A New Approach to Through-the-Lens Camera Control

the exact viewing of a 3D scene in mind. The situation is even worse for computer animation, in which a continuous The through-the-lens camera control technique originally proposed by M. Gleicher and A. Witkin [Comput. Graphics camera motion is often required to generate a smooth 26(2), 1992, 331–340], provides a powerful user interface for scene change. With a poor camera model, the computer the control of the virtual camera in 3D computer graphics and animator has to spend considerable time in fully describing animation. Their techique is based on locally inverting the natural scene changes in the animation movie. The virtual nonlinear perspective viewing transformation. However, given camera model thus plays an important role in 3D computer m image control points, the Jacobian matrix is derived as a graphics and animation. quite complex 2m 3 8 matrix; furthermore, the Jacobian matrix The camera status is usually described by seven paramealways has at least one redundant column since its rank can ters: one for focus, three for position, and three for orientabe 7 at most. For the overconstrained case of m $ 4, the tion. In some specialized systems such as RenderMan [27], Lagrange equation is always singular since its 2m 3 2m square other parameters are also used to control the optical propmatrix has rank 7 at most. All these complications result from removing the constraint qw 1 qx 1 qy 1 qz 5 1 for unit quaternierties of the camera (e.g., the depth of field, shutter speed, ons (qw , qx , qy , qz) [ S which represent the camera rotations. atmospheric effects) and the image properties (e.g., the In this paper, we interpret the problem as a target tracking pixel aspect ratio). In this paper, we assume a simple camproblem and formulate it as a constrianed nonlinear inversion era model which allows the user to control the virtual problem. The problem is then solved by integrating a tangent camera with seven degrees of freedom. However, even vector field defined on the configuration space of the virtual with such a simple camera model, it is not easy to control all camera. The vector field is given by the least-squares solutions of seven camera parameters simultaneously. This is because the Jacobian matrix equations. The row and column weighting most user interfaces (e.g., mouse) do not support the conscheme for the Jacobian matrix provides a convenient way to trol of all the required seven parameters at the same time. control the desired least-squares solutions and the associated For some camera effects (requiring certain coordinated vector field. The Lie group structure of the unit quaternion control of all camera parameters), it is not easy to generate space S enables us to derive a simple 2m 3 7 Jacobian matrix, which improves both the computational efficiency and numerismooth camera motion that produces scene changes which cal stability of the overall algorithm. For the overconstrained appear natural to the human eye. For example, when the case of m $ 4, the Jacobian matrix equation is solved (in the relative speeds of the translation and rotation of a camera least-squares sense) by using an efficient projection method are not synchronized, the animated scene shakes. with O(m) time complexity.  1996 Academic Press, Inc. Virtual cameras are usually described by specialized viewing transformations [10]. Using the geometric relationship between the world space and the view space, Blinn [3]