相关论文: A Construction of the Total Spherical Perspective …
We provide an explicit geometric algorithm involving only ruler and compass constructions in order to specify the specular reflection point on the surface of a reflecting sphere of radius $r$ given two focal points $A$ and $B$ lying outside…
In this paper alternative method for real-time 3D model rasterization is given. Surfaces are drawn in perspective-map space which acts as a virtual camera lens. It can render single-pass 360{\deg} angle of view (AOV) image of unlimited…
360$^{\circ}$ panoramas are a rich medium, yet notoriously difficult to visualize in the 2D image plane. We explore how intelligent rotations of a spherical image may enable content-aware projection with fewer perceptible distortions.…
In this paper, we present a novel method to draw a circle tangent to three given circles lying on a plane. Using the analytic geometry and inversion (reflection) theorems, the center and radius of the inversion circle are obtained. Inside…
This paper proposes a novel method for omnidirectional 360$\degree$ perception. Most common previous methods relied on equirectangular projection. This representation is easily applicable to 2D operation layers but introduces distortions…
The purpose of this short manuscript is to show that all point constructions that can be done via ruler and compass, can also be done with compass exclusively. If we are using compass and ruler the way we construct new points is by first…
This paper explores a full generalization of the classical corner-vector method for constructing weighted spherical designs, which we call the {\it generalized corner-vector method}. First we establish a uniform upper bound for the degree…
Being able to edit panoramic images is crucial for creating realistic 360{\deg} visual experiences. However, existing perspective-based image editing methods fail to model the spatial structure of panoramas. Conventional cube-map…
A range of ferroic glasses, magnetic, polar, relaxor and strain glasses, are considered together from the perspective of spin glasses. Simple mathematical modelling is shown to provide a possible conceptual unification to back similarities…
We propose a novel coaxial spherical-lens shaping system to achieve a flat-top focus profile by exploiting the spherical aberration of the lens. The well-known aspherical-lens shaping system is compared to ours, and a comparison of etching…
We introduce a new type of lens that focuses a plane wave into a spherical one, where light comes from all directions. Our method also suggests the design of ideal optical tweezers or, in the reverse direction, photo-detection of nearly all…
This paper provides a survey of spherical designs and their applications, with a particular emphasis on the perspective of ``numerical analysis''. A set \(X_N\) of \(N\) points on the unit sphere \(\mathbb{S}^d\) is called a…
Based on a recent purely geometric construction of observables for the spatial diffeomorphism constraint, we propose two distinct quantum reductions to spherical symmetry within full 3+1-dimensional loop quantum gravity. The construction of…
Sphere eversions have been described so far by either pictures with minimal topological complexity, numerical evolution or complex equations. We write down relatively simple explicit formulas for the whole eversion, both analytic and…
Spherical spin glasses are canonical models for smooth random functions in high dimensions. In this review, we survey several interrelated lines of research on their geometric structure. We begin with results concerning critical points and…
Geometric constructions are widely used in computer graphics and engineering drawing. A right generalized cylinder is a ruled surface whose base curve is a plane curve perpendicular to the rulings. The paper discusses relations between the…
This article provides an overview of the techniques related to classification of spherical and more general objects within triangulated categories, and its relationship with algebraic geometry, representation theory and symplectic geometry.…
The object of this study is an integral operator $\mathcal{S}$ which averages functions in the Euclidean upper half-space $\mathbb{R}_{+}^{n}$ over the half-spheres centered on the topological boundary $\partial \mathbb{R}_{+}^{n}$. By…
By recasting metrical geometry in a purely algebraic setting, both Euclidean and non-Euclidean geometries can be studied over a general field with an arbitrary quadratic form. Both an affine and a projective version of this new theory are…
Perception is an essential part of robotic manipulation in a semi-structured environment. Traditional approaches produce a narrow task-specific prediction (e.g., object's 6D pose), that cannot be adapted to other tasks and is ill-suited for…