AUTOMATIC TESSELLATION OF QUADRIC SURFACES USING GRASSMANN-CAYLEY ALGEBRA

被引：0
|
作者：
Jourdan, Frederic [1 ]
Hegron, Gerard [2 ]
Mace, Pierre [3 ]
机构：
[1] Ecole Mines Nantes, 4 Rue Alfred Kastler,BP 20722, F-44307 Nantes, France
[2] Ecole Architecture Nantes, CERMA, F-44319 Nantes, France
[3] Ecole Architecture Paris La Villette, ARIAM, F-750I9 Paris, France
来源：
COMPUTER VISION AND GRAPHICS (ICCVG 2004) | 2006年 / 32卷
关键词：
Grassmann-Cayley algebra; conics and quadrics; surface modeling; tessellations;
D O I：
10.1007/1-4020-4179-9_97
中图分类号：
TP18 [人工智能理论];
学科分类号：
081104 ; 0812 ; 0835 ; 1405 ;
摘要：
Grassmann-Cayley algebra (GCA) provides an efficient formulation of projectice geometry, allowing work with elementary geometrical objects at a low computational cost. In this paper we use GCA as a mathematical framework for modeling conic curves and quadric surfaces of 3D space, and for computing rational parameterizations of these. Then, through ad hoc sampling of the parameter space, we derive tessellations of conics and quadrics.
引用
收藏
页码：674 / 682
页数：9
相关论文
共 50 条
  • [21] Singularity Analysis of a Six-Dof Parallel Manipulator Using Grassmann-Cayley Algebra and Grobner Bases
    Caro, Stephane
    Moroz, Guillaume
    Gayral, Thibault
    Chablat, Damien
    Chen, Chao
    BRAIN, BODY AND MACHINE, 2010, 83 : 341 - +
  • [22] Grassmann-Cayley algebra for modelling systems of cameras and the algebraic equations of the manifold of trifocal tensors
    Faugeras, O
    Papadopoulo, T
    PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 1998, 356 (1740): : 1123 - 1150
  • [23] A Formalization of Grassmann-Cayley Algebra in COQ and Its Application to Theorem Proving in Projective Geometry
    Fuchs, Laurent
    Thery, Laurent
    AUTOMATED DEDUCTION IN GEOMETRY, 2011, 6877 : 51 - +
  • [24] A geometric approach for singularity analysis of 3-DOF planar parallel manipulators using Grassmann-Cayley algebra
    Wen, Kefei
    Seo, TaeWon
    Lee, Jeh Won
    ROBOTICA, 2017, 35 (03) : 511 - 520
  • [25] SinguLab - A Graphical User Interface for the Singularity Analysis of Parallel Robots Based on Grassmann-Cayley Algebra
    Ben-Horin, Patricia
    Shoham, Moshe
    Caro, Stephane
    Chablat, Damien
    Wenger, Philippe
    ADVANCES IN ROBOT KINEMATICS: ANALYSIS AND DESIGN, 2008, : 49 - +
  • [26] SINGULARITY ANALYSIS OF THE 4-(R)under-barUU PARALLEL MANIPULATOR BASED ON GRASSMANN-CAYLEY ALGEBRA AND GRASSMANN GEOMETRY
    Amine, Semaan
    Masouleh, Mehdi Tale
    Caro, Stephane
    Wenger, Philippe
    Gosselin, Clement
    PROCEEDINGS OF THE ASME INTERNATIONAL DESIGN ENGINEERING TECHNICAL CONFERENCES AND COMPUTERS AND INFORMATION IN ENGINEERING CONFERENCE - 2011, VOL 6, PTS A AND B, 2012, : 1017 - +
  • [27] Singularity condition of six-degree-of-freedom three-legged parallel robots based on Grassmann-Cayley algebra
    Ben-Horin, Patricia
    Shoham, Moshe
    IEEE TRANSACTIONS ON ROBOTICS, 2006, 22 (04) : 577 - 590
  • [28] Cayley-Hamilton theorem for 2 x 2 matrices over the Grassmann algebra
    Domokos, M
    JOURNAL OF PURE AND APPLIED ALGEBRA, 1998, 133 (1-2) : 69 - 81
  • [29] Representing quadric surfaces using NURBS surfaces
    Kaihuai Qin
    Journal of Computer Science and Technology, 1997, 12 (3) : 210 - 216
  • [30] Representing Quadric Surfaces Using NURBS Surfaces
    秦开怀
    Journal of Computer Science and Technology, 1997, (03) : 210 - 216
12345