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.

This article presents a virtual cameraman which allows us to obtain the whole set of camera movements satisfying user defined constraints specified in the image space and/or constraints on the objects of the scene. This research follows the "Declarative Modelling" approach, which focuses on a 3-phase modeller concept : description; generation; result exploration. Our tool is based on a solver using interval arithmetic. The time dimension is treated as another variable, thus constraints can be specified for the total duration of the animation or could last only for a given amount of time. There is no keyframing and no interpolation, thereby, for the solutions obtained, the satisfaction of the specified constraints are guaranteed. Several ways to include time dimension efficiently are discussed. We claim that the method is simple enough to be implemented easily without the need of any external solver.After a presentation of previous work, the declarative modelling concept will be exposed. We then explain the necessary mathematical models for the scene objects, the camera and the treated movements. After this, the description process and the properties used to specify a desired sequence will be described. The constraint solver based on interval computation will be exposed before the solution space navigation process. finally, some results will be shown. The paper ends with some future research directions.

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