Linear programming: methods and applications (5th ed.)
Linear programming: methods and applications (5th ed.)
Computational geometry: an introduction
Computational geometry: an introduction
On the numerical condition of polynomials in Berstein form
Computer Aided Geometric Design
Algorithms for polynomials in Bernstein form
Computer Aided Geometric Design
Algorithm for algebraic curve intersection
Computer-Aided Design
Generalised characteristic polynomials
Journal of Symbolic Computation - Special issue on computational algebraic complexity
Singular points of algebraic curves
Journal of Symbolic Computation
Curves and surfaces for computer aided geometric design
Curves and surfaces for computer aided geometric design
Ray tracing trimmed rational surface patches
SIGGRAPH '90 Proceedings of the 17th annual conference on Computer graphics and interactive techniques
Geometric Hermite approximation of surface patch intersection curves
Computer Aided Geometric Design
Finding intersections of B-spline represented geometries using recursive subdivision techniques
Computer Aided Geometric Design
Reliable Implementation of Real Number Algorithms: Theory and Practice
Computation of singularities and intersections of offsets of planar curves
Computer Aided Geometric Design
Topologically reliable approximation of composite Bézier curves
Computer Aided Geometric Design
Regularity criteria for the topology of algebraic curves and surfaces
Proceedings of the 12th IMA international conference on Mathematics of surfaces XII
Polytope-based computation of polynomial ranges
Proceedings of the 2010 ACM Symposium on Applied Computing
Proceedings of the 14th ACM Symposium on Solid and Physical Modeling
Theoretical Computer Science
Linear programming for Bernstein based solvers
ADG'08 Proceedings of the 7th international conference on Automated deduction in geometry
GPU-based parallel solver via the Kantorovich theorem for the nonlinear Bernstein polynomial systems
Computers & Mathematics with Applications
A hybrid parallel solver for systems of multivariate polynomials using CPUs and GPUs
Computer-Aided Design
Polytope-based computation of polynomial ranges
Computer Aided Geometric Design
Solving polynomial systems using no-root elimination blending schemes
Computer-Aided Design
Solving polynomial systems using no-root elimination blending schemes
Computer-Aided Design
Tracking point-curve critical distances
GMP'06 Proceedings of the 4th international conference on Geometric Modeling and Processing
GMP'06 Proceedings of the 4th international conference on Geometric Modeling and Processing
Subdivision termination criteria in subdivision multivariate solvers
GMP'06 Proceedings of the 4th international conference on Geometric Modeling and Processing
GMP'10 Proceedings of the 6th international conference on Advances in Geometric Modeling and Processing
Computer Aided Geometric Design
SMI 2012: Full Curve intersection using hybrid clipping
Computers and Graphics
The Bernstein polynomial basis: A centennial retrospective
Computer Aided Geometric Design
Technical note: Modeling by composition
Computer-Aided Design
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Abstract: A fundamental problem in computer aided design is the efficient computation of all roots of a system of nonlinear polynomial equations inn variables which lie within ann-dimensional @?. We present two techniques designed to solve such problems, which rely on representation of polynomials in the multivariate Bernstein basis and subdivision. In order to isolate all of the roots within the given domain, each method uses a different scheme for constructing a series of bounding @?es; the first method projects control polyhedra onto a set of coordinate planes, and the second employs linear optimization. We also examine in detail the local convergence properties of the two methods, proving that the former is quadratically convergent forn=1 and linearly convergent forn 1, while the latter is quadratically convergent for alln. Worst-case complexity analysis, as well as analysis of actual running times are performed.