Fixed the original ray-sphere intersection

Changed the original analytic method to a geometrical.

The errors in the original intersection calculation:
The function has a sphere center parameter, but ignores it and assumes
that the sphere is in the origo.
It calculates the length of the ray direction vector, but later on uses
this vector as a unit vector.
The position calculation is simply wrong. It multiplies the direction
vector with the radius of the sphere instead of the calculated
intersection distance.

The quadratic equation solving could be improved too:
There should be an early exit for negative discriminant.
The naive implementation sould be changed to a floating-point
specialized one.

glm/gtx/intersect.hpp

@@ -81,9 +81,9 @@ namespace glm
 	//! From GLM_GTX_intersect extension.
 	template <typename genType>
 	bool intersectRaySphere(
-		genType const & orig, genType const & dir,
+		genType const & rayStarting, genType const & rayNormalizedDirection,
-		genType const & center, typename genType::value_type radius,
+		genType const & sphereCenter, const typename genType::value_type sphereRadius,
-		genType & position, genType & normal);
+		genType & intersectionPosition, genType & intersectionNormal);
 
     //! Compute the intersection of a line and a sphere.
 	//! From GLM_GTX_intersect extension

glm/gtx/intersect.inl

@@ -151,31 +151,16 @@ namespace glm
 	template <typename genType>
 	GLM_FUNC_QUALIFIER bool intersectRaySphere
 	(
-		genType const & rayStarting, genType const & rayDirection,
+		genType const & rayStarting, genType const & rayNormalizedDirection,
-		genType const & sphereCenter, typename genType::value_type sphereRadius,
+		genType const & sphereCenter, const typename genType::value_type sphereRadius,
-		genType & position, genType & normal
+		genType & intersectionPosition, genType & intersectionNormal
 	)
 	{
-		typename genType::value_type Epsilon = std::numeric_limits<typename genType::value_type>::epsilon();
+		typename genType::value_type distance;
-
+		if( intersectRaySphere( rayStarting, rayNormalizedDirection, sphereCenter, sphereRadius * sphereRadius, distance ) )
-		typename genType::value_type a = dot(rayDirection, rayDirection);
-		typename genType::value_type b = typename genType::value_type(2) * dot(rayStarting, rayDirection);
-		typename genType::value_type c = dot(rayStarting, rayStarting) - sphereRadius * sphereRadius;
-		typename genType::value_type d = b * b - typename genType::value_type(4) * a * c;
-		typename genType::value_type e = sqrt(d);
-		typename genType::value_type x1 = (-b - e) / (typename genType::value_type(2) * a);
-		typename genType::value_type x2 = (-b + e) / (typename genType::value_type(2) * a);
-
-		if(x1 > Epsilon)
-		{
-			position = rayStarting + rayDirection * sphereRadius;
-			normal = (position - sphereCenter) / sphereRadius;
-			return true;
-		}
-		else if(x2 > Epsilon)
 		{
-			position = rayStarting + rayDirection * sphereRadius;
+			intersectionPosition = rayStarting + rayNormalizedDirection * distance;
-			normal = (position - sphereCenter) / sphereRadius;
+			intersectionNormal = (intersectionPosition - sphereCenter) / sphereRadius;
 			return true;
 		}
 		return false;