Robust Ray Intersection with Interval Arithmetic
نویسنده
چکیده
For more general types of equations f (t) = 0, the problem of finding roots can be divided into two steps. First the roots must be isolated by finding intervals [ti , ti+1] which are known to contain one and only one root of the function. Secondly, the intervals about each root can be refined by reducing the size of the isolating interval until the root is located as accurately as possible using machine arithmetic.
منابع مشابه
Reliable Algorithms for Ray Intersection in Computer Graphics Based on Interval Arithmetic
In this work we study the reliability and performance of interval arithmetic for ray tracing implicit surfaces. We analyze when and how to use interval arithmetic as an alternative to the methods used in POV-Ray for ray intersection. Interval methods are applied as robust approaches for solving the ray-surface intersection problem; i.e. to find the minimal root in a set of analytic functions. P...
متن کاملInterval arithmetic algorithms for rendering isosurfaces
The use of interval arithmetic for ray tracing implicit surfaces is analyzed in terms of its reliability and performance. This paper analyzes when and how to use interval arithmetic as an alternative to the methods used in POV-Ray for ray intersection. Interval methods are applied as robust approaches for solving the ray-surface intersection problem; i.e. to find the minimal root in a set of an...
متن کاملSphere Tracing: Simple Robust Antialiased Rendering of Distance-Based Implicit Surfaces
Sphere tracing is a new numerical method for nd-ing the intersection of a ray with an implicit surface. Unlike Newton's method or regula falsi, it is robust, converging if and only if the ray intersects the implicit surface, and it converges on the rst intersection | the intersection closest to the ray origin. It is signiicantly simpler to implement than other robust intersection techniques, su...
متن کاملFast Ray Tracing of Arbitrary Implicit Surfaces with Interval and Affine Arithmetic
Existing techniques for rendering arbitrary-form implicit surfaces are limited, either in performance, correctness or flexibility. Ray tracing algorithms employing interval arithmetic (IA) or affine arithmetic (AA) for root-finding are robust and general in the class of surfaces they support, but traditionally slow. Nonetheless, implemented efficiently using a stack-driven iterative algorithm a...
متن کاملComputations with Tight Bounding Volumes for General Parametric Surfaces
Methods for computing tight bounding volumes for general parametric surfaces, for testing if two bounding volumes intersect and for computing inclusions for the intersection of two bounding volumes are discussed. These methods together with interval arithmetic are the basis for a robust algorithm for computing inclusions for all parts of the intersection curve of two general parametric surfaces.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2000