Marc Christie

Interval constraint solving for camera control and motion planning

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.

A Semantic Space Partitioning Approach to Virtual Camera Composition

In this paper, we present a semantic space partitioning (SSP) approach to the virtual camera composition problem. Virtual camera composition (VCC) consists in positioning a camera in a virtual world, such that the resulting image satises a set of visual cinematographic properties. Whereas most related works concentrate on numerically computing a unique camera position satisfying the problem, we offer to isolate identical possible solutions in 3D volumes with respect to their visual properties, and to propose them to the user. We introduce the notion of semantic volumes as an extension of visual aspects to characterize, compute and manipulate distinct solution sets. Our approach relies on (1) a space partitioning process derived from a study of possible camera locations w.r.t. to the objects in the scene and (2) local search numerical techniques to compute good representatives of each volume. This work is motivated by the lack of VCC tools in 3D software and the will to integrate cinematographic semantics in the description, solving and interaction processes. Experimental results illustrate the suitability of our approach for identifying and providing distinct solution sets. Furthermore, the exploitation of the semantic volumes lays the groundwork for natural and efcient user interaction by providing knowledge and reasoning on possible classes of solutions.

Automated Staging for Virtual Cinematography

While the topic of virtual cinematography has essentially focused on the problem of computing the best viewpoint in a virtual environment given a number of objects placed beforehand, the question of how to place the objects in the environment with relation to the camera (referred to as staging in the film industry) has received little attention. This paper first proposes a staging language for both characters and cameras that extends existing cinematography languages with multiple cameras and character staging. Second, the paper proposes techniques to operationalize and solve staging specifications given a 3D virtual environment. The novelty holds in the idea of exploring how to position the characters and the cameras simultaneously while maintaining a number of spatial relationships specific to cinematography. We demonstrate the relevance of our approach through a number of simple and complex examples.