Explicit formulas for the multivariate resultant, Journal of Pure and Applied Algebra, vol.164, issue.1-2, pp.59-86, 2001. ,
DOI : 10.1016/S0022-4049(00)00145-6
A survey of intersection algorithms for curved surfaces, Computers & Graphics, vol.15, issue.1, pp.109-124, 1993. ,
DOI : 10.1016/0097-8493(91)90037-I
Controlled iterative methods for solving polynomial systems, Proceedings of the 1998 international symposium on Symbolic and algebraic computation , ISSAC '98, pp.252-59, 1998. ,
DOI : 10.1145/281508.281629
Some effective methods for unconstrained optimization based on the solution of systems of ordinary differential equations, Journal of Optimization Theory and Applications, vol.8, issue.2, pp.211-235, 1989. ,
DOI : 10.1007/BF00941054
Collision detection by four-dimensional intersection testing, IEEE Transactions on Robotics and Automation, vol.6, issue.3, pp.291-304, 1990. ,
DOI : 10.1109/70.56661
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.52.4265
Using multivariate resultants to find the intersection of three quadric surfaces, ACM Transactions on Graphics, vol.10, issue.4, pp.378-400, 1991. ,
DOI : 10.1145/116913.116917
On the minors of the implicitization B??zout matrix for a rational plane curve, Computer Aided Geometric Design, vol.18, issue.1, pp.21-36, 2001. ,
DOI : 10.1016/S0167-8396(00)00034-0
Numerical methods for unconstrained optimization and nonlinear equations, 1983. ,
DOI : 10.1137/1.9781611971200
An algebraic approach to curves and surfaces on the sphere and on other quadrics, Computer Aided Geometric Design, vol.10, issue.3-4, pp.3-4211, 1993. ,
DOI : 10.1016/0167-8396(93)90037-4
Near-optimal parameterization of the intersection of quadrics, Proceedings of the nineteenth conference on Computational geometry , SCG '03, pp.246-55, 2003. ,
DOI : 10.1145/777792.777830
URL : https://hal.archives-ouvertes.fr/inria-00099789
The intersection of a bicubic B??zier patch and a plane, Computer Aided Geometric Design, vol.7, issue.6, pp.475-88, 1990. ,
DOI : 10.1016/0167-8396(90)90010-O
Computing the distance between general convex objects in three-dimensional space, IEEE Transactions on Robotics and Automation, vol.6, issue.1, pp.53-61, 1990. ,
DOI : 10.1109/70.88117
A fast procedure for computing the distance between complex objects in three-dimensional space, IEEE Journal on Robotics and Automation, vol.4, issue.2, pp.193-203, 1988. ,
DOI : 10.1109/56.2083
Geometric and solid modeling: An introduction, 1989. ,
3D collision detection: a survey, Computers & Graphics, vol.25, issue.2, pp.269-85, 2001. ,
DOI : 10.1016/S0097-8493(00)00130-8
A framework for efficient minimum distance computations, Proceedings. 1998 IEEE International Conference on Robotics and Automation (Cat. No.98CH36146), pp.3678-84, 1998. ,
DOI : 10.1109/ROBOT.1998.681403
Minimum distance between a canal surface and a simple surface, Computer-Aided Design, vol.35, issue.10, pp.871-880, 2003. ,
DOI : 10.1016/S0010-4485(02)00123-9
Torus/Sphere Intersection Based on a Configuration Space Approach, Graphical Models and Image Processing, vol.60, issue.1, pp.77-92, 1998. ,
DOI : 10.1006/gmip.1997.0451
An efficient surface intersection algorithm based on lower-dimensional formulation, ACM Transactions on Graphics, vol.16, issue.1, pp.74-106, 1997. ,
DOI : 10.1145/237748.237751
Robot motion planning, 1991. ,
DOI : 10.1007/978-1-4615-4022-9
Intersecting quadrics, Proceedings of the twentieth annual symposium on Computational geometry , SCG '04, pp.419-447, 2004. ,
DOI : 10.1145/997817.997880
URL : https://hal.archives-ouvertes.fr/inria-00104003
Efficient distance computation for quadratic curves and surfaces, Geometric Modeling and Processing. Theory and Applications. GMP 2002. Proceedings, pp.60-69, 2002. ,
DOI : 10.1109/GMAP.2002.1027497
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.7.4540
A parametric algorithm for drawing pictures of solid objects composed of quadric surfaces, Communications of the ACM, vol.19, issue.10, pp.555-63, 1976. ,
DOI : 10.1145/360349.360355
A fast algorithm for incremental distance calculation, Proceedings. 1991 IEEE International Conference on Robotics and Automation, pp.1008-1022, 1991. ,
DOI : 10.1109/ROBOT.1991.131723
Collision detection between geometric models: A survey In: Proceedings of IMA conference on mathematics of surfaces, volume VIII, pp.37-56, 1998. ,
Collision and proximity queries Handbook of discrete and computational geometry, 2nd, pp.787-807, 2004. ,
Impulse-based simulation of rigid bodies, Proceedings of the 1995 symposium on Interactive 3D graphics , SI3D '95, 1995. ,
DOI : 10.1145/199404.199436
On the computation of an arrangement of quadrics in 3D, Computational Geometry, vol.30, issue.2, pp.145-64, 2005. ,
DOI : 10.1016/j.comgeo.2004.05.003
