Related papers: Catenary and Mercator projection
This paper constructs the geometrically natural objects which are associated with any projection tensor field on a manifold with any affine connection. The approaches to projection tensor fields which have been used in general relativity…
The convex feasibility problem asks to find a point in the intersection of a collection of nonempty closed convex sets. This problem is of basic importance in mathematics and the physical sciences, and projection (or splitting) methods…
Geometric calibration of cameras and projectors is an essential step that must be performed before any imaging system can be used. There are many well-known geometric calibration methods for calibrating systems comprised of multiple…
We provide criteria for deciding whether a given planar curve is an image of a given spatial curve, obtained by a central or a parallel projection with unknown parameters. These criteria reduce the projection problem to a certain…
The problem of construction of the surfaces with given sets of the points with horizontal tangential planes is considered. Such considerations are of interest in the problem of computer simulations of the waved ocean surfaces.
In this article we describe a program -- called planar_draw -- to draw maps on oriented surfaces in the plane. The drawings are coded as tikz files that can easily be manipulated and used in latex documents. Next to plane maps -- a case for…
The obliquity of a terrestrial planet is an important clue about its formation and critical to its climate. Previous studies using simulated photometry of Earth show that continuous observations over most of a planet's orbit can be inverted…
Vectors fields defined on surfaces constitute relevant and useful representations but are rarely used. One reason might be that comparing vector fields across two surfaces of the same genus is not trivial: it requires to transport the…
While the proposal of the Tri-plane representation has advanced the development of the 3D-aware image generative models, problems rooted in its inherent structure, such as multi-face artifacts caused by sharing the same features in…
When light scatters off an object its polarization, in general, changes - a transformation described by the object's Mueller matrix. Mueller matrix imaging polarimetry is an important technique in science and technology to image the…
A transformation optics approach was used to derive a general method for designing electromagnetic devices able to manipulate the wave vectors in the specific manner required by the functionality of the device. While the wave paths inside…
The geometry of binocular projection is analyzed, with reference to the primate visual system. In particular, the effects of coordinated eye movements on the retinal images are investigated. An appropriate oculomotor parameterization is…
A single Panorama can be drawn perspectively without distortions in arbitrary viewing directions and field-of-views when the camera position is at the origin. This is a key advantage in VR and virtual tour applications because it enables…
Formerly the geometry was based on shapes, but since the last centuries this founding mathematical science deals with transformations, projections and mappings. Projective geometry identifies a line with a single point, like the perspective…
Computed Tomography (CT) is an imaging technique where information about an object are collected at different angles (called projections or scans). Then the cross-sectional image showing the internal structure of the slice is produced by…
Random projection is often used to project higher-dimensional vectors onto a lower-dimensional space, while approximately preserving their pairwise distances. It has emerged as a powerful tool in various data processing tasks and has…
We fully characterize orthogonal projections of infinite right circular (round) cones in real Hilbert spaces. Another interpretation is that, given two vectors in a real Hilbert space, we establish the optimal estimate on the angle between…
Conventional multi-projector calibration requires projecting and capturing structured light patterns for each projector sequentially, causing calibration time and effort to increase linearly with the number of projectors. This scalability…
Let $M$ be a K\"ahler manifold with complex structure $J$ and K\"ahler metric $g$. A c-projective vector field is a vector field on $M$ whose flow sends $J$-planar curves to $J$-planar curves, where $J$-planar curves are analogs of what…
In the last ten years, the technology of differential geometry, ubiquitous in gravitational physics, has found its place in the field of optics. It has been successfully used in the design of optical metamaterials, through a technique now…