Results 141 to 150 of about 352 (177)

Geometric Product of Two Oriented Points in Conformal Geometric Algebra

Advances in Applied Clifford Algebras
The author studies products of oriented points in the framework of conformal geometric algebra (CGA) of the three-dimensional Euclidean space, i.e., the Clifford algebra \(Cl(4,1)\). After a brief introduction, the notion of an oriented point in CGA is explained in detail, and then the geometric product of such points is calculated explicitly in ...
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Geometric Error Modeling of Parallel Manipulators Based on Conformal Geometric Algebra

Advances in Applied Clifford Algebras, 2018
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Visual Servoing on the Sphere Using Conformal Geometric Algebra

Advances in Applied Clifford Algebras, 2012
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
López-Franco, Carlos, Arana-Daniel, Nancy, Alanis, Alma Y.   +2 more
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Rigid Body Dynamics and Conformal Geometric Algebra

2011
We discuss a fully covariant Lagrangian-based description of 3D rigid body motion, employing spinors in 5D conformal space. The use of this space enables the translational and rotational degrees of freedom of the body to be expressed via a unified rotor structure, and the equations of motion in terms of a generalised ‘moment of inertia tensor’ are ...
Anthony Lasenby, Robert Lasenby, Chris Doran   +2 more
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Quadric Conformal Geometric Algebra of R^{9,6}

2018
Geometric Algebra can be understood as a set of tools to represent, construct and transform geometric objects. Some Geometric Algebras like the well-de ned Conformal Geometric Algebra constructs lines, circles, planes, and spheres from control points just by using the outer product.
Breuils, Stephane, Nozick, Vincent, Sugimoto, Akihiro, Hitzer, Eckhard   +3 more
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Kinematics and grasping using conformal geometric algebra

2006
In this paper we introduce the conformal geometric algebra in the field of robot grasping. It help us to tackle problems of object modelling, hand kinematics and vision system using a unifying geometric language. We present an grasp algorithm using velocity control.
J. Zamora-Esquivel, E. Bayro-Corrochano
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Inverse Kinematics Solutions Using Conformal Geometric Algebra

2011
This paper describes a novel iterative Inverse Kinematics (IK) solver, FABRIK, that is implemented using Conformal Geometric Algebra (CGA). FABRIK uses a forward and backward iterative approach, finding each joint position via locating a point on a line. We use the IK of a human hand as an example of implementation where a constrained version of FABRIK
Andreas Aristidou, Joan Lasenby
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Constrained Dynamics in Conformal and Projective Geometric Algebra

2020
In this paper we tackle the problem of constrained rigid body dynamics in the Conformal and Projective Geometric Algebras (CGA, PGA). First we construct a screw-theory based formulation of dynamics in CGA and note the equivalence between this and the PGA dynamics presented by Gunn in[1]. After verifying the formulation via simulation, we move on to the
Hadfield, H, Lasenby, J
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Parameterization of 3D Conformal Transformations in Conformal Geometric Algebra

2010
Conformal geometric algebra is a powerful mathematical language for describing and manipulating geometric configurations and their conformal transformations. By providing a 5D algebraic representation of 3D geometric configurations, conformal geometric algebra proves to be very helpful in pose estimation, motion design, and neuron-based machine ...
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Geometric Algebra Tensor Voting, Hough Transform, Voting and Perception Using Conformal Geometric Algebra

2018
The first section presents a non-iterative algorithm that combines the power of expression of geometric algebra with the robustness of Tensor Voting to find the correspondences between two sets of 3D points with an underlying rigid transformation. In addition, we present experiments of the conformal geometric algebra voting scheme using synthetic and ...
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