Merge branch 'feature-free-functions' into 'master'

Feature free functions

Closes #52

See merge request !168

CI/Windows.bat

@@ -117,6 +117,8 @@ cd unittests
 
 unittests.exe --gtest_output=xml
 
+unittests_customvec.exe --gtest_output=xml
+
 cd ..
 
 cd ..
@@ -143,6 +145,8 @@ cd unittests
 
 unittests.exe --gtest_output=xml
 
+unittests_customvec.exe --gtest_output=xml
+
 IF %errorlevel% NEQ 0 exit /b %errorlevel%
 
 cd ..

CI/ci-linux.sh

@@ -96,6 +96,15 @@ cd Unittests
 #execute tests
 ./unittests --gtest_color=yes --gtest_output=xml
 
+echo -e "${OUTPUT}"
+echo ""
+echo "======================================================================"
+echo "Running unittests Release version with custom vector type"
+echo "======================================================================"
+echo -e "${NC}"
+
+./unittests_customvec --gtest_color=yes --gtest_output=xml
+
 cd ..
 cd ..
 
@@ -134,5 +143,14 @@ cd Unittests
 #execute tests
 ./unittests --gtest_color=yes --gtest_output=xml
 
+echo -e "${OUTPUT}"
+echo ""
+echo "======================================================================"
+echo "Running unittests Debug version with custom vector type"
+echo "======================================================================"
+echo -e "${NC}"
+
+./unittests_customvec --gtest_color=yes --gtest_output=xml
+
 cd ..
 cd ..

CI/ci-mac.sh

@@ -78,6 +78,15 @@ cd Unittests
 #execute tests
 ./unittests --gtest_color=yes --gtest_output=xml
 
+echo -e "${OUTPUT}"
+echo ""
+echo "======================================================================"
+echo "Running unittests Release version with minimal vector type"
+echo "======================================================================"
+echo -e "${NC}"
+
+./unittests_customvec --gtest_color=yes --gtest_output=xml
+
 cd ..
 cd ..
 
@@ -116,6 +125,15 @@ cd Unittests
 #execute tests
 ./unittests --gtest_color=yes --gtest_output=xml
 
+echo -e "${OUTPUT}"
+echo ""
+echo "======================================================================"
+echo "Running unittests Debug version with minimal vector type"
+echo "======================================================================"
+echo -e "${NC}"
+
+./unittests_customvec --gtest_color=yes --gtest_output=xml
+
 cd ..
 cd ..
 

src/OpenMesh/Core/Geometry/Vector11T.hh

@@ -718,6 +718,47 @@ noexcept(noexcept(_v1.swap(_v2))) {
     _v1.swap(_v2);
 }
 
+/// \relates OpenMesh::VectorT
+/// non-member norm
+template<typename Scalar, int DIM>
+Scalar norm(const VectorT<Scalar, DIM>& _v) {
+    return _v.norm();
+}
+
+/// \relates OpenMesh::VectorT
+/// non-member sqrnorm
+template<typename Scalar, int DIM>
+Scalar sqrnorm(const VectorT<Scalar, DIM>& _v) {
+    return _v.sqrnorm();
+}
+/// \relates OpenMesh::VectorT
+/// non-member vectorize
+template<typename Scalar, int DIM, typename OtherScalar>
+VectorT<Scalar, DIM>& vectorize(VectorT<Scalar, DIM>& _v, OtherScalar const& _val) {
+    return _v.vectorize(_val);
+}
+
+/// \relates OpenMesh::VectorT
+/// non-member normalize
+template<typename Scalar, int DIM>
+VectorT<Scalar, DIM>& normalize(VectorT<Scalar, DIM>& _v) {
+    return _v.normalize();
+}
+
+/// \relates OpenMesh::VectorT
+/// non-member maximize
+template<typename Scalar, int DIM>
+VectorT<Scalar, DIM>& maximize(VectorT<Scalar, DIM>& _v1, VectorT<Scalar, DIM>& _v2) {
+    return _v1.maximize(_v2);
+}
+
+/// \relates OpenMesh::VectorT
+/// non-member minimize
+template<typename Scalar, int DIM>
+VectorT<Scalar, DIM>& minimize(VectorT<Scalar, DIM>& _v1, VectorT<Scalar, DIM>& _v2) {
+    return _v1.minimize(_v2);
+}
+
 //== TYPEDEFS =================================================================
 
