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2. Precision Improvements for Ray/Sphere Intersection
 
 # Precision Improvements for Ray/Sphere Intersection

  ![](/sites/default/files/styles/wide/public/publications/article1cropLores.png?itok=_MSIJLWZ)

 The traditional quadratic formula is often presented as the way to compute the intersection of a ray with a sphere. While mathematically correct, this factorization can be numerically unstable when using floating-point arithmetic. We give two little-known reformulations and show how each can improve precision.



 ## Authors



Eric Haines (NVIDIA)

Johannes Gunther (Intel)

[Tomas Akenine-Möller](/person/tomas-akenine-moller)

 

 

 ## Publication Date



Friday, March 1, 2019

 

 ## Published in



[Ray Tracing Gems](http://www.realtimerendering.com/raytracinggems/)

 

 ## Research Area



[Computer Graphics](/research-area/computer-graphics)

[Real-Time Rendering](/research-area/real-time-rendering)