Intuitive and Efficient Camera Control with the Toric Space
Automatically positioning a virtual camera in a 3D environment given the specification of visual properties to be satisfied (on-screen layout of subjects, vantage angles, visibility) is a complex and challenging problem. Most approaches tackle the problem by expressing visual properties as constraints or functions to optimize, and rely on computationally expensive search techniques to explore the solution space.
We present a simple and very efficient technique to express and solve the exact on-screen positioning of two or three subjects. We express the solution space for each couple of subjects as a 2D manifold surface. Using this manifold surface, one can then solve Blinn's spacecraft problem [Blinn88] with a straightforward algebraic approach. This solution can then be extended to three subjects and one can cast a complex 6D optimization problem tackled by most contributions in the field in a simple 2D optimization on the manifold surface, by pruning large portions of the search space. The result is a robust and very efficient technique which finds a wide range of applications in virtual camera control and more generally in computer graphics.
If looking for the on-screen positioning of more than 2 targets : for 3 targets there is an algebraic solution (two possible camera configurations); but for more than 3 targets, the problem is over-constrained, no exact solution exist in the general case. What we propose is thus to fix 2 of the targets and minimize the error on the on-screen positions of all other targets.
We packaged the code of our manifold surface, with utilities to compute very classical cinematic single- or two-target viewpoints. It is easy to integrate with any 3D rendering engine, and we provided sample examples showing how to use it with a few lines of code.
If you use it in your research projects, please cite the original papers :
- Intuitive and Efficient Camera Control with the Toric Space. C. Lino, M. Christie. ACM Transactions on Graphics (TOG) - Proceedings of SIGGRAPH, 2015.
- Efficient Composition for Virtual Camera Control. C. Lino, M. Christie. ACM SIGGRAPH / Eurographics Symposium on Computer Animation, 2012.
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