 /** 1-byte signed vector */

src/OpenMesh/Core/Geometry/VectorT.hh

@@ -274,6 +274,52 @@ cross(const VectorT<Scalar,N>& _v1, const VectorT<Scalar,N>& _v2) {
 }
 
 
+/// \relates OpenMesh::VectorT
+/// non-member norm
+template<typename Scalar, int DIM>
+Scalar norm(const VectorT<Scalar, DIM>& _v) {
+    return _v.norm();
+}
+
+
+/// \relates OpenMesh::VectorT
+/// non-member sqrnorm
+template<typename Scalar, int DIM>
+Scalar sqrnorm(const VectorT<Scalar, DIM>& _v) {
+    return _v.sqrnorm();
+}
+
+
+/// \relates OpenMesh::VectorT
+/// non-member vectorize
+template<typename Scalar, int DIM, typename OtherScalar>
+VectorT<Scalar, DIM>& vectorize(VectorT<Scalar, DIM>& _v, OtherScalar const& _val) {
+    return _v.vectorize(_val);
+}
+
+
+/// \relates OpenMesh::VectorT
+/// non-member normalize
+template<typename Scalar, int DIM>
+VectorT<Scalar, DIM>& normalize(VectorT<Scalar, DIM>& _v) {
+    return _v.normalize();
+}
+
+
+/// \relates OpenMesh::VectorT
+/// non-member maximize
+template<typename Scalar, int DIM>
+VectorT<Scalar, DIM>& maximize(VectorT<Scalar, DIM>& _v1, VectorT<Scalar, DIM>& _v2) {
+    return _v1.maximize(_v2);
+}
+
+
+/// \relates OpenMesh::VectorT
+/// non-member minimize
+template<typename Scalar, int DIM>
+VectorT<Scalar, DIM>& minimize(VectorT<Scalar, DIM>& _v1, VectorT<Scalar, DIM>& _v2) {
+    return _v1.minimize(_v2);
+}
 
 
 //== TYPEDEFS =================================================================

src/OpenMesh/Core/Mesh/PolyMeshT.cc

@@ -139,18 +139,18 @@ PolyMeshT<Kernel>::calc_face_normal_impl(FaceHandle _fh, PointIs3DTag) const
 
     // Due to traits, the value types of normals and points can be different.
     // Therefore we cast them here.
-    n[0] += static_cast<typename Normal::value_type>(a[1] * b[2]);
-    n[1] += static_cast<typename Normal::value_type>(a[2] * b[0]);
-    n[2] += static_cast<typename Normal::value_type>(a[0] * b[1]);
+    n[0] += static_cast<typename vector_traits<Normal>::value_type>(a[1] * b[2]);
+    n[1] += static_cast<typename vector_traits<Normal>::value_type>(a[2] * b[0]);
+    n[2] += static_cast<typename vector_traits<Normal>::value_type>(a[0] * b[1]);
   }
 
-  const typename vector_traits<Normal>::value_type norm = n.length();
+  const typename vector_traits<Normal>::value_type length = norm(n);
   
   // The expression ((n *= (1.0/norm)),n) is used because the OpenSG
   // vector class does not return self after component-wise
   // self-multiplication with a scalar!!!
-  return (norm != typename vector_traits<Normal>::value_type(0))
-          ? ((n *= (typename vector_traits<Normal>::value_type(1)/norm)), n)
+  return (length != typename vector_traits<Normal>::value_type(0))
+          ? ((n *= (typename vector_traits<Normal>::value_type(1)/length)), n)
           : Normal(0, 0, 0);
 }
 
