Math: Complete Matrix4f w/ Vec[234]f and adopt it throughout Quaternion, Ray, AABBox, Frustum, Stereo*, ... adding hook to PMVMatrix

Motivation was to simplify matrix + vector math usage, ease review and avoid usage bugs.

Matrix4f implementation uses dedicated float fields instead of an array.

Performance didn't increase much,
as JVM >= 11(?) has some optimizations to drop the array bounds check.

AMD64 + OpenJDK17
- Matrix4f.mul(a, b) got a roughly ~10% enhancement over FloatUtil.multMatrix(a, b, dest)
- Matrix4f.mul(b) roughly ~3% slower than FloatUtil.multMatrix(a, b, dest)
- FloatUtil.multMatrix(a, a_off, b, b_off, dest) is considerable slower than all
- Matrix4f.invert(..) roughly ~3% slower than FloatUtil.invertMatrix(..)

RaspberryPi 4b aarch64 + OpenJDK17
- Matrix4f.mul(a, b) got a roughly ~10% enhancement over FloatUtil.multMatrix(a, b, dest)
- Matrix4f.mul(b) roughly ~20% slower than FloatUtil.multMatrix(a, b)
- FloatUtil.multMatrix(a, a_off, b, b_off, dest) is considerable slower than all
- Matrix4f.invert(..) roughly ~4% slower than FloatUtil.invertMatrix(..)

Conclusion
- Matrix4f.mul(b) needs to be revised (esp for aarch64)
- Matrix4f.invert(..) should also not be slower ..

5 files changed, 95 insertions, 72 deletions

diff --git a/src/demos/com/jogamp/opengl/demos/av/MovieSBSStereo.java b/src/demos/com/jogamp/opengl/demos/av/MovieSBSStereo.java
index 3a59216d5..3a0955a05 100644
--- a/src/demos/com/jogamp/opengl/demos/av/MovieSBSStereo.java
+++ b/src/demos/com/jogamp/opengl/demos/av/MovieSBSStereo.java
@@ -61,9 +61,9 @@ import com.jogamp.opengl.GLExtensions;
 import com.jogamp.opengl.GLProfile;
 import com.jogamp.opengl.JoglVersion;
 import com.jogamp.opengl.demos.graph.TextRendererGLELBase;
-import com.jogamp.opengl.math.FloatUtil;
+import com.jogamp.opengl.math.Matrix4f;
 import com.jogamp.opengl.math.Quaternion;
-import com.jogamp.opengl.math.VectorUtil;
+import com.jogamp.opengl.math.Vec3f;
 import com.jogamp.opengl.util.CustomGLEventListener;
 import com.jogamp.opengl.util.GLArrayDataServer;
 import com.jogamp.opengl.util.PMVMatrix;
@@ -641,15 +641,15 @@ public class MovieSBSStereo implements StereoGLEventListener {
         pmvMatrix.glTranslatef(0, 0, zoom0);
     }
 
-    private final float[] mat4Tmp1 = new float[16];
-    private final float[] mat4Tmp2 = new float[16];
-    private final float[] vec3Tmp1 = new float[3];
-    private final float[] vec3Tmp2 = new float[3];
-    private final float[] vec3Tmp3 = new float[3];
+    private final Matrix4f mat4Tmp1 = new Matrix4f();
+    private final Matrix4f mat4Tmp2 = new Matrix4f();
+    private final Vec3f vec3Tmp1 = new Vec3f();
+    private final Vec3f vec3Tmp2 = new Vec3f();
+    private final Vec3f vec3Tmp3 = new Vec3f();
 
     GLArrayDataServer interleavedVBOCurrent = null;
 
-    private static final float[] vec3ScalePos = new float[] { 4f, 4f, 4f };
+    private static final float scalePos = 4f;
 
     @Override
     public void reshapeForEye(final GLAutoDrawable drawable, final int x, final int y, final int width, final int height,
@@ -663,26 +663,38 @@ public class MovieSBSStereo implements StereoGLEventListener {
         if(null == mPlayer) { return; }
         if(null == st) { return; }
 
