Geometric computing

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  • Project Gutenberg’s Conic Sections Treated Geometrically, by W.H. Besant This eBook is for the use of anyone anywhere at no cost and with almost no restrictions whatsoever. You may copy it, give it away or re-use it under the terms of the Project Gutenberg License included with this eBook or online at Title: Conic Sections Treated Geometrically and, George Bell and Sons Educational Catalogue Author: W.H. Besant Release Date: September 6, 2009

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  • It is by now well established that quantum machines can solve certain computational problems much faster than the best algorithms known in the standard Turing machine model. The complexity question of which problems can be feasibly computed by quantum machines has also been extensively investigated in recent years, both in the context of one machine models (quantum polynomial classes) and various flavors of multi-machine models (single and multiple prover quantum interactive proofs).

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  • Lecture 14: Elliptic curve cryptography and digital rights management. The goals of this chapter are: Introduction to elliptic curves, a group structure imposed on the points on an elliptic curve, geometric and algebraic interpretations of the group operator, elliptic curves on prime finite fields, Perl and Python implementations for elliptic curves on prime finite fields,...

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  • NX is one of the world’s most advanced and tightly integrated CAD/CAM/CAE product development solutions. Spanning the entire range of product development, NX delivers immense value to enterprises of all sizes. It simplifies complex product designs, thus speeding up the process of introducing products to the market. The NX software integrates knowledge-based principles, industrial design, geometric modeling, advanced analysis, graphic simulation, and concurrent engineering.

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  • This book is to examine the most important algorithms in use on today's computers and to teach the basic techniques with the increasing number who was interested in computer users becoming increasingly serious. It is appropriate for use as a textbook for a course Monday, Tuesday or Wednesday in the computer Science: After students have had some programming skills and familiarity computer system, but before they have advanced specialized courses field of computer science or computer applications.

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  • Today robots navigate autonomously in office environments as well as outdoors. They show their ability to beside mechanical and electronic barriers in building mobile platforms, perceiving the environment and deciding on how to act in a given situation are crucial problems. In this book we focused on these two areas of mobile robotics, Perception and Navigation.

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  • Journal of Mathematics in Industry (2011) 1:4 DOI 10.1186/2190-5983-1-4 RESEARCH Open Access Geometric computing for freeform architecture Johannes Wallner · Helmut Pottmann Received: 8 December 2010 / Accepted: 3 June 2011 / Published online: 3 June 2011 © 2011 Wallner, Pottmann; licensee Springer.

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  • These lectures intend to give a self-contained exposure of some techniques for computing the evolution of plane curves. The motions of interest are the so-called motions by curvature. They mean that, at any instant, each point of the curve moves with a normal velocity equal to a function of the curvature at this point. This kind of evolution is of some interest in differential geometry, for instance in the problem of minimal surfaces.

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  • Simple algorithm takes O(n3) operations. Want to check if a given matrix multiplication program works correctly Choose a random vector r = (r1, r2, …, rn) in {0,1}n. Compute A(Br) and Cr then comparer the two values: if equal return yes AB=C, else no.

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  • One of the important tools of geometric mechanics is reduction theory (either Lagrangian or Hamiltonian),which provides a well-developed method for dealing with dynamic constraints. In this theory the dynamic constraints and the sym- metry group are used to lower the dimension of the system by constructing an associated reduced system. We develop the Lagrangian version of this theory for nonholonomic systems in this paper. We have focussed on Lagrangian systems because this is a convenient context for applications to control theory. ...

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  • A two-week Summer School on “Structures in Lie Theory, Crystals, Derived Functors, Harish-Chandra Modules, Invariants and Quivers” was held at Jacobs University Bremen during 9–22 August 2009 on both the geometric and algebraic aspects of Lie Theory. The participants were mainly from European countries with strong contingents from Germany, Russia, and Israel. Several high-level graduate courses were given, containing recent or original results on topics of particular current interest. The detailed notes of five of these lecture courses are reproduced in this volume.