@@ -194,20 +194,22 @@ calc_face_normal_impl(const Point& _p0,
   Normal p1p2(vector_cast<Normal>(_p2));  p1p2 -= vector_cast<Normal>(_p1);
 
   Normal n    = cross(p1p2, p1p0);
-  typename vector_traits<Normal>::value_type norm = n.length();
+  typename vector_traits<Normal>::value_type length = norm(n);
 
   // The expression ((n *= (1.0/norm)),n) is used because the OpenSG
   // vector class does not return self after component-wise
   // self-multiplication with a scalar!!!
-  return (norm != typename vector_traits<Normal>::value_type(0)) ? ((n *= (typename vector_traits<Normal>::value_type(1)/norm)),n) : Normal(0,0,0);
+  return (length != typename vector_traits<Normal>::value_type(0))
+          ? ((n *= (typename vector_traits<Normal>::value_type(1)/length)),n)
+          : Normal(0,0,0);
 #else
   Point p1p0 = _p0;  p1p0 -= _p1;
   Point p1p2 = _p2;  p1p2 -= _p1;
 
   Normal n = vector_cast<Normal>(cross(p1p2, p1p0));
-  typename vector_traits<Normal>::value_type norm = n.length();
+  typename vector_traits<Normal>::value_type length = norm(n);
 
-  return (norm != 0.0) ? n *= (1.0/norm) : Normal(0,0,0);
+  return (length != 0.0) ? n *= (1.0/length) : Normal(0,0,0);
 #endif
 }
 
@@ -226,7 +228,7 @@ PolyMeshT<Kernel>::
 calc_face_centroid(FaceHandle _fh) const
 {
   Point _pt;
-  _pt.vectorize(0);
+  vectorize(_pt, 0);
   Scalar valence = 0.0;
   for (ConstFaceVertexIter cfv_it = this->cfv_iter(_fh); cfv_it.is_valid(); ++cfv_it, valence += 1.0)
   {
@@ -331,7 +333,7 @@ calc_halfedge_normal(HalfedgeHandle _heh, const double _feature_angle) const
     for(unsigned int i=0; i<fhs.size(); ++i)
       n += Kernel::normal(fhs[i]);
 
-    return n.normalize();
+    return normalize(n);
   }
 }
 
@@ -378,8 +380,8 @@ calc_vertex_normal(VertexHandle _vh) const
   Normal n;
   calc_vertex_normal_fast(_vh,n);
 
-  Scalar norm = n.length();
-  if (norm != 0.0) n *= (Scalar(1.0)/norm);
+  Scalar length = norm(n);
+  if (length != 0.0) n *= (Scalar(1.0)/length);
 
   return n;
 }
@@ -389,7 +391,7 @@ template <class Kernel>
 void PolyMeshT<Kernel>::
 calc_vertex_normal_fast(VertexHandle _vh, Normal& _n) const
 {
-  _n.vectorize(0.0);
+  vectorize(_n, 0.0);
   for (ConstVertexFaceIter vf_it = this->cvf_iter(_vh); vf_it.is_valid(); ++vf_it)
     _n += this->normal(*vf_it);
 }
@@ -399,7 +401,7 @@ template <class Kernel>
 void PolyMeshT<Kernel>::
 calc_vertex_normal_correct(VertexHandle _vh, Normal& _n) const
 {
-  _n.vectorize(0.0);
+  vectorize(_n, 0.0);
   ConstVertexIHalfedgeIter cvih_it = this->cvih_iter(_vh);
   if (! cvih_it.is_valid() )
   {//don't crash on isolated vertices

src/OpenMesh/Core/Mesh/PolyMeshT.hh

@@ -406,7 +406,7 @@ public:
   {
     Normal edge_vec;
     calc_edge_vector(_heh, edge_vec);
-    return edge_vec.sqrnorm();
+    return sqrnorm(edge_vec);
   }
 
