
- * @param epsilon consider using {@link FloatUtil#EPSILON}
- * @return true if all components differ less than {@code epsilon}, otherwise false.
- */
- public boolean isEqual(final Matrix4f o, final float epsilon) {
- if( this == o ) {
- return true;
- } else {
- return FloatUtil.isEqual(m00, o.m00, epsilon) &&
- FloatUtil.isEqual(m01, o.m01, epsilon) &&
- FloatUtil.isEqual(m02, o.m02, epsilon) &&
- FloatUtil.isEqual(m03, o.m03, epsilon) &&
- FloatUtil.isEqual(m10, o.m10, epsilon) &&
- FloatUtil.isEqual(m11, o.m11, epsilon) &&
- FloatUtil.isEqual(m12, o.m12, epsilon) &&
- FloatUtil.isEqual(m13, o.m13, epsilon) &&
- FloatUtil.isEqual(m20, o.m20, epsilon) &&
- FloatUtil.isEqual(m21, o.m21, epsilon) &&
- FloatUtil.isEqual(m22, o.m22, epsilon) &&
- FloatUtil.isEqual(m23, o.m23, epsilon) &&
- FloatUtil.isEqual(m30, o.m30, epsilon) &&
- FloatUtil.isEqual(m31, o.m31, epsilon) &&
- FloatUtil.isEqual(m32, o.m32, epsilon) &&
- FloatUtil.isEqual(m33, o.m33, epsilon);
- }
- }
-
- /**
- * Equals check using {@link FloatUtil#EPSILON} value and {@link FloatUtil#isEqual(float, float, float)}.
- * <p>
- * Implementation considers following corner cases:
- * <ul>
- * <li>NaN == NaN</li>
- * <li>+Inf == +Inf</li>
- * <li>-Inf == -Inf</li>
- * </ul>
- * @param o comparison value
- * @return true if all components differ less than {@link FloatUtil#EPSILON}, otherwise false.
- */
- public boolean isEqual(final Matrix4f o) {
- return isEqual(o, FloatUtil.EPSILON);
- }
-
- @Override
- public boolean equals(final Object o) {
- if( o instanceof Matrix4f ) {
- return isEqual((Matrix4f)o, FloatUtil.EPSILON);
- } else {
- return false;
- }
- }
-
- //
- // Static multi Matrix ops
- //
-
- /**
- * Map object coordinates to window coordinates.
- * <p>
- * Traditional <code>gluProject</code> implementation.
- * </p>
- *
- * @param obj object position, 3 component vector
- * @param mMv modelview matrix
- * @param mP projection matrix
- * @param viewport Rect4i viewport
- * @param winPos 3 component window coordinate, the result
- * @return true if successful, otherwise false (z is 1)
- */
- public static boolean mapObjToWin(final Vec3f obj, final Matrix4f mMv, final Matrix4f mP,
- final Recti viewport, final Vec3f winPos)
- {
- final Vec4f vec4Tmp1 = new Vec4f(obj, 1f);
-
- // vec4Tmp2 = Mv * o
- // rawWinPos = P * vec4Tmp2
- // rawWinPos = P * ( Mv * o )
- // rawWinPos = P * Mv * o
- final Vec4f vec4Tmp2 = mMv.mulVec4f(vec4Tmp1, new Vec4f());
- final Vec4f rawWinPos = mP.mulVec4f(vec4Tmp2, vec4Tmp1);
-
- if (rawWinPos.w() == 0.0f) {
- return false;
- }
-
- final float s = ( 1.0f / rawWinPos.w() ) * 0.5f;
-
- // Map x, y and z to range 0-1 (w is ignored)
- rawWinPos.scale(s).add(0.5f, 0.5f, 0.5f, 0f);
-
- // Map x,y to viewport
- winPos.set( rawWinPos.x() * viewport.width() + viewport.x(),
- rawWinPos.y() * viewport.height() + viewport.y(),
- rawWinPos.z() );
-
- return true;
- }
-
- /**
- * Map object coordinates to window coordinates.
- * <p>
- * Traditional <code>gluProject</code> implementation.
