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An orthogonal sphere representation of arcs on spatial circles can be used to compactly perform Boolean combinations of such arcs. We formulate this using conformal **geometric** **algebra**, of which the ... distance geometry problem (DMDGP) Conformal **geometric** **algebra**
This article is part of the Topical Collection on Proceedings of AGACSE 2018, IMECC-UNICAMP, Campinas, Brazil, edited by Sebastià Xambó

We consider Villarceau circles as the orbits of specific composite rotors in 3D conformal **geometric** **algebra** that generate knots on nested tori. We compute the conformal parametrization of these ... coordinate-free CGA representations can aid in the analysis of Villarceau circles (and torus knots) as occurring in the Maxwell and Dirac equations.
KeywordsVillarceau circle Conformal **Geometric** **algebra** Hopf

Abstract Pinor and spinor fields are sections of the subbundles whose fibers are the representation spaces of the **Clifford** **algebra** of the forms, equipped with the Graf product. In this context ... dans les espaces spinoriels, J. Geom. Phys. 10 (1992) 19.ADSMathSciNetCrossRefzbMATHGoogle Scholar
[5]
C.I. Lazaroiu, E.M. Babalic and I.A. Coman, The **geometric** **algebra** of Fierz identities in arbitrary

of the **Clifford** **algebra** into the finite part of the spectral triple, the main object that encodes the complete information of a noncommutative space, gives rise to five additional scalar fields in the ... (complexified) **Clifford** **algebra** \(\mathcal {C \ell }(M)\), additional terms should be included in the Dirac operator, as well as a modification to the standard grading in the minimal formalism. As a result of

) × U(1), corresponding to the freedom in choosing representations of the gamma matrices in **Clifford** **algebra**, under which a part of the Dirac spinor function transforms like a fundamental representation

A new method for constructing **Clifford** **algebra**-valued orthogonal polynomials in the open unit ball of Euclidean space is presented. In earlier research, we only dealt with scalar-valued weight ... encompass **Clifford** **algebra**-valued functions. The method consists in transforming the orthogonality relation on the open unit ball into an orthogonality relation on the real axis by means of the so-called

This paper uses **geometric** **algebra** to formulate, in a single framework, the kinematics of a three finger robotic hand, a binocular robotic head, and the interactions between 3D objects, all of which ... Applied Bionics and Biomechanics
Robot object manipulation using stereoscopic vision and conformal **geometric** **algebra**
Julio Zamora-Esquivel
Eduardo Bayro-Corrochano 0
Intel
Jalisco
Mexico
0

A new method for constructing **Clifford** **algebra**-valued orthogonal polynomials in the open unit ball of Euclidean space is presented. In earlier research, we only dealt with scalar-valued weight ... encompass **Clifford** **algebra**-valued functions. The method consists in transforming the orthogonality relation on the open unit ball into an orthogonality relation on the real axis by means of the so-called

that it uses the standard Dirac operator on Euclidean space and is based on a representation of Möbius transformations using 2x2 matrices over a **Clifford** **algebra**. Clifford algebras and the Dirac operator ... as the Atiyah-Singer Index Theorem and the
Dirac equation in relativistic quantum mechanics. Therefore, after a brief introduction, the
intuitive idea of a **Clifford** **algebra** is developed. The Clifford

application, we obtain an explicit representation of the solution of the Dirichlet problem for balls and half spaces with L2, **Clifford** **algebra**-valued, boundary datum. ... should be interested in the idea that certain
features of complex function theory in the plane which are lost in higher dimensions
can be recovered by embedding Cn into a **Clifford** **algebra** of suitable

This paper presents a descriptor for course alignment of point clouds using conformal **geometric** **algebra**. The method is based on selecting keypoints depending on shape factors to identify distinct ... favorably to stateof-the-art methods in an experiment on course alignment of industrial parts to be assembled with robots.
Keypoint descriptor; Conformal **geometric** **algebra**; Initial alignment; Point clouds
1

application, we obtain an explicit representation of the solution of the Dirichlet problem for balls and half spaces with L2, **Clifford** **algebra**-valued, boundary datum. ... should be interested in the idea that certain
features of complex function theory in the plane which are lost in higher dimensions
can be recovered by embedding Cn into a **Clifford** **algebra** of suitable

probe in several contiguous images, we use conformal **geometric** **algebra** to compute the geometric transformations that yield the 3D position of the tumour, which was segmented in the ultrasound image using ... 3D pose of the probe using Conformal **geometric**
**algebra** (CGA) and multiple-view methods. We present the
conclusions in Section 5.
2. Endoscopic image processing
2.1. Tracking the ultrasound probe
The

as versors in the conformal **geometric** **algebra** framework, which build the shape of the object independent of its position in space (coordinate free). Our algorithms were tested with several images ... them with a
constant d .
If a stopping criterion is not yet fulfilled repeat all the
previous steps.
**Geometric** **algebra**
The geometric or **Clifford** **algebra** was introduced by
William K. Clifford (1845

focus on modeling the manifold holistically by a new mathematical tool called **geometric** **algebra**. Compared with existing methods, the presented one has two main advantages. Firstly, it acquires higher ... .
**Geometric** **algebra**; Conformal array; Electromagnetic vector sensors; DOA estimation
1 Introduction
The direction of arrival (DOA) estimation has received a
strong interest in wireless communication systems

We study some properties of a regular function in Clifford analysis and generalize Liouville theorem and Plemelj formula with values in **Clifford** **algebra** . By means of the classical Riemann boundary ... ]). Clifford analysis is an important field of modern mathematics which studies the functions defined in with values in **Clifford** **algebra** space and possesses both theoretical and applicable values, such as

Even today mathematicians typically typecast **Clifford** **Algebra** as the “algebra of a quadratic form,” with no awareness of its grander role in unifying geometry and algebra as envisaged by Clifford ... this opportunity to recall some highlights
of my personal journey and offer my take on lessons to be learned. The first
lesson follows:
2. **Clifford** **Algebra** Versus **Geometric** **Algebra**
A central theme in

] Dechant, P.: **Clifford** **algebra** is the natural framework for root systems and Coxeter groups. Group theory: Coxeter, conformal and modular groups. Clifford Anal. Appl. 27, 17-31 (2017)

Conformal **Geometric** **Algebra** has been introduced into geographic information science as a mathematical theory because of its advantages in terms of uniform multidimensional representation and ... on Conformal **Geometric** **Algebra** to determine the spatial relationships between geographic objects in a unified manner. The unified representation and intersection computation can be realized for

issue of AACA is mainly based on extended contributions to the GACSE 2016 workshop and covers topics ranging from applications of Clifford **Geometric** **Algebra** (GA) in computer graphics, computer vision and