   /** Calculates the midpoint of the halfedge _heh, defined by the positions of
@@ -444,7 +444,7 @@ public:
   {
     Normal v0, v1;
     calc_sector_vectors(_in_heh, v0, v1);
-    Scalar denom = v0.norm()*v1.norm();
+    Scalar denom = norm(v0)*norm(v1);
     if ( denom == Scalar(0))
     {
       return 0;
@@ -470,7 +470,7 @@ public:
     Normal in_vec, out_vec;
     calc_edge_vector(_in_heh, in_vec);
     calc_edge_vector(next_halfedge_handle(_in_heh), out_vec);
-    Scalar denom = in_vec.norm()*out_vec.norm();
+    Scalar denom = norm(in_vec)*norm(out_vec);
     if (is_zero(denom))
     {
       _cos_a = 1;
@@ -479,7 +479,7 @@ public:
     else
     {
       _cos_a = dot(in_vec, out_vec)/denom;
-      _sin_a = cross(in_vec, out_vec).norm()/denom;
+      _sin_a = norm(cross(in_vec, out_vec))/denom;
     }
   }
   */
@@ -499,7 +499,7 @@ public:
   {
     Normal sector_normal;
     calc_sector_normal(_in_heh, sector_normal);
-    return sector_normal.norm()/2;
+    return norm(sector_normal)/2;
   }
 
   /** calculates the dihedral angle on the halfedge _heh
@@ -539,7 +539,7 @@ public:
     calc_sector_normal(_heh, n0);
     calc_sector_normal(this->opposite_halfedge_handle(_heh), n1);
     calc_edge_vector(_heh, he);
-    Scalar denom = n0.norm()*n1.norm();
+    Scalar denom = norm(n0)*norm(n1);
     if (denom == Scalar(0))
     {
       return 0;

src/OpenMesh/Core/Mesh/TriMeshT.hh

@@ -359,9 +359,9 @@ public:
     VertexHandle p2 = this->to_vertex_handle(he2);
 
     // Calculate midpoint coordinates
-    const Point new0 = (this->point(p0) + this->point(p2)) * static_cast< typename Point::value_type >(0.5);
-    const Point new1 = (this->point(p0) + this->point(p1)) * static_cast< typename Point::value_type >(0.5);
-    const Point new2 = (this->point(p1) + this->point(p2)) * static_cast< typename Point::value_type >(0.5);
+    const Point new0 = (this->point(p0) + this->point(p2)) * static_cast<typename vector_traits<Point>::value_type >(0.5);
+    const Point new1 = (this->point(p0) + this->point(p1)) * static_cast<typename vector_traits<Point>::value_type >(0.5);
+    const Point new2 = (this->point(p1) + this->point(p2)) * static_cast<typename vector_traits<Point>::value_type >(0.5);
 
     // Add vertices at midpoint coordinates
     VertexHandle v0 = this->add_vertex(new0);

src/OpenMesh/Core/Utils/vector_cast.hh

@@ -95,7 +95,6 @@ inline void vector_cast( const src_t & /*_src*/, dst_t & /*_dst*/, GenProg::Int2
 {
 }
 
-
 template <typename src_t, typename dst_t, int n>
 inline void vector_copy( const src_t &_src, dst_t &_dst, GenProg::Int2Type<n> )
 {

src/OpenMesh/Tools/Smoother/JacobiLaplaceSmootherT.cc

@@ -181,7 +181,7 @@ compute_new_positions_C1()
       if (diag) uu *= static_cast<typename Mesh::Scalar>(1.0) / diag;
 
       // damping
-      uu *= static_cast<typename Mesh::Normal::value_type>(0.25);
+      uu *= static_cast<typename vector_traits<typename Mesh::Normal>::value_type>(0.25);
     
