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Inverse kinematics computation in computer graphics and robotics using conformal geometric algebra

, 2005
We focus on inverse kinematics applications in computer graphics and robotics based on Conformal Geometric Algebra. Here, geometric objects like spheres and circles that are often needed in inverse kinematics algorithms are simply represented by ...
Bayro-Corrochano, E., Hildenbrand, D., Zamora, J.   +2 more
core   +1 more source

Correspondence Free Multivector Cloud Registration using Conformal Geometric Algebra [PDF]

We present, for the first time, a novel theoretical approach to address the problem of correspondence free multivector cloud registration in conformal geometric algebra. Such formalism achieves several favorable properties.
Nascimento, Jacinto C., Vasconcelos, Francisco Xavier   +1 more
core   +1 more source

Kinematic Analysis of Industrial Robots Based on Conformal Geometric Algebra

Jixie chuandong
In order to solve the problem of high complexity and large amount of computation for kinematics of industrial robots, conformal geometric algebra (CGA) is introduced to the construction of kinematics model of industrial robots.
Yu Yang, Wei Mengdi, Xu Guipeng, Ren Simin, Wei Yaxin   +4 more
doaj  

Geometric computing in computer graphics and robotics using conformal geometric algebra

, 2007
In computer graphics and robotics a lot of different mathematical systems like vector algebra, homogenous coordinates, quaternions or dual quaternions are used for different applications.
Hildenbrand, D.
core   +1 more source

Lie Symmetries of the Wave Equation on the Sphere Using Geometry

Dynamics
A semilinear quadratic equation of the form Aij(x)uij=Bi(x,u)ui+F(x,u) defines a metric Aij; therefore, it is possible to relate the Lie point symmetries of the equation with the symmetries of this metric. The Lie symmetry conditions break into two sets:
Michael Tsamparlis, Aniekan Magnus Ukpong   +1 more
doaj   +1 more source

Generalized Cross-Curvature Solitons of 3D Lorentzian Lie Groups

Axioms
We investigate left-invariant generalized cross-curvature solitons on simply connected three-dimensional Lorentzian Lie groups. Working with the assumption that the contravariant tensor Pij (defined from the Ricci tensor and scalar curvature) is ...
Mehdi Jafari
doaj   +1 more source

Conformal geometric algebra by extended Vahlen matrices

, 2009
The classical Vahlen matrix representation of conformal transformations on R(n) is directly related to the versor representation of conformal geometric algebra (CGA) using R(n+1;1).
Dorst, L.
core   +3 more sources

Bulk reconstruction from generalized free fields

Journal of High Energy Physics
We propose a generalized protocol for constructing a dual free bulk theory from any boundary model of generalized free fields (GFFs). To construct the bulk operators, we employ a linear ansatz similar to the Hamilton-Kabat-Liftschytz-Lowe (HKLL ...
Tamra Nebabu, Xiao-Liang Qi
doaj   +1 more source

Perturbed conformal field theory, nonlinear integral equations and spectral problems [PDF]

, 2000
This thesis is concerned with various aspects of perturbed conformal field theory and the methods used to calculate finite-size effects of integrable quantum field theories.
Dunning, Tania Clare, Tania Clare Dunning, Dunning, T.C.   +2 more
core  

Aspects of Geometric Algebra in Euclidean, Projective and Conformal Space [PDF]

, 2003
This report is meant to be a script of a tutorial on Clifford (or Geometric) algebra. It is therefore not complete in the description of the algebra and neither completely rigorous.
Perwass, Christian B.U., Hildenbrand, Dietmar   +1 more
core   +1 more source