A Coordinate Free Geometry

نویسندگان

  • Stephen Mann
  • Nathan Litke
  • Tony DeRose
چکیده

An algebra for geometric reasoning is developed that is amenable to software implementation. The features of the algebra are chosen to support geometric programming of the variety found in computer graphics and computer aided geometric design applications. The implementation of the algebra in C++ is described, and several examples illustrating the use of this software are given.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Simulation of Styrene Polymerization in Arbitrary Cross-Sectional Duct Reactors by Boundary-Fitted Coordinate Transformation Method

The non-orthogonal boundary-fitted coordinate transformation method is applied to the solution of steady three-dimensional conservation equations of mass, momentum, energy and speciescontinuity to obtain the laminar velocity, temperature and concentration fields for simulation of polymerization of styrene in arbitrary cross-sectional duct reactors. Variable physical properties (except for speci...

متن کامل

Free vibration analysis of variable stiffness composite laminated thin skew plates using IGA

A NURBS-based isogeometric finite element formulation is developed and adopted to the free vibration analysis of finite square and skew laminated plates. Variable stiffness plies are assumed due to implementation of curvilinear fiberreinforcements. It is assumed due to employment of tow placement technology, in each ply of variable stiffness composite laminated plate the fiber reinforceme...

متن کامل

Who’s afraid of coordinate systems? An essay on representation of spacetime structure

Coordinate-based approaches to physical theories remain standard in mainstream physics but are largely eschewed in foundational discussion in favour of coordinate-free differential-geometric approaches. I defend the conceptual and mathematical legitimacy of the coordinate-based approach for foundational work. In doing so, I provide an account of the Kleinian conception of geometry as a theory o...

متن کامل

Elastic Behavior of Functionally Graded Two Tangled Circles Chamber

This paper presents the numerical elastic solution for a real problem, functionally graded chamber of hydraulic gear pumps under internal pressure. Because of the similarity and complexity for the considering geometry, a bipolar cylindrical coordinate system is used to extract the governing equations. The material properties are considered to vary along the two tangled circles with a power-law ...

متن کامل

Manifolds with boundary and of bounded geometry

For non-compact manifolds with boundary we prove that bounded geometry defined by coordinate-free curvature bounds is equivalent to bounded geometry defined using bounds on the metric tensor in geodesic coordinates. We produce a nice atlas with subordinate partition of unity on manifolds with boundary of bounded geometry, and we study the change of geodesic coordinate maps.

متن کامل

Analysis of Geometrical Theorems in Coordinate-Free Form by Using Anticommutative Gröbner Bases Method

In this paper we consider the Gröbner bases of Grassman algebra and their application to the algebraic geometry. Geometrical statements of constructive type should be given in the coordinate-free form.

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 1997