Computational Geometry Problems in REDLOG
نویسندگان
چکیده
We solve algorithmic geometrical problems in real 3-space or the real plane arising from applications in the area of cad, computer vision, and motion planning. The problems include parallel and central projection problems, shade and cast shadow problems, reconstruction of objects from images, oosets of objects, Voronoi diagrams of a nite families of objects, and collision of moving objects. Our tools are real elimination algorithms implemented in the reduce package redlog. In many cases the problems can be solved uniformly in unspeciied parameters. The power of the method is illustrated by examples many of which have been outside the scope of real elimination methods so far.
منابع مشابه
An Algebraic Approach to O setting and Blending of Solids
We propose to broaden the framework of csg to a representation of solids as Boolean combinations of polynomial equations and inequalities describing regular closed semialgebraic sets of points in 3-space. As intermediate results of our operations we admit arbitrary semialgebraic sets. This allows to overcome well-known problems with the computation of blendings via oosets. The operations common...
متن کاملSweep Line Algorithm for Convex Hull Revisited
Convex hull of some given points is the intersection of all convex sets containing them. It is used as primary structure in many other problems in computational geometry and other areas like image processing, model identification, geographical data systems, and triangular computation of a set of points and so on. Computing the convex hull of a set of point is one of the most fundamental and imp...
متن کاملREDLOG – First-Order Logic for the Masses
redlog is a system for computing with first-order logic and propositional logic with quantification. It is tightly integrated into the computer algebra system reduce. Assuming a broad audience, we motivate the use of first-order logic to model problems. Then, by employing quantifier elimination methods, simplification techniques and normal form computations, highly non-trivial problems can be s...
متن کاملParleda: a Library for Parallel Processing in Computational Geometry Applications
ParLeda is a software library that provides the basic primitives needed for parallel implementation of computational geometry applications. It can also be used in implementing a parallel application that uses geometric data structures. The parallel model that we use is based on a new heterogeneous parallel model named HBSP, which is based on BSP and is introduced here. ParLeda uses two main lib...
متن کاملThree Different Methods for Approximate Analysis of Bar Structures
In this paper, modified solutions were compared through utilizing three different approximate methods for bar structures. The modifications considered various changes in the initial design. To authors' best of knowledge, the studies have carried out on this matter so far are not broad enough and have considerred the simeltaneous variations of size, geometry and topology on the bar structures. I...
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 1996