Let S be a smooth real surface in C and let p ∈ S be a point at which the tangent plane is a complex line. Many problems in function theory depend on knowing whether S is locally polynomially convex at such a p — i.e. at a CR singularity. Even when the order of contact of Tp(S) with S at p equals 2, no clean characterisation exists; difficulties are posed by parabolic points. Hence, we study no...

While 360° cameras offer tremendous new possibilities in vision, graphics, and augmented reality, the spherical images they produce make core feature extraction non-trivial. Convolutional neural networks (CNNs) trained on images from perspective cameras yield “flat" filters, yet 360° images cannot be projected to a single plane without significant distortion. A naive solution that repeatedly pr...

This paper presents a novel method for estimating specular roughness and tangent vectors, per surface point, from polarized second order spherical gradient illumination patterns. We demonstrate that for isotropic BRDFs, only three second order spherical gradients are sufficient to robustly estimate spatially varying specular roughness. For anisotropic BRDFs, an additional two measurements yield...

A spherical object has been introduced into central catadioptric camera calibration through utilizing the properties of an image conic, which is the projection of the occluding contour of a sphere in the catadioptric image. However, previous calibration method using sphere images employs nonlinear optimization method and requires a good initial estimation to start the minimization. In this pape...

Previous work [7] showed that the Cubed-Sphere grid offers a suitable discrete framework for extending Hermitian compact operators [6] to the spherical setup. In this paper we further investigate the design of high-order accurate approximations of spherical differential operators on the Cubed-Sphere with an emphasis on the spherical divergence of a tangent vector field. The basic principle of t...

In this paper, the tangent, binormal, normal and unit Darboux vectors of the dual curve on the one–parameter dual spherical motion are obtained with respect to a unit dual orthogonal frame for dual 3–space D.

The spherical harmonics discrete ordinate method for plane-parallel data assimilation (SHDOMPPDA) model is an unpolarized plane-parallel radiative transfer forward model, with corresponding tangent linear and adjoint models, suitable for use in assimilating cloudy sky visible and infrared radiances. It is derived from the spherical harmonics discrete ordinate method plane-parallel (SHDOMPP, als...

A tangent developable is a developable surface constructed by the union of the tangent lines of a space curve. These surfaces have applications not only in mathematics but also in engineering, such as for designing cars, ships, and apparel. However, since tangent developables typically have complicated and twisted surfaces, it is difficult to understand their structures from their images on a 2...