A curve of constant width has the property that any two parallel supporting lines are the same distance apart in all directions. A fundamental problem involving these curves is to find one which encloses the smallest amount of area for a given width. This problem was resolved long ago and has a few relatively simple solutions.…
An important problem in computer vision is to understand the space of images that can be captured by an arrangement of cameras. A description of this space allows for statistical estimation methods to reconstruct three-dimensional models of the scene that was imaged. The set of images captured by an arrangement of pinhole cameras is usually…
Many biological organisms are comprised of deformable porous media, with additional complexity of an embedded muscle. Using geometric variational methods, we derive the equations of motion for the dynamics of such active porous media. The use of variational methods allows to incorporate both the muscle action and incompressibility of the fluid and the elastic matrix…