-        pmvMatrix.glMatrixMode(GLMatrixFunc.GL_PROJECTION);
-        final float[] mat4Projection = FloatUtil.makePerspective(mat4Tmp1, 0, true, eyeParam.fovhv, zNear, zFar);
-        pmvMatrix.glLoadMatrixf(mat4Projection, 0);
-
-        pmvMatrix.glMatrixMode(GLMatrixFunc.GL_MODELVIEW);
-        final Quaternion rollPitchYaw = new Quaternion();
-        final float[] shiftedEyePos = rollPitchYaw.rotateVector(vec3Tmp1, 0, viewerPose.position, 0);
-        VectorUtil.scaleVec3(shiftedEyePos, shiftedEyePos, vec3ScalePos); // amplify viewerPose position
-        VectorUtil.addVec3(shiftedEyePos, shiftedEyePos, eyeParam.positionOffset);
-
-        rollPitchYaw.mult(viewerPose.orientation);
-        final float[] up = rollPitchYaw.rotateVector(vec3Tmp2, 0, VectorUtil.VEC3_UNIT_Y, 0);
-        final float[] forward = rollPitchYaw.rotateVector(vec3Tmp3, 0, VectorUtil.VEC3_UNIT_Z_NEG, 0);
-        final float[] center = VectorUtil.addVec3(forward, shiftedEyePos, forward);
-
-        final float[] mLookAt = FloatUtil.makeLookAt(mat4Tmp1, 0, shiftedEyePos, 0, center, 0, up, 0, mat4Tmp2);
-        final float[] mViewAdjust = FloatUtil.makeTranslation(mat4Tmp2, true, eyeParam.distNoseToPupilX, eyeParam.distMiddleToPupilY, eyeParam.eyeReliefZ);
-        final float[] mat4Modelview = FloatUtil.multMatrix(mViewAdjust, mLookAt);
-        pmvMatrix.glLoadMatrixf(mat4Modelview, 0);
-        pmvMatrix.glTranslatef(0, 0, zoom0);
+        {
+            //
+            // Projection
+            //
+            final Matrix4f mat4 = new Matrix4f();
+            pmvMatrix.glMatrixMode(GLMatrixFunc.GL_PROJECTION);
+            mat4.setToPerspective(eyeParam.fovhv, zNear, zFar);
+            pmvMatrix.glLoadMatrixf(mat4);
+
+            //
+            // Modelview
+            //
+            pmvMatrix.glMatrixMode(GLMatrixFunc.GL_MODELVIEW);
+            final Quaternion rollPitchYaw = new Quaternion();
+            // private final float eyeYaw = FloatUtil.PI; // 180 degrees in radians
+            // rollPitchYaw.rotateByAngleY(eyeYaw);
+            final Vec3f shiftedEyePos = rollPitchYaw.rotateVector(viewerPose.position, vec3Tmp1);
+            shiftedEyePos.scale(scalePos); // amplify viewerPose position
+            shiftedEyePos.add(eyeParam.positionOffset);
+
+            rollPitchYaw.mult(viewerPose.orientation);
+            final Vec3f up = rollPitchYaw.rotateVector(Vec3f.UNIT_Y, vec3Tmp2);
+            final Vec3f forward = rollPitchYaw.rotateVector(Vec3f.UNIT_Z_NEG, vec3Tmp3); // -> center
+            final Vec3f center = forward.add(shiftedEyePos);
+
+            final Matrix4f mLookAt = mat4Tmp2.setToLookAt(shiftedEyePos, center, up, mat4Tmp1);
+            mat4.mul( mat4Tmp1.setToTranslation( eyeParam.distNoseToPupilX,
+                                                 eyeParam.distMiddleToPupilY,
+                                                 eyeParam.eyeReliefZ ), mLookAt);
+            mat4.translate(0, 0, zoom0, mat4Tmp1);
+            pmvMatrix.glLoadMatrixf(mat4);
+        }
         st.useProgram(gl, true);
         st.uniform(gl, pmvMatrixUniform);
         st.useProgram(gl, false);
diff --git a/src/demos/com/jogamp/opengl/demos/av/StereoDemo01.java b/src/demos/com/jogamp/opengl/demos/av/StereoDemo01.java
index 88a49a09a..139c9f140 100644
--- a/src/demos/com/jogamp/opengl/demos/av/StereoDemo01.java
+++ b/src/demos/com/jogamp/opengl/demos/av/StereoDemo01.java
@@ -52,6 +52,7 @@ import com.jogamp.newt.event.KeyEvent;
 import com.jogamp.newt.opengl.GLWindow;
 import com.jogamp.newt.opengl.util.stereo.StereoDeviceUtil;
 import com.jogamp.opengl.math.FovHVHalves;
+import com.jogamp.opengl.math.Vec3f;
 import com.jogamp.opengl.util.Animator;
 import com.jogamp.opengl.util.AnimatorBase;
 import com.jogamp.opengl.util.av.GLMediaPlayer;
@@ -289,9 +290,9 @@ public class StereoDemo01 {
         }
 
