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Boolean Combination of Circular Arcs using Orthogonal Spheres

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

Conformal Villarceau Rotors

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

New spinor classes on the Graf-Clifford algebra

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

Clifford-based spectral action and renormalization group analysis of the gauge couplings

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

Group theoretic approach to fermion production

) × 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

Clifford algebra-valued orthogonal polynomials in the open unit ball of Euclidean space

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

Robot Object Manipulation Using Stereoscopic Vision and Conformal Geometric Algebra

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

Clifford algebra-valued orthogonal polynomials in the open unit ball of Euclidean space

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

Early Investigations in Conformal and Differential Geometry

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

Szegő projections for hardy spaces of monogenic functions and applications

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

A Curvature-Based Descriptor for Point Cloud Alignment Using Conformal Geometric Algebra

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

Szegő projections for hardy spaces of monogenic functions and applications

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

Tracking of Brain Tumors using Vision and Neurosonography

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

Surface Approximation using Growing Self-Organizing Nets and Gradient Information

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

DOA estimation for conformal vector-sensor array using geometric algebra

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

Linear BVPs and SIEs for Generalized Regular Functions in Clifford Analysis

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

The Genesis of Geometric Algebra: A Personal Retrospective

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

Erratum to: The Genesis of Geometric Algebra: A Personal Retrospective

] 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)

Unified Spatial Intersection Algorithms Based on Conformal Geometric Algebra

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

Preface for Special Issue on Geometric Algebra in Computer Science and Engineering

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