       // store new position
       p  = vector_cast<typename Mesh::Normal>(Base::mesh_.point(*v_it));

src/OpenMesh/Tools/Smoother/SmootherT.cc

@@ -263,13 +263,13 @@ set_relative_local_error(Scalar _err)
     bb_min = bb_max = mesh_.point(*v_it);
     for (++v_it; v_it!=v_end; ++v_it)
     {
-      bb_min.minimize(mesh_.point(*v_it));
-      bb_max.maximize(mesh_.point(*v_it));
+        minimize(bb_min, mesh_.point(*v_it));
+        maximize(bb_max, mesh_.point(*v_it));
     }
 
 
     // abs. error = rel. error * bounding-diagonal
-    set_absolute_local_error(_err * (bb_max-bb_min).norm());
+    set_absolute_local_error(norm(_err * (bb_max-bb_min)));
   }
 }
 

src/OpenMesh/Tools/Subdivider/Uniform/CatmullClarkT.cc

@@ -346,7 +346,7 @@ CatmullClarkT<MeshType,RealType>::update_vertex( MeshType& _m, const VertexHandl
     for ( ve_itr = _m.ve_iter( _vh); ve_itr.is_valid(); ++ve_itr)
       if ( _m.is_boundary( *ve_itr))
         pos += _m.property( ep_pos_, *ve_itr);
-    pos /= static_cast<typename MeshType::Point::value_type>(3.0);
+    pos /= static_cast<typename vector_traits<typename MeshType::Point>::value_type>(3.0);
   }
   else // inner vertex
   {

src/Unittests/CMakeLists.txt

@@ -30,22 +30,28 @@ if ( OPENMESH_BUILD_UNIT_TESTS )
     FILE(GLOB UNITTEST_SRC *.cc)
           # Create unittest executable
           acg_add_executable(unittests ${UNITTEST_SRC})
+          acg_add_executable(unittests_customvec ${UNITTEST_SRC})
+          target_compile_definitions(unittests_customvec PRIVATE TEST_CUSTOM_TRAITS)
  
           # For the unittest we don't want the install rpath as set by acg_add_executable 
-          set_target_properties ( unittests PROPERTIES  BUILD_WITH_INSTALL_RPATH 0 )
+          set_target_properties ( unittests PROPERTIES  BUILD_WITH_INSTALL_RPATH 0 )          
+          set_target_properties ( unittests_customvec PROPERTIES  BUILD_WITH_INSTALL_RPATH 0 )
 
    # Set output directory to ${BINARY_DIR}/Unittests
     set (OUTPUT_DIR "${CMAKE_BINARY_DIR}/Unittests")
       set_target_properties(unittests PROPERTIES RUNTIME_OUTPUT_DIRECTORY ${OUTPUT_DIR}) 
+      set_target_properties(unittests_customvec PROPERTIES RUNTIME_OUTPUT_DIRECTORY ${OUTPUT_DIR})
       foreach(CONFIG ${CMAKE_CONFIGURATION_TYPES})
         string(TOUPPER ${CONFIG} UPCONFIG)
         set_target_properties(unittests PROPERTIES RUNTIME_OUTPUT_DIRECTORY_${UPCONFIG} ${OUTPUT_DIR})
+        set_target_properties(unittests_customvec PROPERTIES RUNTIME_OUTPUT_DIRECTORY_${UPCONFIG} ${OUTPUT_DIR})
     endforeach()
 
 	
 	if ( NOT WIN32)
            # Link against all necessary libraries
            target_link_libraries(unittests OpenMeshCore OpenMeshTools ${GTEST_LIBRARIES} ${GTEST_MAIN_LIBRARIES} pthread)
+           target_link_libraries(unittests_customvec OpenMeshCore OpenMeshTools ${GTEST_LIBRARIES} ${GTEST_MAIN_LIBRARIES} pthread)
 	  
 	  
 	
@@ -56,6 +62,7 @@ if ( OPENMESH_BUILD_UNIT_TESTS )
 
 		endif()
       target_link_libraries(unittests OpenMeshCore OpenMeshTools ${GTEST_LIBRARIES} ${GTEST_MAIN_LIBRARIES}) 
+      target_link_libraries(unittests_customvec OpenMeshCore OpenMeshTools ${GTEST_LIBRARIES} ${GTEST_MAIN_LIBRARIES})
     endif()
 	
