Related papers: Catenary and Mercator projection
An exact transition matrix was formulated for electromagnetic scattering by a vacuum-like sphere with magnetoelectric gyrotropy. Both the total scattering and forward scattering efficiencies are lower when the magnetoelectric gyrotropy…
Optical sections of the cornea are obtained by illumination with a collimated beam expanded in a fan shape by a small rotary cylindrical lens. The light diffused from the cornea is observed by two cameras and processed in order to yield the…
There are several methods to focus light behind a scattering medium, but very few use fluorescence light as feedback or can be used without access to the distal side of the scatterer. Among all the wave-front shaping techniques, retrieving…
This gives some information about the conformal point and the calibrating conic, and their relationship one to the other. These concepts are useful for visualizing image geometry, and lead to intuitive ways to compute geometry, such as…
We investigate connections between the geometry of linear subspaces and the convergence of the alternating projection method for linear projections. The aim of this article is twofold: in the first part, we show that even in Euclidean…
Projections onto sets are used in a wide variety of methods in optimization theory but not every method that uses projections really belongs to the class of projection methods as we mean it here. Here projection methods are iterative…
We consider the popular and classical method of alternating projections for finding a point in the intersection of two closed sets. By situating the algorithm in a metric space, equipped only with well-behaved geodesics and angles (in the…
On any compact space one can consider the map which sends a point to the set of points farthest from this point. In nice cases, there is just a single point farthest from a given point and so by restricting the domain slightly one can form…
In computer graphics, the field of view of a camera is represented by a viewing frustum and a corresponding projection matrix, the properties of which, in the absence of restrictions on rectangular shape of the near plane and its…
Manipulation planning is the task of computing robot trajectories that move a set of objects to their target configuration while satisfying physically feasibility. In contrast to existing works that assume known object templates, we are…
High-precision pose estimation based on visual markers has been a thriving research topic in the field of computer vision. However, the suitability of traditional flat markers on curved objects is limited due to the diverse shapes of curved…
An efficient way to get implicit equations of conics on five points and quadrics on nine, using pencils of conics and quadrics, is revealed. Parallel axis right cones intersect on a conic. An example, to show how to place five coplanar…
The Method of Alternating Projections (MAP), a classical algorithm for solving feasibility prob- lems, has recently been intensely studied for nonconvex sets. However, intrinsically available are only local convergence results: convergence…
The circumcentered-reflection method (CRM) has been applied for solving convex feasibility problems. CRM iterates by computing a circumcenter upon a composition of reflections with respect to convex sets. Since reflections are based on…
We consider the problem of projecting a convex set onto a subspace, or equivalently formulated, the problem of computing a set obtained by applying a linear mapping to a convex feasible set. This includes the problem of approximating convex…
Consider an analytic map of a neighborhood of 0 in a vector space to a Euclidean space. Suppose that this map takes all germs of lines passing through 0 to germs of circles. Such a map is called rounding. We introduce a natural equivalence…
Satellite imagery and maps, as two fundamental data modalities in remote sensing, offer direct observations of the Earth's surface and human-interpretable geographic abstractions, respectively. The task of bidirectional translation between…
Tensor diagrams are a handy way to depict complicated relationships between objects in projective geometry. One of the simpler ones takes two copies of a $3\times 3$ matrix and computes its adjugate. In this paper, we give a geometric…
We present a technique for Stereoscopic Cylindrical Screen (SCS) Projection of a world scene to a 360-degree canvas for viewing with 3D glasses. To optimize the rendering pipeline, we render the scene to four cubemaps, before sampling…
Neutrino telescopes offer an alternative way to explore the Universe. Several projects are in operation or under construction. A detector under the ocean is very promising because of the very accurate angular resolution that it provides.…