diff --git a/apps/openmw/mwphysics/heightfield.cpp b/apps/openmw/mwphysics/heightfield.cpp
index 52aed9c072..e1448116bf 100644
--- a/apps/openmw/mwphysics/heightfield.cpp
+++ b/apps/openmw/mwphysics/heightfield.cpp
@@ -7,12 +7,48 @@
 
 #include <LinearMath/btTransform.h>
 
+#include <type_traits>
+
+namespace
+{
+    template <class T>
+    auto makeHeights(const T* heights, float sqrtVerts)
+        -> std::enable_if_t<std::is_same<btScalar, T>::value, std::vector<btScalar>>
+    {
+        return {};
+    }
+
+    template <class T>
+    auto makeHeights(const T* heights, float sqrtVerts)
+        -> std::enable_if_t<!std::is_same<btScalar, T>::value, std::vector<btScalar>>
+    {
+        return std::vector<btScalar>(heights, heights + static_cast<std::ptrdiff_t>(sqrtVerts * sqrtVerts));
+    }
+
+    template <class T>
+    auto getHeights(const T* floatHeights, const std::vector<btScalar>&)
+        -> std::enable_if_t<std::is_same<btScalar, T>::value, const btScalar*>
+    {
+        return floatHeights;
+    }
+
+    template <class T>
+    auto getHeights(const T*, const std::vector<btScalar>& btScalarHeights)
+        -> std::enable_if_t<!std::is_same<btScalar, T>::value, const btScalar*>
+    {
+        return btScalarHeights.data();
+    }
+}
+
 namespace MWPhysics
 {
     HeightField::HeightField(const float* heights, int x, int y, float triSize, float sqrtVerts, float minH, float maxH, const osg::Object* holdObject)
+        : mHeights(makeHeights(heights, sqrtVerts))
     {
         mShape = new btHeightfieldTerrainShape(
-            sqrtVerts, sqrtVerts, heights, 1,
+            sqrtVerts, sqrtVerts,
+            getHeights(heights, mHeights),
+            1,
             minH, maxH, 2,
             PHY_FLOAT, false
         );
diff --git a/apps/openmw/mwphysics/heightfield.hpp b/apps/openmw/mwphysics/heightfield.hpp
index f248186db3..2ba58afff8 100644
--- a/apps/openmw/mwphysics/heightfield.hpp
+++ b/apps/openmw/mwphysics/heightfield.hpp
@@ -3,6 +3,10 @@
 
 #include <osg/ref_ptr>
 
+#include <LinearMath/btScalar.h>
+
+#include <vector>
+
 class btCollisionObject;
 class btHeightfieldTerrainShape;
 
@@ -27,6 +31,7 @@ namespace MWPhysics
         btHeightfieldTerrainShape* mShape;
         btCollisionObject* mCollisionObject;
         osg::ref_ptr<const osg::Object> mHoldObject;
+        std::vector<btScalar> mHeights;
 
         void operator=(const HeightField&);
         HeightField(const HeightField&);
diff --git a/apps/openmw_test_suite/detournavigator/recastmeshbuilder.cpp b/apps/openmw_test_suite/detournavigator/recastmeshbuilder.cpp
index 6c474765de..c86dee6e55 100644
--- a/apps/openmw_test_suite/detournavigator/recastmeshbuilder.cpp
+++ b/apps/openmw_test_suite/detournavigator/recastmeshbuilder.cpp
@@ -363,11 +363,11 @@ namespace
             AreaType_ground
         );
         const auto recastMesh = builder.create(mGeneration, mRevision);
-        EXPECT_EQ(recastMesh->getVertices(), std::vector<float>({
+        EXPECT_THAT(recastMesh->getVertices(), Pointwise(FloatNear(1e-5), std::vector<float>({
             1.41421353816986083984375, 0, 1.1920928955078125e-07,
             -1.41421353816986083984375, 0, -1.1920928955078125e-07,
             1.1920928955078125e-07, 0, -1.41421353816986083984375,
-        }));
+        })));
         EXPECT_EQ(recastMesh->getIndices(), std::vector<int>({0, 1, 2}));
         EXPECT_EQ(recastMesh->getAreaTypes(), std::vector<AreaType>({AreaType_ground}));
     }
diff --git a/apps/openmw_test_suite/nifloader/testbulletnifloader.cpp b/apps/openmw_test_suite/nifloader/testbulletnifloader.cpp
index 36f2512462..6ec94fd68f 100644
--- a/apps/openmw_test_suite/nifloader/testbulletnifloader.cpp
+++ b/apps/openmw_test_suite/nifloader/testbulletnifloader.cpp
@@ -9,6 +9,8 @@
 #include <gtest/gtest.h>
 #include <gmock/gmock.h>
 
+#include <algorithm>
+
 namespace
 {
     template <class T>
@@ -30,6 +32,34 @@ namespace
         shape.processAllTriangles(&callback, aabbMin, aabbMax);
         return result;
     }
+
+    bool isNear(btScalar lhs, btScalar rhs)
+    {
+        return std::abs(lhs - rhs) <= 1e-5;
+    }
+
+    bool isNear(const btVector3& lhs, const btVector3& rhs)
+    {
+        return std::equal(
+            static_cast<const btScalar*>(lhs),
+            static_cast<const btScalar*>(lhs) + 3,
+            static_cast<const btScalar*>(rhs),
+            [] (btScalar lhs, btScalar rhs) { return isNear(lhs, rhs); }
+        );
+    }
+
+    bool isNear(const btMatrix3x3& lhs, const btMatrix3x3& rhs)
+    {
+        for (int i = 0; i < 3; ++i)
+            if (!isNear(lhs[i], rhs[i]))
+                return false;
+        return true;
+    }
+
+    bool isNear(const btTransform& lhs, const btTransform& rhs)
+    {
+        return isNear(lhs.getOrigin(), rhs.getOrigin()) && isNear(lhs.getBasis(), rhs.getBasis());
+    }
 }
 
 static std::ostream& operator <<(std::ostream& stream, const btVector3& value)
@@ -157,7 +187,7 @@ static bool operator ==(const btCompoundShape& lhs, const btCompoundShape& rhs)
     for (int i = 0; i < lhs.getNumChildShapes(); ++i)
     {
         if (!compareObjects(lhs.getChildShape(i), rhs.getChildShape(i))
-                || !(lhs.getChildTransform(i) == rhs.getChildTransform(i)))
+                || !isNear(lhs.getChildTransform(i), rhs.getChildTransform(i)))
             return false;
     }
     return true;
@@ -165,13 +195,13 @@ static bool operator ==(const btCompoundShape& lhs, const btCompoundShape& rhs)
 
 static bool operator ==(const btBoxShape& lhs, const btBoxShape& rhs)
 {
-    return lhs.getLocalScaling() == rhs.getLocalScaling()
+    return isNear(lhs.getLocalScaling(), rhs.getLocalScaling())
         && lhs.getHalfExtentsWithoutMargin() == rhs.getHalfExtentsWithoutMargin();
 }
 
 static bool operator ==(const btBvhTriangleMeshShape& lhs, const btBvhTriangleMeshShape& rhs)
 {
-    return lhs.getLocalScaling() == rhs.getLocalScaling()
+    return isNear(lhs.getLocalScaling(), rhs.getLocalScaling())
         && lhs.usesQuantizedAabbCompression() == rhs.usesQuantizedAabbCompression()
         && lhs.getOwnsBvh() == rhs.getOwnsBvh()
         && getTriangles(lhs) == getTriangles(rhs);