We present an approach to semantic scene analysis using deep convolutional networks. Our approach is based on tangent convolutions – a new construction for convolutional networks on 3D data. In contrast to volumetric approaches, our method operates directly on surface geometry. Crucially, the construction is applicable to unstructured point clouds and other noisy real-world data. We show that t...

Shoen and Uhlenbeck showed that “tangent maps” can be defined at singular points of energy minimizing maps. Unfortunately these are not unique, even for generic boundary conditions. Examples are discussed which have isolated singularities with a continuum of distinct tangent maps. Let Ω be a bounded domain in R (or more generally a compact riemannian manifold with boundary) and let N be a compa...

A method is described whereby a G* planar curve consisting of clothoid (Comu spiral) segments, circular arcs and straight line segments is constructed. The curve passes through given points, is expressed parametrically. and has the attractive feature that the arc length and curvature are piecewise linear functions of the parameter. The given points through which the curve passes must be restric...

We describe the construction of suboptimal trajectories of the problem of a planar motion with bounded derivative of the curvature and we prove their suboptimality. ‘Suboptimal’ means longer than the optimal by no more than a constant depending only on the bound B for the curvature’s derivative. The initial and final coordinates, curvatures and tangent angles are given. The tangent angle and th...

We study the achievable rate region and optimal power allocation for broadcast channels (BC) under orthogonal access schemes. The channel follows a block fading model with channel side information (CSI) perfectly known at the receiver but not at the transmitter. The region boundary is determined by finding the optimal power allocation associated with all boundary points. For the two-user case, ...

This paper deals with the problem of C2 cubic spline interpolation under geometric boundary conditions, that is, fixing the unit-tangent vector and the curvature at the end points of a planar point-set. The solvability of the resulting non-linear problem, which is equivalent to a quadratic system with respect to the lengths of the boundary tangent vectors, is exhaustively studied, leading to ne...

Abstract-In this paper, the influences of local (individual member) buckling and minor variations in member properties on the global response of truss-type structures are studied. A simple and effective way of forming the tangent stiffness matrix of the structure and a modified arc length method are devised to trace the nonlinear response of the structure beyond limit points, etc. Several examp...

This paper presents a geometric interpolation method for curve approximation in 3 R space. Given a curve, the new method is to find an approximation Bézier curve of degree 4 tangent with the given curve at the two end points and at an inner point as well. The resulting Bézier curve is explicitly expressed in the parameters of the tangent inner point of both the given curve and the approximation...

In no other area of facial aesthetic surgery is such a fragile balance struck between form and function as that in eyelid modification. Owing to the delicate nature of eyelid structural composition and the vital role the eyelids serve in protecting the visual system, iatrogenic alterations in eyelid anatomy must be made with care, precision, and thoughtful consideration of existing soft tissue ...