diff --git a/src/Magnum/Math/Intersection.h b/src/Magnum/Math/Intersection.h
index 7489699838..f069e793b2 100644
--- a/src/Magnum/Math/Intersection.h
+++ b/src/Magnum/Math/Intersection.h
@@ -193,6 +193,7 @@ template<class T> bool aabbFrustum(const Vector3<T>& aabbCenter, const Vector3<T
 
 Checks for each plane of the frustum whether the sphere is behind the plane
 (the points distance larger than the sphere's radius) using
+
 @ref Distance::pointPlaneScaled().
 */
 template<class T> bool sphereFrustum(const Vector3<T>& sphereCenter, T sphereRadius, const Frustum<T>& frustum);
@@ -441,19 +442,16 @@ template<class T> bool aabbFrustum(const Vector3<T>& aabbCenter, const Vector3<T
 }
 
 template<class T> bool sphereFrustum(const Vector3<T>& sphereCenter, const T sphereRadius, const Frustum<T>& frustum) {
-    const T radiusSq = sphereRadius*sphereRadius;
-
     for(const Vector4<T>& plane: frustum) {
         /* The sphere is in front of one of the frustum planes (normals point
            outwards) */
-        if(Distance::pointPlaneScaled<T>(sphereCenter, plane) < -radiusSq)
+        if(Distance::pointPlane<T>(sphereCenter, plane) >= sphereRadius)
             return false;
     }
 
     return true;
 }
 
-
 template<class T> bool pointCone(const Vector3<T>& point, const Vector3<T>& coneOrigin, const Vector3<T>& coneNormal, const Rad<T> coneAngle) {
     const T tanAngleSqPlusOne = Math::pow<2>(Math::tan(coneAngle*T(0.5))) + T(1);
     return pointCone(point, coneOrigin, coneNormal, tanAngleSqPlusOne);
diff --git a/src/Magnum/Math/Test/DistanceTest.cpp b/src/Magnum/Math/Test/DistanceTest.cpp
index 3430eed7d5..e501c40f80 100644
--- a/src/Magnum/Math/Test/DistanceTest.cpp
+++ b/src/Magnum/Math/Test/DistanceTest.cpp
@@ -171,10 +171,26 @@ void DistanceTest::lineSegmentPoint3D() {
 }
 
 void DistanceTest::pointPlane() {
-    Vector3 point{0.0f, 0.0f, 0.0f};
-    Vector4 plane{3.0f, 0.0f, 4.0f, 5.0f};
-
-    CORRADE_COMPARE(Distance::pointPlane(point, plane), 1.0f);
+    {
+        Vector4 plane{3.0f, 0.0f, 4.0f, 5.0f};
+        CORRADE_COMPARE(Distance::pointPlane({}, plane), 1.0f);
+    }
+    {
+        /* Origin plane with normal {0, 1, 0} */
+        Vector4 plane{0.0f, 1.0f, 0.0f, 0.0f};
+        /* Point lies in front of plane, 2 units away */
+        CORRADE_COMPARE(Distance::pointPlane({0.0f, 2.0f, 0.0f}, plane), 2.0f);
+        /* Point lies in begind the plane, 2 units away */
+        CORRADE_COMPARE(Distance::pointPlane({0.0f, -2.0f, 0.0f}, plane), -2.0f);
+    }
+    {
+        /* Origin plane offset by 1 normal with normal {0, 1, 0} */
+        Vector4 plane{0.0f, 1.0f, 0.0f, -1.0f};
+        /* Point lies in front of plane, 2 units away */
+        CORRADE_COMPARE(Distance::pointPlane({0.0f, 2.0f, 0.0f}, plane), 1.0f);
+        /* Point lies in begind the plane, 2 units away */
+        CORRADE_COMPARE(Distance::pointPlane({0.0f, -2.0f, 0.0f}, plane), -3.0f);
+    }
 }
 
 void DistanceTest::pointPlaneScaled() {
diff --git a/src/Magnum/Math/Test/IntersectionTest.cpp b/src/Magnum/Math/Test/IntersectionTest.cpp
index 98b3b4818c..865a5d7960 100644
--- a/src/Magnum/Math/Test/IntersectionTest.cpp
+++ b/src/Magnum/Math/Test/IntersectionTest.cpp
@@ -181,12 +181,12 @@ void IntersectionTest::rangeFrustum() {
 
 void IntersectionTest::aabbFrustum() {
     const Frustum frustum{
-        {1.0f, 0.0f, 0.0f, 0.0f},
         {-1.0f, 0.0f, 0.0f, 5.0f},
-        {0.0f, 1.0f, 0.0f, 0.0f},
+        {1.0f, 0.0f, 0.0f, 0.0f},
         {0.0f, -1.0f, 0.0f, 1.0f},
-        {0.0f, 0.0f, 1.0f, 0.0f},
-        {0.0f, 0.0f, -1.0f, 10.0f}};
+        {0.0f, 1.0f, 0.0f, 0.0f},
+        {0.0f, 0.0f, -1.0f, 10.0f},
+        {0.0f, 0.0f, 1.0f, 0.0f}};
 