 
@@ -63,10 +70,11 @@ if ( OPENMESH_BUILD_UNIT_TESTS )
 	if ( NOT WIN32 )
 	    # Set compiler flags
       set_target_properties(unittests PROPERTIES COMPILE_FLAGS "-g -pedantic -Wno-long-long")
+      set_target_properties(unittests_customvec PROPERTIES COMPILE_FLAGS "-g -pedantic -Wno-long-long")
 	else()
 	    # Set compiler flags
       set_target_properties(unittests PROPERTIES COMPILE_FLAGS "" )
-
+      set_target_properties(unittests_customvec PROPERTIES COMPILE_FLAGS "" )
     endif()
     
     if ( OPENMESH_BUILD_SHARED )
@@ -80,12 +88,19 @@ if ( OPENMESH_BUILD_UNIT_TESTS )
                             "$<TARGET_FILE:${TAR}>"
                             "${CMAKE_BINARY_DIR}/Unittests/$<TARGET_FILE_NAME:${TAR}>" 
                             COMMENT "Copying OpenMesh targets to unittests directory")
+         add_custom_command(TARGET unittests_customvec POST_BUILD
+                            COMMAND "${CMAKE_COMMAND}" -E copy
+                            "$<TARGET_FILE:${TAR}>"
+                            "${CMAKE_BINARY_DIR}/Unittests/$<TARGET_FILE_NAME:${TAR}>"
+                            COMMENT "Copying OpenMesh targets to unittests directory")
        endforeach(TAR)
      endif()
 	
     acg_copy_after_build(unittests ${CMAKE_CURRENT_SOURCE_DIR}/TestFiles ${CMAKE_BINARY_DIR}/Unittests/)
+    acg_copy_after_build(unittests_customvec ${CMAKE_CURRENT_SOURCE_DIR}/TestFiles ${CMAKE_BINARY_DIR}/Unittests/)
 
     add_test(NAME AllTestsIn_OpenMesh_tests WORKING_DIRECTORY "${CMAKE_BINARY_DIR}/Unittests" COMMAND "${CMAKE_BINARY_DIR}/Unittests/unittests")
+    add_test(NAME AllTestsIn_OpenMesh_tests_with_minimal_vector WORKING_DIRECTORY "${CMAKE_BINARY_DIR}/Unittests" COMMAND "${CMAKE_BINARY_DIR}/Unittests/unittests_customvec")
 
   else(GTEST_FOUND)
       message(STATUS "Google testing framework was not found, unittests disabled.")

src/Unittests/unittests_common.hh

@@ -7,8 +7,13 @@
 #include <OpenMesh/Core/Mesh/TriMesh_ArrayKernelT.hh>
 #include <OpenMesh/Core/Mesh/PolyMesh_ArrayKernelT.hh>
 
+#ifdef TEST_CUSTOM_TRAITS
+#include <Unittests/unittests_common_customtraits.hh>
+#else
 struct CustomTraits : public OpenMesh::DefaultTraits {
 };
+#endif
+
 
 typedef OpenMesh::TriMesh_ArrayKernelT<CustomTraits> Mesh;
 

