Volume below a plane

include/ignition/math/Plane.hh

@@ -157,8 +157,8 @@ namespace ignition
         Vector3<T> rotatedXAxis = rotation * Vector3<T>::UnitX;
         Vector3<T> rotatedYAxis = rotation * Vector3<T>::UnitY;
 
-        auto xBasis = rotatedXAxis.VectorProjectionLength(intersection);
-        auto yBasis = rotatedYAxis.VectorProjectionLength(intersection);
+        auto xBasis = rotatedXAxis.Dot(intersection);
+        auto yBasis = rotatedYAxis.Dot(intersection);
 
         if (std::abs(xBasis) < this->Size().X() / 2 &&
             std::abs(yBasis) < this->Size().Y() / 2)

include/ignition/math/Vector3.hh

@@ -264,15 +264,6 @@ namespace ignition
         return n.Normalize();
       }
 
-      /// \brief Get Length of a Vector Projection of another onto this vector
-      /// \param[in] _v the vector
-      /// \return the projection. Note: If the length of the current vector is
-      /// zero this method will return a NaN
-      public: T VectorProjectionLength(const Vector3<T> &_v) const
-      {
-        return this->Dot(_v) / this->Length();
-      }
-
       /// \brief Get distance to an infinite line defined by 2 points.
       /// \param[in] _pt1 first point on the line
       /// \param[in] _pt2 second point on the line

include/ignition/math/detail/Box.hh

@@ -128,6 +128,7 @@ std::vector<std::pair<Triangle3<T>, T>> TrianglesInPlane(
 {
   std::vector<std::pair<Triangle3<T>, T>> triangles;
   std::vector<Vector3<T>> pointsInPlane;
+
   Vector3<T> centroid;
   for (const auto &pt : _vertices)
   {
@@ -154,11 +155,14 @@ std::vector<std::pair<Triangle3<T>, T>> TrianglesInPlane(
       auto aDisplacement = _a - centroid;
       auto bDisplacement = _b - centroid;
 
-      auto aX = axis1.VectorProjectionLength(aDisplacement);
-      auto aY = axis2.VectorProjectionLength(aDisplacement);
+      // project line onto the new basis vectors
+      // The axis length will never be zero as we have three different points
+      // and the centroid will be different.
+      auto aX = axis1.Dot(aDisplacement) / axis1.Length();
+      auto aY = axis2.Dot(aDisplacement) / axis2.Length();
 
-      auto bX = axis1.VectorProjectionLength(bDisplacement);
-      auto bY = axis2.VectorProjectionLength(bDisplacement);
+      auto bX = axis1.Dot(bDisplacement) / axis1.Length();
+      auto bY = axis2.Dot(bDisplacement) / axis2.Length();
 
       return atan2(aY, aX) < atan2(bY, bX);
     });
@@ -178,7 +182,7 @@ template<typename T>
 T Box<T>::VolumeBelow(const Plane<T> &_plane) const
 {
   auto verticesBelow = this->VerticesBelow(_plane);
-  if (verticesBelow.size() == 0)
+  if (verticesBelow.empty())
     return 0;
 
   auto intersections = this->Intersections(_plane);
@@ -225,7 +229,7 @@ std::optional<Vector3<T>>
   Box<T>::CenterOfVolumeBelow(const Plane<T> &_plane) const
 {
   auto verticesBelow = this->VerticesBelow(_plane);
-  if (verticesBelow.size() == 0)
+  if (verticesBelow.empty())
     return std::nullopt;
 
   auto intersections = this->Intersections(_plane);
@@ -314,7 +318,7 @@ IntersectionPoints<T> Box<T>::Intersections(
     Vector3<T>{-this->size.X()/2, this->size.Y()/2, this->size.Z()/2}
   };
 
-  // Axises
+  // Axes
   std::vector<Vector3<T>> axes
   {
     Vector3<T>{1, 0, 0},

src/Vector3_TEST.cc

@@ -435,18 +435,6 @@ TEST(Vector3dTest, Multiply)
   EXPECT_EQ(v*v, math::Vector3d(0.01, 0.04, 0.09));
 }
 
-/////////////////////////////////////////////////
-TEST(Vector3dTest, Projection)
-{
-  math::Vector3d v1(0, 0, 2);
-  math::Vector3d v2(0, 1, 0);
-  math::Vector3d v3(2, 3, 2);
-
-  EXPECT_NEAR(v1.VectorProjectionLength(v3), 2, 1e-15);
-  EXPECT_NEAR(v2.VectorProjectionLength(v3), 3, 1e-15);
-  EXPECT_NEAR(v1.VectorProjectionLength(v2), 0, 1e-15);
-}
-
 /////////////////////////////////////////////////
 TEST(Vector3dTest, NotEqual)
 {