Add a new implementation for cone/ray intersect to simplify code and fix issue with current implementation (#3902)

* add a new implementation for cone/ray intersect to simplify and fix existing issue

Signed-off-by: hultonha <hultonha@amazon.co.uk>

* move new ray/cone intersection function to AzToolsFramework - repond to PR comments

Signed-off-by: hultonha <hultonha@amazon.co.uk>

* updates following PR feedback

Signed-off-by: hultonha <hultonha@amazon.co.uk>

* add additional comment to give more context to the intersection function

Signed-off-by: hultonha <hultonha@amazon.co.uk>

* update google test expect usage

Signed-off-by: hultonha <hultonha@amazon.co.uk>

Code/Framework/AzCore/AzCore/Math/IntersectSegment.cpp

@@ -628,7 +628,7 @@ int AZ::Intersect::IntersectRayCappedCylinder(
 int AZ::Intersect::IntersectRayCone(
     const Vector3& rayOrigin, const Vector3& rayDir,
     const Vector3& coneApex, const Vector3& coneDir, float coneHeight,
-    float coneBaseRaidus, float& t1, float& t2)
+    float coneBaseRadius, float& t1, float& t2)
 {
     // Q = rayOrgin, A = coneApex
     Vector3 AQ = rayOrigin - coneApex;
@@ -646,7 +646,7 @@ int AZ::Intersect::IntersectRayCone(
         return 0;
     }
 
-    float r2 = coneBaseRaidus * coneBaseRaidus;
+    float r2 = coneBaseRadius * coneBaseRadius;
     float h2 = coneHeight * coneHeight;
 
     float m2 = m * m;

Code/Framework/AzCore/AzCore/Math/IntersectSegment.h

@@ -240,7 +240,7 @@ namespace AZ
         //! @return                    The number of intersecting points.
         int IntersectRayCone(
             const Vector3& rayOrigin, const Vector3& rayDir,
-            const Vector3& coneApex, const Vector3& coneDir, float coneHeight, float coneBaseRaidus,
+            const Vector3& coneApex, const Vector3& coneDir, float coneHeight, float coneBaseRadius,
             float& t1, float& t2);
 
         //! Test intersection between a ray and a plane in 3D.

Code/Framework/AzCore/Tests/Math/IntersectionTests.cpp

@@ -609,6 +609,21 @@ namespace UnitTest
         EXPECT_EQ(hits, 0);
     }
 
+    // replicates a scenario in the Editor using a cone and a pick ray which should have failed but passed
+    // note: To replicate this, select an entity so the default translation manipulator appears, move very close to the
+    // entity, hover the mouse over one of the manipulator linear manipulator arrows (cone part) and move the mouse away
+    // notice the manipulator will remain highlighted as a successful intersection is still reported
+    TEST(MATH_IntersectRayConeTestEditor, DISABLED_RayConeEditorScenarioTest)
+    {
+        auto rayOrigin = Vector3(0.0f, -0.808944702f, 0.0f);
+        auto rayDir = Vector3(0.301363617f, 0.939044654f, 0.165454566f);
+        float t1 = 0.0f;
+        float t2 = 0.0f;
+        int hits = Intersect::IntersectRayCone(
+            rayOrigin, rayDir, AZ::Vector3(0.0f, 0.0f, 0.161788940f), AZ::Vector3(0.0f, 0.0f, -1.0f), 0.0453009047, 0.0113252262, t1, t2);
+        EXPECT_EQ(hits, 0);
+    }
+
     class MATH_IntersectRayQuadTest
         : public AllocatorsFixture
     {