Geometric Algebra - The mathematical language for Computational Engineering?
نویسنده
چکیده
This work reviews some current engineering applications of geometric algebra and observes the potential of this mathematical language to become a basis for a wide range of computational engineering applications. Geometric algebra unifies many other mathematical concepts like quaternions and projective geometry and is able to easily deal with geometric objects, operations and transformations. For computational engineering, not only these nice properties are important, but also the computational point-of-view. We describe the big potential of geometric algebra for optimizations leading to highly efficient implementations.
منابع مشابه
Foundations of Geometric Algebra Computing
The author defines “Geometric Algebra Computing” as the geometrically intuitive development of algorithms using geometric algebra with a focus on their efficient implementation, and the goal of this book is to lay the foundations for the widespread use of geometric algebra as a powerful, intuitive mathematical language for engineering applications in academia and industry. The related technolog...
متن کاملIntroducing Geometric Algebra to Geometric Computing Software Developers: A Computational Thinking Approach
Designing software systems for Geometric Computing applications can be a challenging task. Software engineers typically use software abstractions to hide and manage the high complexity of such systems. Without the presence of a unifying algebraic system to describe geometric models, the use of software abstractions alone can result in many design and maintenance problems. Geometric Algebra (GA)...
متن کاملEngineering Graphics in Geometric Algebra
We illustrate the suitability of geometric algebra for representing structures and developing algorithms in computer graphics, especially for engineering applications. A number of example applications are reviewed. Geometric algebra unites many underpinning mathematical concepts in computer graphics such as vector algebra and vector fields, quaternions, kinematics and projective geometry, and i...
متن کاملEstimation of Concentrations in Chemical Systems at Equilibrium Using Geometric Programming
Geometric programming is a mathematical technique, which has been developed for nonlinear optimization problems. This technique is based on the dual program with linear constraints. Determination of species concentrations in chemical equilibrium conditions is one of its applications in chemistry and chemical engineering fields. In this paper, the principles of geometric programming and its comp...
متن کاملBuilding Content Dictionaries for Geometric Algebra in the XML Markup Language
This paper describes why and how to build Content Dictionaries for Geometric Algebra implementing in the XML markup language. Geometric Algebra is a powerful and general language available for the development of mathematical physics. Mathematical Markup Language (MathML) enables to write the XML-based language to display mathematical formulae on web browsers and OpenMath makes the text semantic...
متن کامل