The complexity of robot motion planning
The complexity of robot motion planning
Geometric and solid modeling: an introduction
Geometric and solid modeling: an introduction
A dimensionality paradigm for surface interrogations
Computer Aided Geometric Design
Curve intersection using Be´zier clipping
Computer-Aided Design - Special Issue: Be´zier Techniques
Algebraic solution for geometry from dimensional constraints
SMA '91 Proceedings of the first ACM symposium on Solid modeling foundations and CAD/CAM applications
Algorithms for intersecting parametric and algebraic curves
Proceedings of the conference on Graphics interface '92
Multipolynomial resultant algorithms
Journal of Symbolic Computation
Algebraic and numeric techniques in modeling and robotics
Algebraic and numeric techniques in modeling and robotics
LAPACK Users' guide (third ed.)
LAPACK Users' guide (third ed.)
IEEE Computer Graphics and Applications
Voronoi Diagrams of Set-Theoretic solid Models
IEEE Computer Graphics and Applications
An Efficient Algorithm for the Sparse Mixed Resultant
AAECC-10 Proceedings of the 10th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
Ray tracing parametric patches
SIGGRAPH '82 Proceedings of the 9th annual conference on Computer graphics and interactive techniques
Design of a Parallel Nonsymmetric Eigenroutine Toolbox, Part I
Design of a Parallel Nonsymmetric Eigenroutine Toolbox, Part I
Implicit and parametric curves and surfaces for computer aided geometric design
Implicit and parametric curves and surfaces for computer aided geometric design
Computing selected solutions of polynomial equations
ISSAC '94 Proceedings of the international symposium on Symbolic and algebraic computation
Algebraic geometry and group theory in geometric constraint satisfaction
ISSAC '94 Proceedings of the international symposium on Symbolic and algebraic computation
The singular value decomposition for polynomial systems
ISSAC '95 Proceedings of the 1995 international symposium on Symbolic and algebraic computation
Superior augmented reality registration by integrating landmark tracking and magnetic tracking
SIGGRAPH '96 Proceedings of the 23rd annual conference on Computer graphics and interactive techniques
An efficient surface intersection algorithm based on lower-dimensional formulation
ACM Transactions on Graphics (TOG)
Solving algebraic systems using matrix computations
ACM SIGSAM Bulletin
The structure of sparse resultant matrices
ISSAC '97 Proceedings of the 1997 international symposium on Symbolic and algebraic computation
MARS: a MAPLE/MATLAB/C resultant-based solver
ISSAC '98 Proceedings of the 1998 international symposium on Symbolic and algebraic computation
Implicit Polynomials, Orthogonal Distance Regression, and the Closest Point on a Curve
IEEE Transactions on Pattern Analysis and Machine Intelligence
A subdivision-based algorithm for the sparse resultant
Journal of the ACM (JACM)
Symbolic and numeric methods for exploiting structure in constructing resultant matrices
Journal of Symbolic Computation
Efficient And Accurate Interference Detection For Polynomial Deformation
CA '96 Proceedings of the Computer Animation
Efficient max-norm distance computation and reliable voxelization
Proceedings of the 2003 Eurographics/ACM SIGGRAPH symposium on Geometry processing
Kinematic and Static Analysis of a Three-degree-of-freedom Spatial Modular Tensegrity Mechanism
International Journal of Robotics Research
Matrix representations for toric parametrizations
Computer Aided Geometric Design
Design for dynamic loads: lack of uniqueness
Structural and Multidisciplinary Optimization
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Geometric and solid modelling deal with the representation and manipulation of physical objects. Currently most geometric objects are formulated in terms of polynomial equations, thereby reducing many application problems to manipulating polynomial systems. Solving systems of polynomial equations is a fundamental problem in these geometric computations. The author presents an algorithm for solving polynomial equations. The combination of multipolynomial resultants and matrix computations underlies this efficient, robust and accurate algorithm.