- * </p>
- *
- * @param obj object position, 3 component vector
- * @param mPMv [projection] x [modelview] matrix, i.e. P x Mv
- * @param viewport Rect4i viewport
- * @param winPos 3 component window coordinate, the result
- * @return true if successful, otherwise false (z is 1)
- */
- public static boolean mapObjToWin(final Vec3f obj, final Matrix4f mPMv,
- final Recti viewport, final Vec3f winPos)
- {
- final Vec4f vec4Tmp2 = new Vec4f(obj, 1f);
-
- // rawWinPos = P * Mv * o
- final Vec4f rawWinPos = mPMv.mulVec4f(vec4Tmp2, new Vec4f());
-
- if (rawWinPos.w() == 0.0f) {
- return false;
- }
-
- final float s = ( 1.0f / rawWinPos.w() ) * 0.5f;
-
- // Map x, y and z to range 0-1 (w is ignored)
- rawWinPos.scale(s).add(0.5f, 0.5f, 0.5f, 0f);
-
- // Map x,y to viewport
- winPos.set( rawWinPos.x() * viewport.width() + viewport.x(),
- rawWinPos.y() * viewport.height() + viewport.y(),
- rawWinPos.z() );
-
- return true;
- }
-
- /**
- * Map window coordinates to object coordinates.
- * <p>
- * Traditional <code>gluUnProject</code> implementation.
- * </p>
- *
- * @param winx
- * @param winy
- * @param winz
- * @param mMv 4x4 modelview matrix
- * @param mP 4x4 projection matrix
- * @param viewport Rect4i viewport
- * @param objPos 3 component object coordinate, the result
- * @param mat4Tmp 16 component matrix for temp storage
- * @return true if successful, otherwise false (failed to invert matrix, or becomes infinity due to zero z)
- */
- public static boolean mapWinToObj(final float winx, final float winy, final float winz,
- final Matrix4f mMv, final Matrix4f mP,
- final Recti viewport,
- final Vec3f objPos,
- final Matrix4f mat4Tmp)
- {
- // invPMv = Inv(P x Mv)
- final Matrix4f invPMv = mat4Tmp.mul(mP, mMv);
- if( !invPMv.invert() ) {
- return false;
- }
-
- final Vec4f winPos = new Vec4f(winx, winy, winz, 1f);
-
- // Map x and y from window coordinates
- winPos.add(-viewport.x(), -viewport.y(), 0f, 0f).scale(1f/viewport.width(), 1f/viewport.height(), 1f, 1f);
-
- // Map to range -1 to 1
- winPos.scale(2f, 2f, 2f, 1f).add(-1f, -1f, -1f, 0f);
-
- // rawObjPos = Inv(P x Mv) * winPos
- final Vec4f rawObjPos = invPMv.mulVec4f(winPos, new Vec4f());
-
- if ( rawObjPos.w() == 0.0f ) {
- return false;
- }
- objPos.set( rawObjPos.scale( 1f / rawObjPos.w() ) );
-
- return true;
- }
-
- /**
- * Map window coordinates to object coordinates.
- * <p>
- * Traditional <code>gluUnProject</code> implementation.
- * </p>
- *
- * @param winx
- * @param winy
- * @param winz
- * @param invPMv inverse [projection] x [modelview] matrix, i.e. Inv(P x Mv), if null method returns false
- * @param viewport Rect4i viewport
- * @param objPos 3 component object coordinate, the result
- * @return true if successful, otherwise false (null invert matrix, or becomes infinity due to zero z)
- */
- public static boolean mapWinToObj(final float winx, final float winy, final float winz,
- final Matrix4f invPMv,
- final Recti viewport,
- final Vec3f objPos)
- {
- if( null == invPMv ) {
- return false;
- }
- final Vec4f winPos = new Vec4f(winx, winy, winz, 1f);
-
- // Map x and y from window coordinates
- winPos.add(-viewport.x(), -viewport.y(), 0f, 0f).scale(1f/viewport.width(), 1f/viewport.height(), 1f, 1f);
-
- // Map to range -1 to 1
- winPos.scale(2f, 2f, 2f, 1f).add(-1f, -1f, -1f, 0f);
-
- // rawObjPos = Inv(P x Mv) * winPos
- final Vec4f rawObjPos = invPMv.mulVec4f(winPos, new Vec4f());
-
- if ( rawObjPos.w() == 0.0f ) {
- return false;
- }
- objPos.set( rawObjPos.scale( 1f / rawObjPos.w() ) );
-
- return true;
- }
-
- /**
- * Map two window coordinates to two object coordinates,
- * distinguished by their z component.
- * <p>
- * Traditional <code>gluUnProject</code> implementation.
