Merge pull request #1759 from mesilliac/fix_matrix_rotation_decompose

Fix Matrix4x4t Decompose to rotation vector.

include/assimp/matrix4x4.inl

@@ -424,12 +424,18 @@ inline void aiMatrix4x4t<TReal>::Decompose(aiVector3t<TReal>& pScaling, aiVector
 {
 	ASSIMP_MATRIX4_4_DECOMPOSE_PART;
 
-	/*
-	    |  CE     -CF      D   0 |
-	M = |  BDE+AF -BDF+AE -BC  0 |
-	    | -ADE+BF -ADF+BE  AC  0 |
-	    |  0       0       0   1 |
-
+    /*
+    assuming a right-handed coordinate system
+    and post-multiplication of column vectors,
+    the rotation matrix for an euler XYZ rotation is M = Rz * Ry * Rx.
+    combining gives:
+    
+        |  CE  BDE-AF  ADE+BF  0  |
+    M = |  CF  BDF+AE  ADF-BE  0  |
+        |  -D    CB      AC    0  |
+        |   0     0       0    1  |
+
+    where
 	A = cos(angle_x), B = sin(angle_x);
 	C = cos(angle_y), D = sin(angle_y);
 	E = cos(angle_z), F = sin(angle_z);
@@ -438,20 +444,20 @@ inline void aiMatrix4x4t<TReal>::Decompose(aiVector3t<TReal>& pScaling, aiVector
 	// Use a small epsilon to solve floating-point inaccuracies
     const TReal epsilon = 10e-3f;
 
-	pRotation.y  = std::asin(vCols[2].x);// D. Angle around oY.
+	pRotation.y  = std::asin(-vCols[0].z);// D. Angle around oY.
 
 	TReal C = std::cos(pRotation.y);
 
 	if(std::fabs(C) > epsilon)
 	{
 		// Finding angle around oX.
-		TReal tan_x =  vCols[2].z / C;// A
-		TReal tan_y = -vCols[2].y / C;// B
+		TReal tan_x = vCols[2].z / C;// A
+		TReal tan_y = vCols[1].z / C;// B
 
 		pRotation.x = std::atan2(tan_y, tan_x);
 		// Finding angle around oZ.
-		tan_x =  vCols[0].x / C;// E
-		tan_y = -vCols[1].x / C;// F
+		tan_x = vCols[0].x / C;// E
+		tan_y = vCols[0].y / C;// F
 		pRotation.z = std::atan2(tan_y, tan_x);
 	}
 	else
@@ -459,8 +465,8 @@ inline void aiMatrix4x4t<TReal>::Decompose(aiVector3t<TReal>& pScaling, aiVector
 		pRotation.x = 0;// Set angle around oX to 0. => A == 1, B == 0, C == 0, D == 1.
 
 		// And finding angle around oZ.
-		TReal tan_x = vCols[1].y;// -BDF+AE => E
-		TReal tan_y = vCols[0].y;//  BDE+AF => F
+		TReal tan_x =  vCols[1].y;// BDF+AE => E
+		TReal tan_y = -vCols[1].x;// BDE-AF => F
 
 		pRotation.z = std::atan2(tan_y, tan_x);
 	}