2019/02/27 by Stéphane Breuils, Vincent Nozick, Breuils, Stéphane +5
Computer Science · Engineering · Mathematics · #Advanced Numerical Analysis Techniques #Algebra over a field #Algebraic and Geometric Analysis #Binary quadratic form #Combinatorics #Computational Geometry (cs.CG) #Computer science #Engineering #FOS: Computer and information sciences #Geometry #Intersection (aeronautics) #Isotropic quadratic form #Mathematical optimization #Mathematics #Mathematics and Applications #Polynomial and algebraic computation #Pure mathematics #Quadratic equation #Quadratic form (statistics) #Quadratic function #Quadratic programming #Representation (politics) #Unification #cs.CG
paper · pdf · doi:10.48550/arxiv.1903.02444
published in arXiv (Cornell University) (Cornell University)
openalex publication_date 2019/02/27 · arxiv created 2019/03/05 · arxiv updated 2019/03/07 · openalex created_date 2022/07/29 · openalex updated_date 2026/07/28
Quadratic surfaces gain more and more attention among the Geometric Algebra\ncommunity and some frameworks were proposed in order to represent, transform,\nand intersect these quadratic surfaces. As far as the authors know, none of\nthese frameworks support all the operations required to completely handle these\nsurfaces. Some frameworks do not allow the construction of quadratic surfaces\nfrom control points when others do not allow to transform these quadratic\nsurfaces. However , if we consider all the frameworks together, then all the\nrequired operations over quadratic are covered. This paper presents a\nunification of these frameworks that enables to represent any quadratic\nsurfaces either using control points or from the coefficients of its implicit\nform. The proposed approach also allows to transform any quadratic surfaces and\nto compute their intersection and to easily extract some geometric properties .\n