         final boolean usesLenses = 0 != ( StereoDeviceRenderer.DISTORTION_BARREL & stereoDevice.getMinimumDistortionBits() );
-        final float[] eyePositionOffset = null != movieSimple && usesLenses ? new float[] { 0f, 0.3f, 0f }                // better fixed movie position w/ lenses
-                                                                            : stereoDevice.getDefaultEyePositionOffset(); // default
-        System.err.println("Eye Position Offset: "+Arrays.toString(eyePositionOffset));
+        final Vec3f eyePositionOffset = null != movieSimple && usesLenses ? new Vec3f( 0f, 0.3f, 0f )                     // better fixed movie position w/ lenses
+                                                                          : stereoDevice.getDefaultEyePositionOffset(); // default
+        System.err.println("Eye Position Offset: "+eyePositionOffset);
 
         final int textureUnit = 0;
         final int reqDistortionBits;
@@ -382,7 +383,7 @@ public class StereoDemo01 {
         System.err.println("Window.1.surfaceSize: "+window.getSurfaceWidth()+" x "+window.getSurfaceHeight());
 
         if( useAnimator ) {
-            animator.setUpdateFPSFrames(60, System.err);
+            animator.setUpdateFPSFrames(60*10, System.err);
         }
 
         final long t0 = System.currentTimeMillis();
diff --git a/src/demos/com/jogamp/opengl/demos/es2/GearsES2.java b/src/demos/com/jogamp/opengl/demos/es2/GearsES2.java
index 02c451e9f..5ad6ede76 100644
--- a/src/demos/com/jogamp/opengl/demos/es2/GearsES2.java
+++ b/src/demos/com/jogamp/opengl/demos/es2/GearsES2.java
@@ -33,9 +33,9 @@ import com.jogamp.newt.event.GestureHandler.GestureEvent;
 import com.jogamp.opengl.GLRendererQuirks;
 import com.jogamp.opengl.JoglVersion;
 import com.jogamp.opengl.demos.GearsObject;
-import com.jogamp.opengl.math.FloatUtil;
+import com.jogamp.opengl.math.Matrix4f;
 import com.jogamp.opengl.math.Quaternion;
-import com.jogamp.opengl.math.VectorUtil;
+import com.jogamp.opengl.math.Vec3f;
 import com.jogamp.opengl.util.CustomGLEventListener;
 import com.jogamp.opengl.util.PMVMatrix;
 import com.jogamp.opengl.util.TileRendererBase;
@@ -397,49 +397,58 @@ public class GearsES2 implements StereoGLEventListener, TileRendererBase.TileRen
     }
     // private boolean useAndroidDebug = false;
 
-    private final float[] mat4Tmp1 = new float[16];
-    private final float[] mat4Tmp2 = new float[16];
-    private final float[] vec3Tmp1 = new float[3];
-    private final float[] vec3Tmp2 = new float[3];
-    private final float[] vec3Tmp3 = new float[3];
+    private final Matrix4f mat4Tmp1 = new Matrix4f();
+    private final Matrix4f mat4Tmp2 = new Matrix4f();
+    private final Vec3f vec3Tmp1 = new Vec3f();
+    private final Vec3f vec3Tmp2 = new Vec3f();
+    private final Vec3f vec3Tmp3 = new Vec3f();
 
-    private static final float[] vec3ScalePos = new float[] { 20f, 20f, 20f };
+    private static final float scalePos = 20f;
 