- * </p>
- *
- * @param winx
- * @param winy
- * @param winz1
- * @param winz2
- * @param invPMv inverse [projection] x [modelview] matrix, i.e. Inv(P x Mv), if null method returns false
- * @param viewport Rect4i viewport vector
- * @param objPos1 3 component object coordinate, the result
- * @return true if successful, otherwise false (null invert matrix, or becomes infinity due to zero z)
- */
- public static boolean mapWinToObj(final float winx, final float winy, final float winz1, final float winz2,
- final Matrix4f invPMv,
- final Recti viewport,
- final Vec3f objPos1, final Vec3f objPos2)
- {
- if( null == invPMv ) {
- return false;
- }
- final Vec4f winPos = new Vec4f(winx, winy, winz1, 1f);
-
- // Map x and y from window coordinates
- winPos.add(-viewport.x(), -viewport.y(), 0f, 0f).scale(1f/viewport.width(), 1f/viewport.height(), 1f, 1f);
-
- // Map to range -1 to 1
- winPos.scale(2f, 2f, 2f, 1f).add(-1f, -1f, -1f, 0f);
-
- // rawObjPos = Inv(P x Mv) * winPos1
- final Vec4f rawObjPos = invPMv.mulVec4f(winPos, new Vec4f());
-
- if ( rawObjPos.w() == 0.0f ) {
- return false;
- }
- objPos1.set( rawObjPos.scale( 1f / rawObjPos.w() ) );
-
- //
- // winz2
- //
- // Map Z to range -1 to 1
- winPos.setZ( winz2 * 2f - 1f );
-
- // rawObjPos = Inv(P x Mv) * winPos2
- invPMv.mulVec4f(winPos, rawObjPos);
-
- if ( rawObjPos.w() == 0.0f ) {
- return false;
- }
- objPos2.set( rawObjPos.scale( 1f / rawObjPos.w() ) );
-
- return true;
- }
-
- /**
- * Map window coordinates to object coordinates.
- * <p>
- * Traditional <code>gluUnProject4</code> implementation.
- * </p>
- *
- * @param winx
- * @param winy
- * @param winz
- * @param clipw
- * @param mMv 4x4 modelview matrix
- * @param mP 4x4 projection matrix
- * @param viewport Rect4i viewport vector
- * @param near
- * @param far
- * @param obj_pos 4 component object coordinate, the result
- * @param mat4Tmp 16 component matrix for temp storage
- * @return true if successful, otherwise false (failed to invert matrix, or becomes infinity due to zero z)
- */
- public static boolean mapWinToObj4(final float winx, final float winy, final float winz, final float clipw,
- final Matrix4f mMv, final Matrix4f mP,
- final Recti viewport,
- final float near, final float far,
- final Vec4f objPos,
- final Matrix4f mat4Tmp)
- {
- // invPMv = Inv(P x Mv)
- final Matrix4f invPMv = mat4Tmp.mul(mP, mMv);
- if( !invPMv.invert() ) {
- return false;
- }
-
- final Vec4f winPos = new Vec4f(winx, winy, winz, clipw);
-
- // Map x and y from window coordinates
- winPos.add(-viewport.x(), -viewport.y(), -near, 0f).scale(1f/viewport.width(), 1f/viewport.height(), 1f/(far-near), 1f);
-
- // Map to range -1 to 1
- winPos.scale(2f, 2f, 2f, 1f).add(-1f, -1f, -1f, 0f);
-
- // objPos = Inv(P x Mv) * winPos
- invPMv.mulVec4f(winPos, objPos);
-
- if ( objPos.w() == 0.0f ) {
- return false;
- }
- return true;
- }
-
- /**
- * Map window coordinates to object coordinates.
- * <p>
- * Traditional <code>gluUnProject4</code> implementation.
- * </p>
- *
- * @param winx
- * @param winy
- * @param winz
- * @param clipw
- * @param invPMv inverse [projection] x [modelview] matrix, i.e. Inv(P x Mv), if null method returns false
- * @param viewport Rect4i viewport vector
- * @param near
- * @param far
- * @param obj_pos 4 component object coordinate, the result
- * @return true if successful, otherwise false (null invert matrix, or becomes infinity due to zero z)
- */
- public static boolean mapWinToObj4(final float winx, final float winy, final float winz, final float clipw,
- final Matrix4f invPMv,
- final Recti viewport,
- final float near, final float far,
- final Vec4f objPos)
- {
- if( null == invPMv ) {
- return false;
- }
- final Vec4f winPos = new Vec4f(winx, winy, winz, clipw);
-
- // Map x and y from window coordinates
- winPos.add(-viewport.x(), -viewport.y(), -near, 0f).scale(1f/viewport.width(), 1f/viewport.height(), 1f/(far-near), 1f);
-
- // Map to range -1 to 1
- winPos.scale(2f, 2f, 2f, 1f).add(-1f, -1f, -1f, 0f);
-
- // objPos = Inv(P x Mv) * winPos
- invPMv.mulVec4f(winPos, objPos);
-
- if ( objPos.w() == 0.0f ) {
- return false;
- }
- return true;
- }
-
- /**
- * Map two window coordinates w/ shared X/Y and distinctive Z
- * to a {@link Ray}. The resulting {@link Ray} maybe used for <i>picking</i>
- * using a {@link AABBox#getRayIntersection(Vec3f, Ray, float, boolean)}.
