Feature/gunderman/bezier polygon

src/axom/core/numerics/Matrix.hpp

@@ -118,6 +118,11 @@ class Matrix
 {
 public:
 
+  /*!
+   * \brief Default constructor
+   */
+  Matrix() : m_rows(0), m_cols(0), m_data(nullptr), m_usingExternal(false) {}
+
   /*!
    * \brief Constructor, creates a Matrix with the given rows and columns.
    *
@@ -530,12 +535,6 @@ class Matrix
 
 private:
 
-  /*!
-   * \brief Default constructor. Does nothing.
-   * \note Made private to prevent host-code from calling this.
-   */
-  Matrix() : m_rows(0), m_cols(0), m_data(nullptr) { };
-
   /// \name Private Helper Methods
   /// @{
 

src/axom/core/tests/utils_utilities.cpp

@@ -116,3 +116,90 @@ TEST(core_Utilities,minmax)
     EXPECT_EQ(a, axom::utilities::max(a,b));
   }
 }
+
+TEST(core_Utilities, binomial_coefficient)
+{
+  std::cout<<"Testing binomial coefficient function."<< std::endl;
+
+  // test n less than zero
+  {
+    const int n = -1;
+    const int exp = 0;
+    for(int k=-1 ; k < 10 ; ++k)
+    {
+      auto binom_k_n = axom::utilities::binomialCoefficient(n,k);
+      EXPECT_EQ( exp, binom_k_n);
+    }
+  }
+
+  // test n := 0
+  {
+    const int n = 0;
+
+    EXPECT_EQ( 1, axom::utilities::binomialCoefficient(n,0));
+
+    EXPECT_EQ( 0, axom::utilities::binomialCoefficient(n,-1));
+    EXPECT_EQ( 0, axom::utilities::binomialCoefficient(n, 1));
+
+  }
+
+  // test n := 1
+  {
+    const int n = 1;
+
+    EXPECT_EQ( 0, axom::utilities::binomialCoefficient(n,-1));
+
+    EXPECT_EQ( 1, axom::utilities::binomialCoefficient(n, 0));
+    EXPECT_EQ( 1, axom::utilities::binomialCoefficient(n, 1));
+
+    EXPECT_EQ( 0, axom::utilities::binomialCoefficient(n, 2));
+
+  }
+
+  // test n := 2
+  {
+    const int n = 2;
+
+    EXPECT_EQ( 1, axom::utilities::binomialCoefficient(n,0));
+    EXPECT_EQ( 2, axom::utilities::binomialCoefficient(n,1));
+    EXPECT_EQ( 1, axom::utilities::binomialCoefficient(n,2));
+
+  }
+
+  // test n := 3
+  {
+    const int n = 3;
+
+    EXPECT_EQ( 1, axom::utilities::binomialCoefficient(n,0));
+    EXPECT_EQ( 3, axom::utilities::binomialCoefficient(n,1));
+    EXPECT_EQ( 3, axom::utilities::binomialCoefficient(n,2));
+    EXPECT_EQ( 1, axom::utilities::binomialCoefficient(n,3));
+  }
+
+  // test n := 4
+  {
+    const int n = 4;
+
+    EXPECT_EQ( 1, axom::utilities::binomialCoefficient(n,0));
+    EXPECT_EQ( 4, axom::utilities::binomialCoefficient(n,1));
+    EXPECT_EQ( 6, axom::utilities::binomialCoefficient(n,2));
+    EXPECT_EQ( 4, axom::utilities::binomialCoefficient(n,3));
+    EXPECT_EQ( 1, axom::utilities::binomialCoefficient(n,4));
+  }
+
+  // test recurrence relation  nCk = (n-1)C(k-1) + (n-1)C(k)
+  {
+    for(int n = 1 ; n < 10 ; ++n)
+    {
+      for(int k=1 ; k <= n ; ++k)
+      {
+        auto binom_n_k = axom::utilities::binomialCoefficient(n,k);
+        auto binom_n1_k1 = axom::utilities::binomialCoefficient(n-1,k-1);
+        auto binom_n1_k  = axom::utilities::binomialCoefficient(n-1,k);
+
+        EXPECT_EQ(binom_n_k, binom_n1_k1 + binom_n1_k );
+      }
+    }
+  }
+
+}

src/axom/core/utilities/Utilities.cpp

@@ -40,5 +40,29 @@ void processAbort()
 #endif
 }
 
+int binomialCoefficient(int n, int k)
+{
+  if(k > n || k < 0) // check if out-of-bounds
+  {
+    return 0;
+  }
+  if(k == n || k == 0) // early return
+  {
+    return 1;
+  }
+  if (k > n-k) // exploit symmetry to reduce work
+  {
+    k= n-k;
+  }
+
+  int val = 1;
+  for (int i=1 ; i<=k ; ++i)
+  {
+    val*=(n-k+i);
+    val/=i;
+  }
+  return val;
+}
+
 }   // end namespace utilities
 }   // end namespace axom

src/axom/core/utilities/Utilities.hpp

@@ -144,6 +144,14 @@ T clampLower(T val, T lower)
   return val < lower ? lower : val;
 }
 
+/*!
+ * \brief Computes the binomial coefficient `n choose k`
+ *
+ * \return \f$ {n\choose k}  = n! / (k! * (n-k)!)\f$
+ * when \f$ n \ge k \ge 0 \f$, 0 otherwise.
+ */
+int binomialCoefficient(int n, int k);
+
 /*!
  * \brief Returns a random real number within the specified interval
  *

src/axom/primal/CMakeLists.txt

@@ -20,6 +20,7 @@ set( primal_headers
      ## geometry
      geometry/BezierCurve.hpp
      geometry/BoundingBox.hpp
+     geometry/CurvedPolygon.hpp
      geometry/OrientedBoundingBox.hpp
      geometry/OrientationResult.hpp
      geometry/NumericArray.hpp
@@ -44,6 +45,7 @@ set( primal_headers
 
      operators/detail/clip_impl.hpp
      operators/detail/intersect_bezier_impl.hpp
+     operators/detail/intersect_curved_poly_impl.hpp
      operators/detail/intersect_impl.hpp
    )