     @Override
     public void reshapeForEye(final GLAutoDrawable drawable, final int x, final int y, final int width, final int height,
                               final EyeParameter eyeParam, final ViewerPose viewerPose) {
         final GL2ES2 gl = drawable.getGL().getGL2ES2();
-        pmvMatrix.glMatrixMode(GLMatrixFunc.GL_PROJECTION);
-        final float[] mat4Projection = FloatUtil.makePerspective(mat4Tmp1, 0, true, eyeParam.fovhv, zNear, zFar);
-        if( flipVerticalInGLOrientation && gl.getContext().getGLDrawable().isGLOriented() ) {
-            pmvMatrix.glLoadIdentity();
-            pmvMatrix.glScalef(1f, -1f, 1f);
-            pmvMatrix.glMultMatrixf(mat4Projection, 0);
-        } else {
-            pmvMatrix.glLoadMatrixf(mat4Projection, 0);
-        }
-
-        pmvMatrix.glMatrixMode(GLMatrixFunc.GL_MODELVIEW);
 
-        final Quaternion rollPitchYaw = new Quaternion();
-        // private final float eyeYaw = FloatUtil.PI; // 180 degrees in radians
-        // rollPitchYaw.rotateByAngleY(eyeYaw);
-        // final float[] shiftedEyePos = rollPitchYaw.rotateVector(vec3Tmp1, 0, viewerPose.position, 0);
-        final float[] shiftedEyePos = VectorUtil.copyVec3(vec3Tmp1, 0, viewerPose.position, 0);
-        VectorUtil.scaleVec3(shiftedEyePos, shiftedEyePos, vec3ScalePos); // amplify viewerPose position
-        VectorUtil.addVec3(shiftedEyePos, shiftedEyePos, eyeParam.positionOffset);
-
-        rollPitchYaw.mult(viewerPose.orientation);
-        final float[] up = rollPitchYaw.rotateVector(vec3Tmp2, 0, VectorUtil.VEC3_UNIT_Y, 0);
-        final float[] forward = rollPitchYaw.rotateVector(vec3Tmp3, 0, VectorUtil.VEC3_UNIT_Z_NEG, 0);
-        final float[] center = VectorUtil.addVec3(forward, shiftedEyePos, forward);
-
-        final float[] mLookAt = FloatUtil.makeLookAt(mat4Tmp1, 0, shiftedEyePos, 0, center, 0, up, 0, mat4Tmp2);
-        final float[] mViewAdjust = FloatUtil.makeTranslation(mat4Tmp2, true, eyeParam.distNoseToPupilX, eyeParam.distMiddleToPupilY, eyeParam.eyeReliefZ);
-        final float[] mat4Modelview = FloatUtil.multMatrix(mViewAdjust, mLookAt);
-
-        pmvMatrix.glLoadMatrixf(mat4Modelview, 0);
-        pmvMatrix.glTranslatef(0.0f, 0.0f, -zViewDist);
+        {
+            //
+            // Projection
+            //
+            final Matrix4f mat4 = new Matrix4f();
+            pmvMatrix.glMatrixMode(GLMatrixFunc.GL_PROJECTION);
+            if( flipVerticalInGLOrientation && gl.getContext().getGLDrawable().isGLOriented() ) {
+                mat4Tmp1.setToScale(1f, -1f, 1f);
+                mat4Tmp2.setToPerspective(eyeParam.fovhv, zNear, zFar);
+                mat4.mul(mat4Tmp1, mat4Tmp2);
+            } else {
+                mat4.setToPerspective(eyeParam.fovhv, zNear, zFar);
+            }
+            pmvMatrix.glLoadMatrixf(mat4);
+
+            //
+            // Modelview
+            //
+            pmvMatrix.glMatrixMode(GLMatrixFunc.GL_MODELVIEW);
+            final Quaternion rollPitchYaw = new Quaternion();
+            // private final float eyeYaw = FloatUtil.PI; // 180 degrees in radians
+            // rollPitchYaw.rotateByAngleY(eyeYaw);
+            // final Vec3f shiftedEyePos = rollPitchYaw.rotateVector(viewerPose.position, vec3Tmp1);
+            final Vec3f shiftedEyePos = vec3Tmp1.set(viewerPose.position);
+            shiftedEyePos.scale(scalePos); // amplify viewerPose position
