make the dot product linear in the second variable, not the first variable

Eigen/src/Geometry/Hyperplane.h

@@ -71,7 +71,7 @@ public:
     : m_coeffs(n.size()+1)
   {
     normal() = n;
-    offset() = -e.dot(n);
+    offset() = -n.dot(e);
   }
 
   /** Constructs a plane from its normal \a n and distance to the origin \a d
@@ -92,7 +92,7 @@ public:
   {
     Hyperplane result(p0.size());
     result.normal() = (p1 - p0).unitOrthogonal();
-    result.offset() = -result.normal().dot(p0);
+    result.offset() = -p0.dot(result.normal());
     return result;
   }
 
@@ -104,7 +104,7 @@ public:
     EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(VectorType, 3)
     Hyperplane result(p0.size());
     result.normal() = (p2 - p0).cross(p1 - p0).normalized();
-    result.offset() = -result.normal().dot(p0);
+    result.offset() = -p0.dot(result.normal());
     return result;
   }
 
@@ -116,7 +116,7 @@ public:
   explicit Hyperplane(const ParametrizedLine<Scalar, AmbientDimAtCompileTime>& parametrized)
   {
     normal() = parametrized.direction().unitOrthogonal();
-    offset() = -normal().dot(parametrized.origin());
+    offset() = -parametrized.origin().dot(normal());
   }
 
   ~Hyperplane() {}
@@ -133,7 +133,7 @@ public:
   /** \returns the signed distance between the plane \c *this and a point \a p.
     * \sa absDistance()
     */
-  inline Scalar signedDistance(const VectorType& p) const { return p.dot(normal()) + offset(); }
+  inline Scalar signedDistance(const VectorType& p) const { return normal().dot(p) + offset(); }
 
   /** \returns the absolute distance between the plane \c *this and a point \a p.
     * \sa signedDistance()
@@ -231,7 +231,7 @@ public:
                                 TransformTraits traits = Affine)
   {
     transform(t.linear(), traits);
-    offset() -= t.translation().dot(normal());
+    offset() -= normal().dot(t.translation());
     return *this;
   }
 

Eigen/src/Geometry/ParametrizedLine.h

@@ -84,8 +84,8 @@ public:
     */
   RealScalar squaredDistance(const VectorType& p) const
   {
-    VectorType diff = p-origin();
-    return (diff - diff.dot(direction())* direction()).squaredNorm();
+    VectorType diff = p - origin();
+    return (diff - direction().dot(diff) * direction()).squaredNorm();
   }
   /** \returns the distance of a point \a p to its projection onto the line \c *this.
     * \sa squaredDistance()
@@ -94,7 +94,7 @@ public:
 
   /** \returns the projection of a point \a p onto the line \c *this. */
   VectorType projection(const VectorType& p) const
-  { return origin() + (p-origin()).dot(direction()) * direction(); }
+  { return origin() + direction().dot(p-origin()) * direction(); }
 
   Scalar intersection(const Hyperplane<_Scalar, _AmbientDim>& hyperplane);
 
@@ -148,8 +148,8 @@ inline ParametrizedLine<_Scalar, _AmbientDim>::ParametrizedLine(const Hyperplane
 template <typename _Scalar, int _AmbientDim>
 inline _Scalar ParametrizedLine<_Scalar, _AmbientDim>::intersection(const Hyperplane<_Scalar, _AmbientDim>& hyperplane)
 {
-  return -(hyperplane.offset()+origin().dot(hyperplane.normal()))
-          /(direction().dot(hyperplane.normal()));
+  return -(hyperplane.offset()+hyperplane.normal().dot(origin()))
+          / hyperplane.normal().dot(direction());
 }
 
 #endif // EIGEN_PARAMETRIZEDLINE_H

Eigen/src/Geometry/Quaternion.h

@@ -358,7 +358,7 @@ inline Quaternion<Scalar>& Quaternion<Scalar>::setFromTwoVectors(const MatrixBas
 {
   Vector3 v0 = a.normalized();
   Vector3 v1 = b.normalized();
-  Scalar c = v0.dot(v1);
+  Scalar c = v1.dot(v0);
 
   // if dot == -1, vectors are nearly opposites
   // => accuraletly compute the rotation axis by computing the