Volume-elements of integration: A geometric algebra approach

2002 ◽  
Vol 116 (5) ◽  
pp. 1825-1833 ◽  
Author(s):  
Janne Pesonen ◽  
Lauri Halonen
Keyword(s):  
Geometric Algebra ◽  
Algebra Approach

Feature preserving multiresolution subdivision and simplification of point clouds: A conformal geometric algebra approach

2017 ◽  
Vol 41 (11) ◽  
pp. 4074-4087 ◽  
Author(s):  
Shuai Yuan ◽  
Shuai Zhu ◽  
Dong-Shuang Li ◽  
Wen Luo ◽  
Zhao-Yuan Yu ◽  
...  
Keyword(s):  
Geometric Algebra ◽  
Point Clouds ◽  
Conformal Geometric Algebra ◽  
Algebra Approach ◽  
Feature Preserving

Anisotropy done right: a geometric algebra approach

2010 ◽  
Vol 49 (3) ◽  
pp. 33006 ◽  
Author(s):  
S. A. Matos ◽  
C. R. Paiva ◽  
A. M. Barbosa
Keyword(s):  
Geometric Algebra ◽  
Algebra Approach

scholarly journals Note on geometric algebras and control problems with SO(3)-symmetries

2021 ◽  
Author(s):  
Jaroslav Hrdina ◽  
Aleš Návrat ◽  
Petr Vašík ◽  
Lenka Zalabova
Keyword(s):  
Control Systems ◽  
Local Control ◽  
Geometric Algebra ◽  
Carnot Group ◽  
Control Problems ◽  
Algebra Approach ◽  
Geometric Algebras ◽  
And Control ◽  
Specific Control

We study the role of symmetries in control systems by means of geometric algebra approach. We discuss two specific control problems on Carnot group of step 2 invariant with respect to the action of$SO(3). We understand geodesics as curves in suitable geometric algebras which allows us to asses an efficient algorithm for local control.

scholarly journals Geometric Algebra Framework Applied to Circuits with Non-sinusoidal Voltages and Currents

2021 ◽  
Author(s):  
Jan Cieśliński ◽  
Cezary Walczyk
Keyword(s):  
Vector Space ◽  
Clifford Algebra ◽  
Geometric Algebra ◽  
First Principles ◽  
Theoretical Physics ◽  
Electrical Circuits ◽  
Algebra Approach ◽  
Physical Components

We apply a well known technique of theoretical physics, known as Geometric Algebra or Clifford algebra, to linear electrical circuits with non-sinusoidal voltages and currents. We rederive from the first principles the Geometric Algebra approach to the apparent power decomposition. The important new point consists in a choice of a natural convenient basis in the Clifford vector space which simplifies considerably the presentation. Thus we are able to derive a number of general results which are missing in the former papers. In particular, a natural correspondence with the Current Physical Components approach is shown.

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