- * <p>
- * Notes for picking <i>winz0</i> and <i>winz1</i>:
- * <ul>
- * <li>see {@link FloatUtil#getZBufferEpsilon(int, float, float)}</li>
- * <li>see {@link FloatUtil#getZBufferValue(int, float, float, float)}</li>
- * <li>see {@link FloatUtil#getOrthoWinZ(float, float, float)}</li>
- * </ul>
- * </p>
- * @param winx
- * @param winy
- * @param winz0
- * @param winz1
- * @param mMv 4x4 modelview matrix
- * @param mP 4x4 projection matrix
- * @param viewport Rect4i viewport
- * @param ray storage for the resulting {@link Ray}
- * @param mat4Tmp1 16 component matrix for temp storage
- * @param mat4Tmp2 16 component matrix for temp storage
- * @return true if successful, otherwise false (failed to invert matrix, or becomes z is infinity)
- */
- public static boolean mapWinToRay(final float winx, final float winy, final float winz0, final float winz1,
- final Matrix4f mMv, final Matrix4f mP,
- final Recti viewport,
- final Ray ray,
- final Matrix4f mat4Tmp1, final Matrix4f mat4Tmp2) {
- // invPMv = Inv(P x Mv)
- final Matrix4f invPMv = mat4Tmp1.mul(mP, mMv);
- if( !invPMv.invert() ) {
- return false;
- }
-
- if( mapWinToObj(winx, winy, winz0, winz1, invPMv, viewport, ray.orig, ray.dir) ) {
- ray.dir.sub(ray.orig).normalize();
- return true;
- } else {
- return false;
- }
- }
-
- /**
- * Map two window coordinates w/ shared X/Y and distinctive Z
- * to a {@link Ray}. The resulting {@link Ray} maybe used for <i>picking</i>
- * using a {@link AABBox#getRayIntersection(Vec3f, Ray, float, boolean)}.
- * <p>
- * Notes for picking <i>winz0</i> and <i>winz1</i>:
- * <ul>
- * <li>see {@link FloatUtil#getZBufferEpsilon(int, float, float)}</li>
- * <li>see {@link FloatUtil#getZBufferValue(int, float, float, float)}</li>
- * <li>see {@link FloatUtil#getOrthoWinZ(float, float, float)}</li>
- * </ul>
- * </p>
- * @param winx
- * @param winy
- * @param winz0
- * @param winz1
- * @param invPMv inverse [projection] x [modelview] matrix, i.e. Inv(P x Mv), if null method returns false
- * @param viewport Rect4i viewport
- * @param ray storage for the resulting {@link Ray}
- * @return true if successful, otherwise false (null invert matrix, or becomes z is infinity)
- */
- public static boolean mapWinToRay(final float winx, final float winy, final float winz0, final float winz1,
- final Matrix4f invPMv,
- final Recti viewport,
- final Ray ray) {
- if( mapWinToObj(winx, winy, winz0, winz1, invPMv, viewport, ray.orig, ray.dir) ) {
- ray.dir.sub(ray.orig).normalize();
- return true;
- } else {
- return false;
- }
- }
-
- //
- // String and internals
- //
-
- /**
- * @param sb optional passed StringBuilder instance to be used
- * @param rowPrefix optional prefix for each row
- * @param f the format string of one floating point, i.e. "%10.5f", see {@link java.util.Formatter}
- * @return matrix string representation
- */
- public StringBuilder toString(final StringBuilder sb, final String rowPrefix, final String f) {
- final float[] tmp = new float[16];
- this.get(tmp);
- return FloatUtil.matrixToString(sb, rowPrefix, f,tmp, 0, 4, 4, false /* rowMajorOrder */);
- }
-
- @Override
- public String toString() {
- return toString(null, null, "%10.5f").toString();
- }
-
- private float m00, m10, m20, m30;
- private float m01, m11, m21, m31;
- private float m02, m12, m22, m32;
- private float m03, m13, m23, m33;
-
- final Stack stack = new Stack(0, 16*16); // start w/ zero size, growSize is half GL-min size (32)
-
- private static class Stack {
- private int position;
- private float[] buffer;
- private final int growSize;
-
- /**
- * @param initialSize initial size
- * @param growSize grow size if {@link #position()} is reached, maybe <code>0</code>
- * 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;
- }
- }
-}