Biomedical subjects
Publications and source records attributed to R Andrew Hicks.
We show that, for any rotationally symmetric projection with a single virtual viewpoint, it is possible to design a two-mirror rotationally symmetric system that realizes the projection exactly. These mirror pairs are derived from two coupled differential equations. We give examples in which the projections from the sphere at infinity are stereographic, perspective, and equiresolution.
We consider the problem of designing a passenger side mirror for an automobile that does not have a blind spot and that does not distort the image. Our model consists of a coupled pair of partial differential equations that do not have a common solution. Using a best mean-square-error functional, we find approximate solutions using nonlinear optimization. In one case a local minimum provides a mirror that solves the problem, but it does not reverse the image.
I present a design technique for realizing given projections as catadioptric sensors. In general, these problems do not have solutions, but approximate solutions may often be found that are visually acceptable. The method described reduces the problem to solving a linear system. A given transformation from the image plane to an object surface is shown to determine a vector field that is normal to the surface in the case where the vector field is a gradient. For the case when the vector field is not a gradient, several functionals are presented that may be minimized to give approximate solutions. As an application several new designs are described, including a mirror that directly gives a full 360-deg cylindrical projection without the need for any digital processing.