src/Unittests/unittests_common_customtraits.hh

+#ifndef UNITTESTS_COMMON_DUMMYTRAITS
+#define UNITTESTS_COMMON_DUMMYTRAITS
+#include <OpenMesh/Core/Mesh/TriMesh_ArrayKernelT.hh>
+#include <OpenMesh/Core/Utils/color_cast.hh>
+#include <array>
+
+namespace Custom {
+
+/// A Vector class with the absolute minimum of built-in methods to test the
+/// interface expected from Vectors used in Traits
+template <int DIM> class Vec {
+  public:
+    // Constructor with DIM components
+	Vec(float x) : data({ x }) {}
+	Vec(float x, float y) : data({ x, y }) {}
+	Vec(float x, float y, float z) : data({ x, y, z }) {}
+	Vec(float x, float y, float z, float w) : data({ x, y, z, w }) {}
+	  
+    Vec() = default;
+    Vec(Vec<DIM> const &) = default;
+
+    float &operator[](int i) { return data[i]; }
+    float operator[](int i) const { return data[i]; }
+
+  private:
+    std::array<float, DIM> data;
+};
+
+template <int DIM> bool operator==(Vec<DIM> const &lhs, Vec<DIM> const &rhs) {
+    for (int i = 0; i < DIM; i++)
+        if (lhs[i] != rhs[i]) return false;
+    return true;
+}
+
+template <int DIM>
+Vec<DIM> operator+(Vec<DIM> const &lhs, Vec<DIM> const &rhs) {
+    Vec<DIM> result;
+    for (int i = 0; i < DIM; i++)
+        result[i] = lhs[i] + rhs[i];
+    return result;
+}
+
+template <int DIM>
+Vec<DIM> operator-(Vec<DIM> const &lhs, Vec<DIM> const &rhs) {
+    Vec<DIM> result;
+    for (int i = 0; i < DIM; i++)
+        result[i] = lhs[i] - rhs[i];
+    return result;
+}
+
+template <int DIM> Vec<DIM> operator*(Vec<DIM> const &lhs, float rhs) {
+    Vec<DIM> result;
+    for (int i = 0; i < DIM; i++)
+        result[i] = lhs[i] * rhs;
+    return result;
+}
+
+template <int DIM> Vec<DIM> operator*(float lhs, Vec<DIM> const &rhs) {
+    return rhs * lhs;
+}
+
+template <int DIM> Vec<DIM> operator/(Vec<DIM> const &lhs, float rhs) {
+    Vec<DIM> result;
+    for (int i = 0; i < DIM; i++)
+        result[i] = lhs[i] / rhs;
+    return result;
+}
+
+template <int DIM> Vec<DIM> &operator+=(Vec<DIM> &lhs, Vec<DIM> const &rhs) {
+    return lhs = lhs + rhs;
+}
+template <int DIM> Vec<DIM> &operator-=(Vec<DIM> &lhs, Vec<DIM> const &rhs) {
+    return lhs = lhs - rhs;
+}
+template <int DIM> Vec<DIM> &operator*=(Vec<DIM> &lhs, float rhs) {
+    return lhs = lhs * rhs;
+}
+template <int DIM> Vec<DIM> &operator/=(Vec<DIM> &lhs, float rhs) {
+    return lhs = lhs / rhs;
+}
+
+template <int DIM> float norm(Vec<DIM> const &v) {
+    float sum = 0.0f;
+    for (int i = 0; i < DIM; i++)
+        sum += v[i] * v[i];
+    return std::sqrt(sum);
+}
+
+template <int DIM> Vec<DIM> &normalize(Vec<DIM> &v) { return v /= norm(v); }
+template <int DIM> Vec<DIM> &vectorize(Vec<DIM> &v, float val) {
+    for (int i = 0; i < DIM; i++)
+        v[i] = val;
+    return v;
+}
+
+template <int DIM> Vec<DIM> &minimize(Vec<DIM> &v1, Vec<DIM> const &v2) {
+    for (int i = 0; i < DIM; i++)
+        v1[i] = std::min(v1[i], v2[i]);
+    return v1;
+}
+
+template <int DIM> Vec<DIM> &maximize(Vec<DIM> &v1, Vec<DIM> const &v2) {
+    for (int i = 0; i < DIM; i++)
+        v1[i] = std::max(v1[i], v2[i]);
+    return v1;
+}
+
+template <int DIM> float dot(Vec<DIM> const &v1, Vec<DIM> const &v2) {
+    float sum = 0.f;
+    for (int i = 0; i < DIM; i++)
+        sum += v1[i] * v2[i];
+    return sum;