+            shiftedEyePos.add(eyeParam.positionOffset);
+
+            rollPitchYaw.mult(viewerPose.orientation);
+            final Vec3f up = rollPitchYaw.rotateVector(Vec3f.UNIT_Y, vec3Tmp2);
+            final Vec3f forward = rollPitchYaw.rotateVector(Vec3f.UNIT_Z_NEG, vec3Tmp3); // -> center
+            final Vec3f center = forward.add(shiftedEyePos);
+
+            final Matrix4f mLookAt = mat4Tmp2.setToLookAt(shiftedEyePos, center, up, mat4Tmp1);
+            mat4.mul( mat4Tmp1.setToTranslation( eyeParam.distNoseToPupilX,
+                                                 eyeParam.distMiddleToPupilY,
+                                                 eyeParam.eyeReliefZ ), mLookAt);
+            mat4.translate(0, 0, -zViewDist, mat4Tmp1);
+            pmvMatrix.glLoadMatrixf(mat4);
+        }
         st.useProgram(gl, true);
         st.uniform(gl, pmvMatrixUniform);
         st.useProgram(gl, false);
diff --git a/src/demos/com/jogamp/opengl/demos/graph/GPUTextNewtDemo.java b/src/demos/com/jogamp/opengl/demos/graph/GPUTextNewtDemo.java
index ad5434b09..5952326c8 100644
--- a/src/demos/com/jogamp/opengl/demos/graph/GPUTextNewtDemo.java
+++ b/src/demos/com/jogamp/opengl/demos/graph/GPUTextNewtDemo.java
@@ -155,7 +155,7 @@ public class GPUTextNewtDemo {
             final AABBox fontNameBox = font2.getMetricBounds(GPUTextRendererListenerBase01.textX1);
             System.err.println("GPU Text Newt Demo: "+font2.fullString());
             System.err.println("GPU Text Newt Demo: screen-dpi: "+sDPI[0]+"x"+sDPI[1]+", font "+font_ptpi+" pt, "+font_ppi+" pixel");
-            System.err.println("GPU Text Newt Demo: textX2: "+fontNameBox+" em, "+fontNameBox.scale(font_ppi, new float[3])+" px");
+            System.err.println("GPU Text Newt Demo: textX2: "+fontNameBox+" em, "+fontNameBox.scale(font_ppi)+" px");
             final MonitorDevice monitor = window.getMainMonitor();
             System.err.println("GPU Text Newt Demo: "+monitor);
             // window.setSurfaceSize((int)(fontNameBox.getWidth()*1.1f), (int)(fontNameBox.getHeight()*2f));
diff --git a/src/demos/com/jogamp/opengl/demos/graph/GPUTextRendererListenerBase01.java b/src/demos/com/jogamp/opengl/demos/graph/GPUTextRendererListenerBase01.java
index dadbcd373..cab25b83d 100644
--- a/src/demos/com/jogamp/opengl/demos/graph/GPUTextRendererListenerBase01.java
+++ b/src/demos/com/jogamp/opengl/demos/graph/GPUTextRendererListenerBase01.java
@@ -51,6 +51,7 @@ import com.jogamp.newt.Window;
 import com.jogamp.newt.event.KeyEvent;
 import com.jogamp.newt.event.KeyListener;
 import com.jogamp.newt.opengl.GLWindow;
+import com.jogamp.opengl.math.Vec3f;
 import com.jogamp.opengl.math.geom.AABBox;
 import com.jogamp.opengl.util.PMVMatrix;
 
@@ -491,7 +492,7 @@ public abstract class GPUTextRendererListenerBase01 extends GPURendererListenerB
         System.err.println("Matrix: " + getXTran() + "/" + getYTran() + " x"+getZTran() + " @"+getAngle() +" fontSize "+fontSizeCenter);
         if(bbox) {
             System.err.println("bbox em: "+font.getMetricBounds(text2));
-            System.err.println("bbox px: "+font.getMetricBounds(text2).scale(nearPlaneS * FontScale.toPixels(fontSizeCenter, dpiV), new float[3]));
+            System.err.println("bbox px: "+font.getMetricBounds(text2).scale( nearPlaneS * FontScale.toPixels(fontSizeCenter, dpiV) ) );
         }
     }