S. Fortune. Polyhedral modeling with multi-precision integer arithmetic. Computer-Aided Design, 29(2):123-133, 1997. Home/Search Document Details and Download
Summary Related Articles Check |
This paper is cited in the following contexts:
Robust Geometric Computation - Yap (1997) (19 citations) (Correct)
....point approximations in EGC. Another approach is to introduce algorithms that use new predicates with low algebraic degrees. This line of work was initiated by Liotta, Preparata and Tamassia [LPT97, BS00] ii) Polyhedral modeling is a natural domain for EGC techniques. Two e#orts are [CM93, For97] The most general viewpoint here uses Nef polyhedra [See01] in which open, closed or half open polyhedral sets are represented. This is a radical departure from the traditional solid modeling based on regularized sets and the associated regularized operators . The regularization of a set S ....
....blackbox scheme of Yap. He also considered controlled perturbation techniques. Comes and Ziegelmann [CZ99] implemented the linear perturbation ideas of Seidel in CGAL. In solid modeling systems, it is very useful to systematically avoid degenerate cases (numerous in this setting) Fortune [For97] uses symbolic perturbation to allow an exact manifold representation of nonregularized polyhedral solids (see Section 47.1) The idea is that a dangling rectangular face (for instance) can be perturbed to look like a very flat rectangular solid, which has a manifold representation. Here, ....
Steven J. Fortune. Polyhedral modeling with multiprecision integer arithmetic. Computer-Aided Design, pages 123--133, 1997. Also, 3rd ACM SIGGRAPH Symp. Solid Modeling and Appl. (1995).
The Convex Hull in a New Model of Computation - Edalat, Lieutier, Kashe (2001) (1 citation) (Correct)
....brief, one can classify existing approaches to robustness into two main categories. The rst is the so called exact computation model. It is based on simulating a real RAM by restricting real computations to a countable sub eld of R, usually the rational numbers or a sub eld of algebraic numbers [8, 6, 5, 13, 1, 14, 31, 20] Department of Computing, Imperial College, London, U.K. y Dassault Systemes Provence, Aix en Provence LMC IMAG, Grenoble, France for which the comparison predicate is computable. The second category, as for example in geometry [16] or in interval geometry [29, 18, 17] tries to devise ....
S. Fortune. Polyhedral modeling with multi-precision integer arithmetic. Computer-Aided Design, 29(2):123-133, 1997.
Shortest Path Geometric Rounding - Milenkovic (2000) (7 citations) (Correct)
....representation of an object, round CSG primitives and then reconstruct the tree. Advantages: works in three dimensions. Disadvantages: suitable for set operations and transformations, not decompositions, convex hull, or Minkowski sum. Topology might be unpleasantly altered. Manifold Rounding [11]: Given a manifold representation of a polyhedral solid, round equations of faces. If rounded solid is self intersecting, retain only the unburied portion of the boundary. Advantages: three dimensional, intuitive topology change, bounded error. Disadvantages: suitable for set operations and ....
S. Fortune. Polyhedral modeling with multiprecision integer arithmetic. Comput. Aided Design, 29(2):123-133, 1997.
Robust Proximity Queries in Implicit Voronoi Diagrams - Liotta, Preparata, Tamassia (1996) (11 citations) (Correct)
....has proved unrealistic and needs to be replaced with a realistic finite precision model where geometric computations can be carried out either exactly or with a guaranteed error bound. This has motivated a great deal of research on the subject of robust computational geometry (see, e.g. [4, 11, 10, 18, 26, 27, 30, 35, 33, 38, 47, 53, 56, 20, 29, 31]) Also, efficiency must be evaluated in a finer framework than the conventional big Oh analysis. In particular, constant factors dependent on the precision requirement of the numerical computations should be taken into account. For an early survey of the different approaches to robust ....
S. Fortune. Polyhedral modeling with multiprecision integer arithmetic. Computer Aided Design, 1996. to appear.
Computing with Real Numbers - I. The LFT Approach to Real.. - Edalat, Heckmann (Correct)
No context found.
S. Fortune. Polyhedral modeling with multi-precision integer arithmetic. Computer-Aided Design, 29(2):123-133, 1997.
Online articles have much greater impact More about CiteSeer.IST Add search form to your site Submit documents Feedback
CiteSeer.IST - Copyright Penn State and NEC