On the numerical condition of polynomials in Berstein form
Computer Aided Geometric Design
Chemical equilibrium systems as numerical test problems
ACM Transactions on Mathematical Software (TOMS)
Interval analysis for computer graphics
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
Through-the-lens camera control
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
CINEMA: a system for procedural camera movements
I3D '92 Proceedings of the 1992 symposium on Interactive 3D graphics
Set inversion via interval analysis for nonlinear bounded-error estimation
Automatica (Journal of IFAC) - Special section on fault detection, supervision and safety for technical processes
ILPS '94 Proceedings of the 1994 International Symposium on Logic programming
Intelligent camera control for graphical environments
Intelligent camera control for graphical environments
Guaranteed tuning, with application to robust control and motion planning
Automatica (Journal of IFAC)
Solving Polynomial Systems Using a Branch and Prune Approach
SIAM Journal on Numerical Analysis
Toward Correctly Rounded Transcendentals
IEEE Transactions on Computers
Animating rotation with quaternion curves
SIGGRAPH '85 Proceedings of the 12th annual conference on Computer graphics and interactive techniques
Revising hull and box consistency
Proceedings of the 1999 international conference on Logic programming
Quantifier elimination for trigonometric polynomials by cylindrical trigonometric decomposition
Journal of Symbolic Computation
A Constraint Satisfaction Approach to a Circuit Design Problem
Journal of Global Optimization
Progress in the Solving of a Circuit Design Problem
Journal of Global Optimization
Where Am I? What Am I Looking At?
IEEE Computer Graphics and Applications
Cinematic Primitives for Multimedia
IEEE Computer Graphics and Applications
Global Consistency for Continuous Constraints
PPCP '94 Proceedings of the Second International Workshop on Principles and Practice of Constraint Programming
Extending Consistent Domains of Numeric CSP
IJCAI '99 Proceedings of the Sixteenth International Joint Conference on Artificial Intelligence
Hauptvortrag: Quantifier elimination for real closed fields by cylindrical algebraic decomposition
Proceedings of the 2nd GI Conference on Automata Theory and Formal Languages
Interval Constraint Logic Programming
Selected Papers from Constraint Programming: Basics and Trends
Modeling Camera Control with Constrained Hypertubes
CP '02 Proceedings of the 8th International Conference on Principles and Practice of Constraint Programming
Heterogeneous Constraint Solving
ALP '96 Proceedings of the 5th International Conference on Algebraic and Logic Programming
Rounding Errors in Algebraic Processes
Rounding Errors in Algebraic Processes
A branch and prune algorithm for the approximation of non-linear AE-solution sets
Proceedings of the 2006 ACM symposium on Applied computing
Constraint-based conversion of fiction text to a time-based graphical representation
Proceedings of the 2007 annual research conference of the South African institute of computer scientists and information technologists on IT research in developing countries
Mechanisms for multimodality: taking fiction to another dimension
AFRIGRAPH '07 Proceedings of the 5th international conference on Computer graphics, virtual reality, visualisation and interaction in Africa
An efficient algorithm for a sharp approximation of universally quantified inequalities
Proceedings of the 2008 ACM symposium on Applied computing
A Constraint-Based Autonomous 3D Camera System
Constraints
Motion overview of human actions
ACM SIGGRAPH Asia 2008 papers
A Branch and Bound Algorithm for Numerical MAX-CSP
CP '08 Proceedings of the 14th international conference on Principles and Practice of Constraint Programming
A Spatio-temporal Reasoning System for Virtual Camera Planning
SG '09 Proceedings of the 10th International Symposium on Smart Graphics
ΣK-constraints for hybrid systems
PSI'09 Proceedings of the 7th international Andrei Ershov Memorial conference on Perspectives of Systems Informatics
Automated camera planning to film robot operations
Artificial Intelligence Review
| Hi-index | 0.00 |
Many problems in robust control and motion planning can be reduced to either finding a sound approximation of the solution space determined by a set of nonlinear inequalities, or to the "guaranteed tuning problem" as defined by Jaulin and Walter, which amounts to finding a value for some tuning parameter such that a set of inequalities be verified for all the possible values of some perturbation vector. A classical approach to solving these problems, which satisfies the strong soundness requirement, involves some quantifier elimination procedure such as Collins' Cylindrical Algebraic Decomposition symbolic method. Sound numerical methods using interval arithmetic and local consistency enforcement to prune the search space are presented in this article as much faster alternatives for both soundly solving systems of nonlinear inequalities, and addressing the guaranteed tuning problem whenever the perturbation vector has dimension 1. The use of these methods in camera control is investigated, and experiments with the prototype of a declarative modeler to express camera motion using a cinematic language are reported and commented upon.