Related papers: Catenary and Mercator projection
A pentagonal geometry PENT($k$, $r$) is a partial linear space, where every line is incident with $k$ points, every point is incident with $r$ lines, and for each point $x$, there is a line incident with precisely those points that are not…
To render a spherical (360 degree or omnidirectional) image on planar displays, a 2D image -- called as viewport -- must be obtained by projecting a sphere region on a plane, according to the users viewing direction and a predefined field…
We introduce the concept of bi-conformal transformation, as a generalization of conformal ones, by allowing two orthogonal parts of a manifold with metric $\G$ to be scaled by different conformal factors. In particular, we study their…
Detecting symmetry is crucial for effective object grasping for several reasons. Recognizing symmetrical features or axes within an object helps in developing efficient grasp strategies, as grasping along these axes typically results in a…
Current technology is not able to map the topography of rocky exoplanets, simply because the objects are too faint and far away to resolve them. Nevertheless, indirect effect of topography should be soon observable thanks to photometry…
We consider a projection from the center of the unit sphere to a tangent space of it, the central projection, and study two area minimizing problems of the image of a closed subset in the sphere. One of the problems is the uniqueness of the…
We have described a novel way to determine the Mueller matrix of any optical element by using projection method. For this purpose, we have used two universal SU(2) gadgets for polarization optics to obtain projection matrix directly from…
Computed tomography is a method for synthesizing volumetric or cross-sectional images of an object from a collection of projections. Popular reconstruction methods for computed tomography are based on idealized models and assumptions that…
The purpose of this article is to introduce projective geometry over composition algebras : the equivalent of projective spaces and Grassmannians over them are defined. It will follow from this definition that the projective spaces are in…
We present an algorithm for creating contiguous cartograms using meshes. We use numerical optimization to minimize cartographic error and distortion by transforming the mesh vertices. The vertices can either be optimized in the plane or…
A novel multi-resolution technique called border mapping multi-resolution (BMMR) is proposed for projection-based particle methods. The BMMR aims to obtain background equivalent particle distributions in the two sides of a border between…
Luminet et al. (2003) suggested that WMAP data are better matched by a Poincar\'e dodecahedral FLRW model of global geometry, rather than by an infinite flat model. The analysis by Cornish et al. (2003) for angular radii 25-90 degrees…
Set projection algorithms are a class of algorithms used in ptychography to help improve the quality of the reconstructed images. The set projection step is important because it helps to ensure that the reconstructed image satisfies the…
The real projective plane has three well know isomorphic constructions: the extended euclidean plane, unit (hemi)sphere, and three dimensional vector space over the reals. In this paper we find the isomorphisms that map between these three…
We provide a simple and efficient algorithm for computing the Euclidean projection of a point onto the capped simplex---a simplex with an additional uniform bound on each coordinate---together with an elementary proof. Both the MATLAB and…
Mapping exoplanets across phases and during secondary eclipse is a powerful technique for characterizing Hot Jupiters in emission. Since these planets are expected to rotate about axes normal to their orbital planes, with rotation periods…
The angular deviation commonly represented by the scattering angle generally serves to provide the characteristic discrimination in the muon scattering tomography. The regular procedure to determine the scattering angle comprises the…
At the most fundamental level, the interaction between light and matter is manifested by the emission and absorption of single photons by single quantum emitters. Controlling light--matter interaction is the basis for diverse applications…
In this paper we introduce the notion of cofrontal mappings, as the dual objects to frontal mappings, and study their basic local and global properties. Cofrontals are very special mappings and far from generic nor stable except for the…
Sky imaging systems use lenses to acquire images concentrating light beams in a sensor. The light beams received by the sky imager have an elevation angle with respect to the device normal. Thus, the pixels in the image contain information…