Journal of Optimization Theory and Applications
Geometric and solid modeling: an introduction
Geometric and solid modeling: an introduction
The intersection of a bicubic Be´zier patch and a plane
Computer Aided Geometric Design
Using multivariate resultants to find the intersection of three quadric surfaces
ACM Transactions on Graphics (TOG)
On determining start points for a surface/surface intersection algorithm
Computer Aided Geometric Design
Surface-to-Surface Intersections
IEEE Computer Graphics and Applications - Special issue on computer-aided geometric design
An algebraic approach to curves and surfaces on the sphere and on other quadrics
Selected papers of the international symposium on Free-form curves and free-form surfaces
Impulse-based simulation of rigid bodies
I3D '95 Proceedings of the 1995 symposium on Interactive 3D graphics
Incremental algorithms for collision detection between solid models
SMA '95 Proceedings of the third ACM symposium on Solid modeling and applications
An efficient surface intersection algorithm based on lower-dimensional formulation
ACM Transactions on Graphics (TOG)
Controlled iterative methods for solving polynomial systems
ISSAC '98 Proceedings of the 1998 international symposium on Symbolic and algebraic computation
Torus/Sphere intersection based on a configuration space approach
Graphical Models and Image Processing
A Laguerre geometric approach to rational offsets
Computer Aided Geometric Design
A parametric algorithm for drawing pictures of solid objects composed of quadric surfaces
Communications of the ACM
On the minors of the implicitization Bézout matrix for a rational plane curve
Computer Aided Geometric Design
An algebraic condition for the separation of two ellipsoids
Computer Aided Geometric Design
Robot Motion Planning
Shape Interrogation for Computer Aided Design and Manufacturing
Shape Interrogation for Computer Aided Design and Manufacturing
Elimination and Resultants - Part 1: Elimination and Bivariate Resultants
IEEE Computer Graphics and Applications
IEEE Computer Graphics and Applications
A Unified Gradient Flow Approach to Constrained Nonlinear Optimization Problems
Computational Optimization and Applications
Near-optimal parameterization of the intersection of quadrics
Proceedings of the nineteenth annual symposium on Computational geometry
Efficient Distance Computation for Quadratic Curves and Surfaces
GMP '02 Proceedings of the Geometric Modeling and Processing — Theory and Applications (GMP'02)
Computing Distances between Surfaces Using Line Geometry
PG '02 Proceedings of the 10th Pacific Conference on Computer Graphics and Applications
Enhancing Levin's method for computing quadric-surface intersections
Computer Aided Geometric Design
Efficient isolation of polynomial's real roots
Journal of Computational and Applied Mathematics - Special issue: Proceedings of the international conference on linear algebra and arithmetic, Rabat, Morocco, 28-31 May 2001
Intersecting quadrics: an efficient and exact implementation
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
Numerical Methods for Unconstrained Optimization and Nonlinear Equations (Classics in Applied Mathematics, 16)
On the computation of an arrangement of quadrics in 3D
Computational Geometry: Theory and Applications - Special issue on the 19th European workshop on computational geometry - EuroCG 03
A robust algorithm for finding the real intersections of three quadric surfaces
Computer Aided Geometric Design
Oriented bounding surfaces with at most six common normals
ICRA'09 Proceedings of the 2009 IEEE international conference on Robotics and Automation
Precise Hausdorff distance computation between polygonal meshes
Computer Aided Geometric Design
Computing the distance between canal surfaces
GMP'10 Proceedings of the 6th international conference on Advances in Geometric Modeling and Processing
Distance computation for canal surfaces using cone-sphere bounding volumes
Computer Aided Geometric Design
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The minimum distance computation problem between two surfaces is very important in many applications such as robotics, CAD/CAM and computer graphics. Given two implicit algebraic surfaces, a new method based on the offset technique is presented to compute the minimum distance and a pair of points where the minimum distance occurs. The new method also works where there are an implicit algebraic surface and a parametric surface. Quadric surfaces, tori and canal surfaces are used to demonstrate our new method. When the two surfaces are a general quadric surface and a surface which is a cylinder, a cone or an elliptic paraboloid, the new method can produce two bivariate equations where the degrees are lower than those of any existing method.