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  • 5 bước quan trọng để tạo mô hình tính toán thủy lực với HEC-RAS: - Starting a new project - Nhập dữ liệu hình học (Geometric data) - Nhập dữ liệu dòng chảy (flow data) và những điều kiện biên (Boudary conditions) - Thực hiện các tính toán thủy lực (Hydraulic computations) - Xem và in kết quả

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  • Solid modeling (or modelling) is a consistent set of principles for mathematical and computer modeling of three dimensional solids. Solid modeling is distinguished from related areas of Geometric modeling and Computer graphics by its emphasis on physical fidelity [1]. Together, the principles of geometric and solid modeling form the foundation of Computer-aided design and in general support the creation, exchange, visualization, animation, interrogation, and annotation of digital models of physical objects....

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  • A coordinate measuring machine (CMM) is a device for measuring the physical geometrical characteristics of an object. This machine may be manually controlled by an operator or it may be computer controlled. Measurements are defined by a probe

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  • Stereopsis is a vision process whose geometrical foundation has been known for a long time, ever since the experiments by Wheatstone, in the 19th century. Nevertheless, its inner workings in biological organisms, as well as its emulation by computer systems, have proven elusive, and stereo vision remains a very active and challenging area of research nowadays. In this volume we have attempted to present a limited but relevant sample of the work being carried out in stereo vision by researchers from around the world.

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  • CHAPTER 47 ROBOTS AND SMART MACHINES Kenneth J. Waldron, Ph.D. Professor of Mechanical Engineering The Ohio State University 47.1 INTRODUCTION / 47.1 47.2 DESIGN AND FUNCTION / 47.6 47.3 STRUCTURAL DESIGN / 47.8 47.4 ACTUATION AND POWER TRANSMISSION SYSTEMS / 47.12 47.5 SENSING SYSTEMS/47.17 47.6 COMPUTER HARDWARE AND SOFTWARE ORGANIZATION / 47.21 47.7 CONTROLLER DESIGN / 47.26 47.8 GEOMETRIC DESIGN / 47.29 47.9 TOOL DESIGN / 47.39 REFERENCES / 47.39 47.7 INTRODUCTION 47.1.

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  • Shimon Even’s Graph Algorithms, published in 1979, was a seminal introductory book on algorithms read by everyone engaged in the field. This thoroughly revised second edition,with a foreword byRichard M.Karp and notes byAndrewV.Goldberg, continues the exceptional presentation from the first edition and explains algorithms in formal but simple language with a direct and intuitive presentation. The material covered by the book begins with basic material, including graphs and shortest paths, trees, depth-first search, and breadth-first search.

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  • The purpose of this section is to get a geometric understanding of linear estimation . First. we outline how projections are computed in linear algebra for finite dimensional vectors . Functional analysis generalizes this procedure to some infinite-dimensional spaces (so-called Hilbert spaces). and finally. we point out that linear estimation is a special case of an infinite-dimensional space

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  • In this paper we present the solution to a longstanding problem of differential geometry: Lie’s third theorem for Lie algebroids. We show that the integrability problem is controlled by two computable obstructions. As applications we derive, explain and improve the known integrability results, we establish integrability by local Lie groupoids, we clarify the smoothness of the Poisson sigma-model for Poisson manifolds, and we describe other geometrical applications. Contents 0. Introduction

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  • 4 portance of collision detection extends to several areas like robot motion planning, dynamic simulation, virtual reality applications and it has been extensively studied in robotics, computational geometry, and computer graphics for more than a decade 3, 4, 11, 13, 17, 41, 43, 45, 51, 53, 63 . Yet, there is no practical, e cient algorithm available yet for general geometric models to perform collision detection in real time. Recently, Pentland has listed collision detection as one of the major bottlenecks towards real time virtual environment simulations 69 .

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