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Precision Improvements for Ray/Sphere Intersection

Haines, Eric ; Gunther, Johannes and Akenine-Möller, Tomas LU (2019) p.87-94
Abstract
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.
Please use this url to cite or link to this publication:
author
; and
organization
publishing date
type
Chapter in Book/Report/Conference proceeding
publication status
published
subject
host publication
Ray Tracing Gems : High-Quality and Real-Time Rendering with DXR and Other APIs - High-Quality and Real-Time Rendering with DXR and Other APIs
editor
Haines, Eric and Akenine-Möller, Tomas
pages
8 pages
publisher
Apress
external identifiers
  • scopus:85076291095
ISBN
978-1-4842-4426-5
978-1-4842-4427-2
DOI
10.1007/978-1-4842-4427-2_7
language
English
LU publication?
yes
id
e576f1aa-02d7-40b7-9534-ccd832098a5d
date added to LUP
2020-09-17 15:00:29
date last changed
2025-10-31 21:35:45
@inbook{e576f1aa-02d7-40b7-9534-ccd832098a5d,
  abstract     = {{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.}},
  author       = {{Haines, Eric and Gunther, Johannes and Akenine-Möller, Tomas}},
  booktitle    = {{Ray Tracing Gems : High-Quality and Real-Time Rendering with DXR and Other APIs}},
  editor       = {{Haines, Eric and Akenine-Möller, Tomas}},
  isbn         = {{978-1-4842-4426-5}},
  language     = {{eng}},
  pages        = {{87--94}},
  publisher    = {{Apress}},
  title        = {{Precision Improvements for Ray/Sphere Intersection}},
  url          = {{http://dx.doi.org/10.1007/978-1-4842-4427-2_7}},
  doi          = {{10.1007/978-1-4842-4427-2_7}},
  year         = {{2019}},
}