     /* Fully inside */
     CORRADE_VERIFY(Intersection::aabbFrustum(Vector3{0.0f}, Vector3{1.0f}, frustum));
@@ -204,20 +204,50 @@ void IntersectionTest::aabbFrustum() {
 }
 
 void IntersectionTest::sphereFrustum() {
+    /* Frustum spanning [(-10, -10, -10), (0, 0, 0)] */
     const Frustum frustum{
+        {-1.0f, 0.0f, 0.0f, -10.0f},
         {1.0f, 0.0f, 0.0f, 0.0f},
-        {-1.0f, 0.0f, 0.0f, 10.0f},
+        {0.0f, -0.5f, 0.0f, -5.0f}, /* Intentionally not normalized */
         {0.0f, 1.0f, 0.0f, 0.0f},
-        {0.0f, -1.0f, 0.0f, 10.0f},
         {0.0f, 0.0f, 1.0f, 0.0f},
-        {0.0f, 0.0f, -1.0f, 10.0f}};
-
-    /* Sphere on edge */
-    CORRADE_VERIFY(Intersection::sphereFrustum({0.0f, 0.0f, -1.0f}, 1.5f, frustum));
+        {0.0f, 0.0f, -2.0f, -20.0f}}; /* Intentionally not normalized */
+
+    /* Sphere overlapping each face by 0.5 */
+    CORRADE_VERIFY(Intersection::sphereFrustum({ 1.0f,  0.0f,  0.0f}, 1.5f, frustum));
+    CORRADE_VERIFY(Intersection::sphereFrustum({-11.0f, 0.0f,  0.0f}, 1.5f, frustum));
+    CORRADE_VERIFY(Intersection::sphereFrustum({ 0.0f,  1.0f,  0.0f}, 1.5f, frustum));
+    CORRADE_VERIFY(Intersection::sphereFrustum({ 0.0f,-11.0f,  0.0f}, 1.5f, frustum));
+    CORRADE_VERIFY(Intersection::sphereFrustum({ 0.0f,  0.0f,  1.0f}, 1.5f, frustum));
+    CORRADE_VERIFY(Intersection::sphereFrustum({ 0.0f,  0.0f,-11.0f}, 1.5f, frustum));
+    /* Sphere touching each face */
+    CORRADE_VERIFY(!Intersection::sphereFrustum({ 1.0f,  0.0f,  0.0f}, 1.0f, frustum));
+    CORRADE_VERIFY(!Intersection::sphereFrustum({-11.0f, 0.0f,  0.0f}, 1.0f, frustum));
+    CORRADE_VERIFY(!Intersection::sphereFrustum({ 0.0f,  1.0f,  0.0f}, 1.0f, frustum));
+    CORRADE_VERIFY(!Intersection::sphereFrustum({ 0.0f,-11.0f,  0.0f}, 1.0f, frustum));
+    CORRADE_VERIFY(!Intersection::sphereFrustum({ 0.0f,  0.0f,  1.0f}, 1.0f, frustum));
+    CORRADE_VERIFY(!Intersection::sphereFrustum({ 0.0f,  0.0f,-11.0f}, 1.0f, frustum));
     /* Sphere inside */
-    CORRADE_VERIFY(Intersection::sphereFrustum({5.5f, 5.5f, 5.5f}, 1.5f,  frustum));
-    /* Sphere outside */
-    CORRADE_VERIFY(!Intersection::sphereFrustum({0.0f, 0.0f, 100.0f}, 0.5f, frustum));
+    CORRADE_VERIFY(Intersection::sphereFrustum({-1.0f, -2.0f, -3.0f}, 1.5f, frustum));
+    /* Sphere outside each face */
+    CORRADE_VERIFY(!Intersection::sphereFrustum({ 1.0f,  0.0f,  0.0f}, 0.5f, frustum));
+    CORRADE_VERIFY(!Intersection::sphereFrustum({-11.0f, 0.0f,  0.0f}, 0.5f, frustum));
+    CORRADE_VERIFY(!Intersection::sphereFrustum({ 0.0f,  1.0f,  0.0f}, 0.5f, frustum));
+    CORRADE_VERIFY(!Intersection::sphereFrustum({ 0.0f,-11.0f,  0.0f}, 0.5f, frustum));
+    CORRADE_VERIFY(!Intersection::sphereFrustum({ 0.0f,  0.0f,  1.0f}, 0.5f, frustum));
+    CORRADE_VERIFY(!Intersection::sphereFrustum({ 0.0f,  0.0f,-11.0f}, 0.5f, frustum));
+
+    /* Some "Corner" cases, sphere touching corner, but shouldn't intersect */
+    CORRADE_VERIFY(!Intersection::sphereFrustum({1.1f, 1.1f, 1.1f}, 1.1f, frustum));
+    CORRADE_VERIFY(!Intersection::sphereFrustum({-11.1f, -11.1f, -11.1f}, 1.1f, frustum));
+    CORRADE_VERIFY(!Intersection::sphereFrustum({1.1f, -11.1f, 1.1f}, 1.1f, frustum));
+    CORRADE_VERIFY(!Intersection::sphereFrustum({-11.1f, 1.1f, -11.1f}, 1.1f, frustum));
+
+    CORRADE_VERIFY(!Intersection::sphereFrustum({-11.1f, 1.1f, 1.1f}, 1.1f, frustum));
+    CORRADE_VERIFY(!Intersection::sphereFrustum({1.1f, -11.1f, -11.1f}, 1.1f, frustum));
+
+    CORRADE_VERIFY(!Intersection::sphereFrustum({1.1f, 1.1f, -11.1f}, 1.1f, frustum));
+    CORRADE_VERIFY(!Intersection::sphereFrustum({-11.1f, -11.1f, 1.1f}, 1.1f, frustum));
 }
 
 void IntersectionTest::pointCone() {