A systematic framework for solving geometric constraints analytically
DOI10.1006/jsco.2000.0392zbMath0967.65029OpenAlexW1991665284MaRDI QIDQ5926297
Christoph M. Hoffmann, Cassiano Durand
Publication date: 21 August 2001
Published in: Journal of Symbolic Computation (Search for Journal in Brave)
Full work available at URL: https://semanticscholar.org/paper/d8a0449dd74cd8cb66574533e8bd5e0a395a3f70
comparison of methodsnonlinear systemselimination methodsgeometric constraintsgeometric reasoningGröbner basis methodshomotopy continuationsymbolic reduction
Numerical computation of solutions to systems of equations (65H10) Numerical aspects of computer graphics, image analysis, and computational geometry (65D18) Global methods, including homotopy approaches to the numerical solution of nonlinear equations (65H20)
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- Bernstein's theorem in affine space
- An introduction to Wu's method for mechanical theorem proving in geometry
- A transformation to avoid solutions at infinity for polynomial systems
- A homotopy for solving polynomial systems
- Basic principles of mechanical theorem proving in elementary geometries
- Variation of geometries based on a geometric-reasoning method
- Coefficient-parameter polynomial continuation
- Newton polyhedra and toroidal varieties
- A new method for solving algebraic systems of positive dimension
- Algebraic method for manipulation of dimensional relationships in geometric models
- Rule-oriented method for parameterized computer-aided design
- Mixed volumes of polytopes
- Multipolynomial resultant algorithms
- A generalized Euclidean algorithm for computing triangular representations of algebraic varieties
- Decomposing polynomial systems into simple systems
- Mechanical theorem proving in geometries. Basic principles. Transl. from the Chinese by Xiaofan Jin and Dongming Wang
- Techniques of scientific computing (Part 2)
- Symbolic constraints in constructive geometric constraint solving
- On the theories of triangular sets
- Solving degenerate sparse polynomial systems faster
- Geometric constraint solver
- Efficient incremental algorithms for the sparse resultant and the mixed volume
- Mixed-volume computation by dynamic lifting applied to polynomial system solving
- On graphs and rigidity of plane skeletal structures
- Associative differential operations
- The Cheater’s Homotopy: An Efficient Procedure for Solving Systems of Polynomial Equations
- Efficient Algorithms for MultiPolynomial Resultant
- On The Complexity of Computing Mixed Volumes
- A Polyhedral Method for Solving Sparse Polynomial Systems
