458 research outputs found
Robustness in solid modeling - a tolerance based, intuitionistic approach
Journal ArticleThis paper presents a new robustness method for geometric modeling operations. It computes geometric relations from the tolerances defined for geometric objects and dynamically updates the tolerances to preserve the properties of the relations, using an intuitionistic self-validation approach. Geometric algorithms using this approach are proved to be robust. A robust Boolean set operation algorithm using this robustness approach has been implemented and test examples are described in this paper as well
Mathematical knowledge and skills expected by higher education in engineering and the social sciences: Implications for high school mathematics curriculum
Cataloged from PDF version of article.One important function of school mathematics curriculum is to prepare high school students with the knowledge and skills needed for university education. Identifying them empirically will help making sound decisions about the contents of high school mathematics curriculum. It will also help students to make informed choices in course selection at high school. In this study, we surveyed university faculty members who teach first year university students about the mathematical knowledge and skills that they would like to see in incoming high school graduates. Data were collected from 122 faculty members from social science (history, law, psychology) and engineering departments (electrical/electronics and computer engineering). Participants were asked to indicate which high school mathematics topics and skills they thought were important to be successful at university education in their field. Results were compared across social science and engineering departments. Implications were drawn for curriculum specialists, students, and mathematics educators
Exploration into technical procedures for vertical integration
Issues in the design and use of a digital geographic information system incorporating landuse, zoning, hazard, LANDSAT, and other data are discussed. An eleven layer database was generated. Issues in spatial resolution, registration, grid versus polygonal structures, and comparison of photointerpreted landuse to LANDSAT land cover are examined
Mathematical knowledge and skills expected by higher education in engineering and the social sciences: Implications for high school mathematics curriculum
One important function of school mathematics curriculum is to prepare high school students with the knowledge and skills needed for university education. Identifying them empirically will help making sound decisions about the contents of high school mathematics curriculum. It will also help students to make informed choices in course selection at high school. In this study, we surveyed university faculty members who teach first year university students about the mathematical knowledge and skills that they would like to see in incoming high school graduates. Data were collected from 122 faculty members from social science (history, law, psychology) and engineering departments (electrical/electronics and computer engineering). Participants were asked to indicate which high school mathematics topics and skills they thought were important to be successful at university education in their field. Results were compared across social science and engineering departments. Implications were drawn for curriculum specialists, students, and mathematics educators. © 2015 by iSER
Minkowski Sum Construction and other Applications of Arrangements of Geodesic Arcs on the Sphere
We present two exact implementations of efficient output-sensitive algorithms
that compute Minkowski sums of two convex polyhedra in 3D. We do not assume
general position. Namely, we handle degenerate input, and produce exact
results. We provide a tight bound on the exact maximum complexity of Minkowski
sums of polytopes in 3D in terms of the number of facets of the summand
polytopes. The algorithms employ variants of a data structure that represents
arrangements embedded on two-dimensional parametric surfaces in 3D, and they
make use of many operations applied to arrangements in these representations.
We have developed software components that support the arrangement
data-structure variants and the operations applied to them. These software
components are generic, as they can be instantiated with any number type.
However, our algorithms require only (exact) rational arithmetic. These
software components together with exact rational-arithmetic enable a robust,
efficient, and elegant implementation of the Minkowski-sum constructions and
the related applications. These software components are provided through a
package of the Computational Geometry Algorithm Library (CGAL) called
Arrangement_on_surface_2. We also present exact implementations of other
applications that exploit arrangements of arcs of great circles embedded on the
sphere. We use them as basic blocks in an exact implementation of an efficient
algorithm that partitions an assembly of polyhedra in 3D with two hands using
infinite translations. This application distinctly shows the importance of
exact computation, as imprecise computation might result with dismissal of
valid partitioning-motions.Comment: A Ph.D. thesis carried out at the Tel-Aviv university. 134 pages
long. The advisor was Prof. Dan Halperi
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