Computational Aspects of Geometric Algebra Products of Two Homogeneous Multivectors

Autor: Breuils, Stephane, Nozick, Vincent, Sugimoto, Akihiro

Studies on time and memory costs of products in geometric algebra have been limited to cases where multivectors with multiple grades have only non-zero elements. This allows to design efficient algorithms for a generic purpose; however, it does not r

Externí odkaz: http://arxiv.org/abs/2002.11313

Tento výsledek nelze pro nepřihlášené uživatele zobrazit.
K zobrazení výsledku je třeba se přihlásit.

Conjecture on Characterisation of Bijective 3D Digitized Reflections and Rotations

Autor: Breuils, Stéphane, Kenmochi, Yukiko, Andres, Eric, Sugimoto, Akihiro

Bijectivity of digitized linear transformations is crucial when transforming 2D/3D objects in computer graphics and computer vision. Although characterisation of bijective digitized rotations in 2D is well known, the extension to 3D is still an open

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=od_______166::6e67418ae9f710317ecdad33ecd3b768
https://hal.science/hal-03764839

Algorithmic structure for geometric algebra operators and application to quadric surfaces

Autor: Breuils, Stéphane

Publikováno v: Operator Algebras [math.OA]. Université Paris-Est, 2018. English. ⟨NNT : 2018PESC1142⟩

Geometric Algebra is considered as a very intuitive tool to deal with geometric problems and it appears to be increasingly efficient and useful to deal with computer graphics problems. The Conformal Geometric Algebra includes circles, spheres, planes

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=dedup_wf_001::060fb089a59fbcd9118758143918ca74
https://pastel.archives-ouvertes.fr/tel-02085820/document

Quadric Conformal Geometric Algebra of ${\mathbb {R}}^{9,6}$

Autor: Breuils, Stéphane, Nozick, Vincent, Sugimoto, Akihiro, Hitzer, Eckhard

Publikováno v: Advances in Applied Clifford Algebras
Advances in Applied Clifford Algebras, Springer Verlag, 2018, 28 (2), pp.35. ⟨10.1007/s00006-018-0851-1⟩

International audience; Geometric Algebra can be understood as a set of tools to represent, construct and transform geometric objects. Some Geometric Algebras like the well-defined Conformal Geometric Algebra constructs lines, circles, planes, and sp

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=dedup_wf_001::521c794c80425dba49c23549dab22c7e
https://hal-upec-upem.archives-ouvertes.fr/hal-01767230/file/QCGA2018.pdf