added unit sphere radius for high dimensions

added tests, too. this should fix #21

Author: AlexVonB

RTree.h

@@ -491,7 +491,16 @@ RTREE_QUAL::RTree()
 
   m_root = AllocNode();
   m_root->m_level = 0;
-  m_unitSphereVolume = (ELEMTYPEREAL)UNIT_SPHERE_VOLUMES[NUMDIMS];
+
+  if (NUMDIMS < 21)
+  {
+    m_unitSphereVolume = (ELEMTYPEREAL)UNIT_SPHERE_VOLUMES[NUMDIMS];
+  } else {
+    // Stirling's approximation, applicable to high dimensions
+    // https://en.wikipedia.org/wiki/Volume_of_an_n-ball#Approximation_for_high_dimensions
+    m_unitSphereVolume = (ELEMTYPEREAL)(1.0 / std::sqrt(NUMDIMS * M_PI) *
+                                        std::pow(2 * M_PI * M_E / NUMDIMS, NUMDIMS / 2.0));
+  }
 }
 
 

tests/CMakeLists.txt

@@ -62,11 +62,22 @@ target_link_libraries(
   GTest::gmock_main
 )
 
+add_executable(
+  highDim
+  highDim.cpp
+)
+target_link_libraries(
+  highDim
+  GTest::gtest_main
+  GTest::gmock_main
+)
+
 include(GoogleTest)
 gtest_discover_tests(basics)
 gtest_discover_tests(memory)
 gtest_discover_tests(badData)
 gtest_discover_tests(largeData)
 gtest_discover_tests(treeList)
 gtest_discover_tests(nearestNeighbour)
+gtest_discover_tests(highDim)
 

tests/highDim.cpp

@@ -0,0 +1,49 @@
+#include "../RTree.h"
+#include "util.hpp"
+#include <gmock/gmock.h>
+#include <gtest/gtest-matchers.h>
+#include <gtest/gtest.h>
+#include <vector>
+#include <random>
+
+std::random_device rd;
+std::mt19937 gen(rd());
+std::uniform_real_distribution<> range(0, 1);
+
+class RectND
+{
+public:
+	RectND(int n)
+	{
+    for (int i = 0; i < n; i++)
+    {
+      m_min.push_back(range(gen));
+      m_max.push_back(range(gen));
+    }
+	}
+
+	std::vector<float> m_min, m_max;
+};
+
+using namespace ::testing;
+
+TEST(HighDim, HighDim) {
+  constexpr uint NDIM = 100;
+  typedef RTree<int, float, NDIM> MyTree;
+  MyTree tree;
+
+  int nrects = 1000;
+
+  for (int i = 0; i < nrects; i++) {
+    const RectND rect(NDIM);
+    tree.Insert(rect.m_min.data(), rect.m_max.data(), i);
+  }
+
+  MyTree::Iterator it;
+  int counter = 0;
+  for (tree.GetFirst(it); !tree.IsNull(it); tree.GetNext(it)) {
+    counter++;
+  }
+
+  ASSERT_EQ(counter, nrects);
+}