URL : https://hal.archives-ouvertes.fr/inria-00350858
On determining start points for a surface/surface intersection algorithm, Computer Aided Geometric Design, vol.8, issue.5, pp.401-409, 1991. ,
DOI : 10.1016/0167-8396(91)90013-2
Surface-to-surface intersections, IEEE Computer Graphics and Applications, vol.13, issue.1, pp.89-95, 1993. ,
DOI : 10.1109/38.180122
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.569.8349
Shape interrogation for computer aided design and manufacturing, 2002. ,
DOI : 10.1007/978-3-642-04074-0
A Laguerre geometric approach to rational offsets, Computer Aided Geometric Design, vol.15, issue.3, pp.223-272, 1998. ,
DOI : 10.1016/S0167-8396(97)00024-1
On the computational geometry of ruled surfaces, Computer-Aided Design, vol.31, issue.1, pp.17-32, 1999. ,
DOI : 10.1016/S0010-4485(98)00077-3
Incremental algorithms for collision detection between solid models, Proceedings of the third ACM symposium on Solid modeling and applications , SMA '95, pp.293-304, 1995. ,
DOI : 10.1145/218013.218076
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.130.8072
Surface/surface intersection problems In: The mathematics of surface I, pp.117-159, 1986. ,
Efficient distance computation between non-convex objects, Proceedings of the 1994 IEEE International Conference on Robotics and Automation, pp.3324-3353, 1994. ,
DOI : 10.1109/ROBOT.1994.351059
Efficient isolation of polynomial's real roots, Journal of Computational and Applied Mathematics, vol.162, issue.1, pp.33-50, 2004. ,
DOI : 10.1016/j.cam.2003.08.015
Numerical solution of constrained non-linear algebraic equations, International Journal for Numerical Methods in Engineering, vol.9, issue.8, pp.1455-81, 1986. ,
DOI : 10.1002/nme.1620230805
Computing distances between surfaces using line geometry, Pacific conference on computer graphics and applications, pp.236-281, 2002. ,
Stochastic algorithm for detecting intersection of implicit surfaces, Computers & Graphics, vol.24, issue.4, pp.523-531, 2000. ,
DOI : 10.1016/S0097-8493(00)00055-8
Signature sequence of intersection curve of two quadrics for exact morphological classification, 2005. ,
URL : https://hal.archives-ouvertes.fr/hal-00123473
Computing distances between NURBS-defined convex objects, Proceedings. 1998 IEEE International Conference on Robotics and Automation (Cat. No.98CH36146), pp.3686-90, 1998. ,
DOI : 10.1109/ROBOT.1998.681406
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.56.414
A unified gradient flow approach to constrained nonlinear optimization problems, Computational Optimization and Applications, vol.25, pp.1-3251, 2003. ,
Enhancing Levin's method for computing quadric-surface intersections, Computer Aided Geometric Design, vol.20, issue.7, pp.401-423, 2003. ,
DOI : 10.1016/S0167-8396(03)00081-5
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.15.600
An algebraic condition for the separation of two ellipsoids, Computer Aided Geometric Design, vol.18, issue.6, pp.531-540, 2001. ,
DOI : 10.1016/S0167-8396(01)00049-8
Eliminations and resultants 1: Elimination and bivariate resultants, IEEE Computer Graphics and Applications, vol.15, issue.1, pp.69-77, 1995. ,
Eliminations and resultants 2: Multivariate resultants, IEEE Computer Graphics and Applications, vol.15, issue.2, pp.60-69, 1995. ,
A robust algorithm for finding the real intersections of three quadric surfaces, Computer Aided Geometric Design, vol.22, issue.6, pp.515-545, 2005. ,
DOI : 10.1016/j.cagd.2005.02.001
Chen is a Ph.D. student in the Department of Computer Science and Technology at Tsinghua University, China. His research interests are computeraided design and computer graphics ,
He received his B.S. and Ph.D. in computer science from the Tsinghua University, China, in 1996 and 2001, respectively. He held a visiting researcher position in the Department of He was a post-doctoral fellow in the, His research interests include computer-aided design, computer graphics, computer animation, and software engineering, 2000. ,
Zheng is an associate professor in the School of Software at Tsinghua University, China. He received his B.S., Master and Ph.D. in mechanical manufacturing from Harbin Institute of Technology, China. His research interests include computer-aided design and software engineering ,
Paul is a senior researcher at CNRS and INRIA (France), and currently visiting professor at Tsinghua University. He received his Ph.D. in Mathematics from Paris University in 1976 His research interests include Numerical Analysis, Physics-Based Modeling and Computer-Aided Design ,
Sun is a professor in the Department of Computer Science and Technology at Tsinghua University , China. His research interests are computer graphics, computer aided design, computer-aided manufacturing , product data management and software en- gineering ,