Generalizes primal::evaluate_integral methods for componentwise integration

RELEASE-NOTES.md

@@ -46,6 +46,8 @@ The Axom project release numbers follow [Semantic Versioning](http://semver.org/
 - Adds the `AXOM_TEST_NUM_OMP_THREADS` configuration variable to control the default OpenMP thread count for tests.
 
 ###  Changed
+- Evaluation methods for line integrals in `axom::primal` have been generalized, and 
+  `evaluate_scalar_line_integral` has been renamed to `evaluate_line_integral`.
 - Treatment of materials on strided-structured Blueprint meshes has changed in `axom::mir`.
   Materials are now expected to be defined only on the valid subset of zones in the mesh.
   This more closely matches VisIt behavior.

src/axom/primal/geometry/BezierCurve.hpp

@@ -59,6 +59,7 @@ template <typename T, int NDIMS>
 class BezierCurve
 {
 public:
+  using NumericType = T;
   using PointType = Point<T, NDIMS>;
   using VectorType = Vector<T, NDIMS>;
   using SegmentType = Segment<T, NDIMS>;

src/axom/primal/geometry/CurvedPolygon.hpp

@@ -34,31 +34,7 @@ namespace primal
 namespace internal
 {
 ///@{
-/// \name Boilerplate to deduce the numeric type from the curve object
-template <typename U>
-struct get_numeric_type;
-
-template <typename T, int NDIMS>
-struct get_numeric_type<BezierCurve<T, NDIMS>>
-{
-  using type = T;
-};
-
-template <typename T, int NDIMS>
-struct get_numeric_type<NURBSCurve<T, NDIMS>>
-{
-  using type = T;
-};
-
-template <typename T>
-struct get_numeric_type<detail::NURBSCurveGWNCache<T>>
-{
-  using type = T;
-};
-///@}
-
-///@{
-/// \name Boilerplate for a compile-time flag for the cached object
+/// \name Type traits for a compile-time flag for the cached object
 template <typename U>
 struct has_cached_data : std::false_type
 { };
@@ -80,8 +56,7 @@ std::ostream& operator<<(std::ostream& os, const CurvedPolygon<CurveType>& poly)
 /*!
  * \class CurvedPolygon
  *
- * \brief Represents a polygon with curved edges defined by BezierCurves
- * \tparam T the coordinate type, e.g., double, float, etc.
+ * \brief Represents a polygon with generic curves for edges
  * \tparam NDIMS the number of dimensions
  * \note The component curves should be ordered in a counter clockwise
  *       orientation with respect to the polygon's normal vector
@@ -90,8 +65,7 @@ template <typename CurveType>
 class CurvedPolygon
 {
 public:
-  using T = typename internal::get_numeric_type<CurveType>::type;
-
+  using NumericType = typename CurveType::NumericType;
   using PointType = typename CurveType::PointType;
   using VectorType = typename CurveType::VectorType;
   using BoundingBoxType = typename CurveType::BoundingBoxType;
@@ -164,7 +138,7 @@ class CurvedPolygon
   void addEdge(CurveType&& c1) { m_edges.push_back(std::move(c1)); }
 
   /// Splits an edge "in place"
-  void splitEdge(int idx, T t)
+  void splitEdge(int idx, NumericType t)
   {
     SLIC_ASSERT(idx >= 0 && idx < static_cast<int>(m_edges.size()));
     AXOM_STATIC_ASSERT_MSG(!internal::has_cached_data<CurveType>::value,

src/axom/primal/geometry/NURBSCurve.hpp

@@ -61,6 +61,7 @@ template <typename T, int NDIMS>
 class NURBSCurve
 {
 public:
+  using NumericType = T;
   using PointType = Point<T, NDIMS>;
   using VectorType = Vector<T, NDIMS>;
   using SegmentType = Segment<T, NDIMS>;

src/axom/primal/geometry/NURBSPatch.hpp

@@ -3111,25 +3111,16 @@ class NURBSPatch
   {
     SLIC_ASSERT(NDIMS == 3);
 
-    // Split the patch along the unique knot values to improve convergence
-    auto split_patches = extractTrimmedBezier();
-
     VectorType ret_vec;
-    for(int n = 0; n < split_patches.size(); ++n)
-    {
-      // Integrand for the surface area integral
-      auto& nPatch = split_patches[n];
-
-      for(int N = 0; N < 3; ++N)
-      {
-        auto avg_surface_normal_integrand = [&nPatch, &N](Point2D x) -> double {
-          return nPatch.normal(x[0], x[1])[N];
-        };
 
-        // Find the area of the resulting projection
-        ret_vec[N] +=
-          evaluate_area_integral(nPatch.getTrimmingCurves(), avg_surface_normal_integrand, npts);
-      }
+    // Split the patch along the unique knot values to improve convergence
+    for(const auto& nPatch : extractTrimmedBezier())
+    {
+      // Integrate the surface normal over the patches
+      ret_vec += evaluate_area_integral(
+        nPatch.getTrimmingCurves(),
+        [&nPatch](Point2D x) -> Vector<T, 3> { return nPatch.normal(x[0], x[1]); },
+        npts);
     }
 
     return ret_vec;
@@ -3397,11 +3388,9 @@ class NURBSPatch
         const double sq_tol = 1e-14;
         const double EPS = 1e-6;
 
-        // Extract the Bezier curves of the NURBS curve
-        auto beziers = curve.extractBezier();
+        // Extract the Bezier curves of the NURBS curve, checking each for intersection
         axom::Array<T> knot_vals = curve.getKnots().getUniqueKnots();
-
-        // Check each Bezier segment for intersection
+        const auto beziers = curve.extractBezier();
         for(int i = 0; i < beziers.size(); ++i)
         {
           axom::Array<T> temp_curve_p;
@@ -3849,11 +3838,9 @@ class NURBSPatch
         const double sq_tol = 1e-14;
         const double EPS = 1e-6;
 
-        // Extract the Bezier curves of the NURBS curve
-        auto beziers = curve.extractBezier();
+        // Extract the Bezier curves of the NURBS curve, and check each for intersection
         axom::Array<T> knot_vals = curve.getKnots().getUniqueKnots();
-
-        // Check each Bezier segment for intersection
+        const auto beziers = curve.extractBezier();
         for(int i = 0; i < beziers.size(); ++i)
         {
           axom::Array<T> temp_curve_p;