Constant angle surfaces constructed on curves

The Frenet-Serret formula is used to characterize the constant angle ruled surfaces in R3. When the surfaces are the tangent developmental and normal surfaces, that is, r（s, v） = tr（s） ＋v（cosα（s） . t（s） ＋sina（s） . n（s））, it is shown that each of these surfaces is locally isometric to a piece of a plane or a certain special surface. When the surfaces are normal and binormal surfaces, that is, r （ s, v ） = σ （ s ） ＋ v （ cosa （ s ） . n（s） ＋ since（s） . b（s））, it is shown that each of these surfaces is locally isometric to a piece of a plane or a cylindrical surface.

Investigation of long-range sound propagation in surface ducts

Understanding the effect of source-receiver geometry on sound propagation in surface ducts can improve the performance of near-surface sonar in deep water. The Lloyd-mirror and normal mode theories are used to analyze the features of surface-duct propagation in this paper. Firstly, according to the Lloyd-mirror theory, a shallow point source generates directional lobes, whose grazing angles are determined by the source depth and frequency. By assuming a part of the first lobe to be just trapped in the surface duct, a method to calculate the minimum cutoff frequency （MCF） is obtained. The presented method is source depth dependent and thus is helpful for determining the working depth for sonar. Secondly, it is found that under certain environments there exists a layer of low transmission loss （TL） in the surface duct, whose thickness is related to the source geometry and can be calculated by the Lloyd-mirror method. The receiver should be placed in this layer to minimize the TL. Finally, the arrival angle on a vertical linear array （VLA） in the surface duct is analyzed based on normal mode theory, which provides a priori knowledge of the beam direction of passive sonar.

Building Damage Extraction from Post-earthquake Airborne LiDAR Data

Building collapse is a significant cause of earthquake-related casualties; therefore, the rapid assessment of buildings damage is important for emergency management and rescue. Airborne light detection and ranging （LiDAR） can acquire point cloud data in combination with height values, which in turn provides detailed information on building damage. However, the most previous approaches have used optical images and LiDAR data, or pre- and post-earthquake LiDAR data, to derive building damage information. This study applied surface normal algorithms to extract the degree of building damage. In this method, the angle between the surface normal and zenith （0） is used to identify damaged parts of a building, while the ratio of the standard deviation to the mean absolute deviation （σ/δ） of θ is used to obtain the degree of building damage. Quantitative analysis of 85 individual buildings with different roof types （i.e., flat top or pitched roofs） was conducted, and the results confirm that post-earthquake single LiDAR data are not affected by roof shape. Furthermore, the results confirm that θ is correlated to building damage, and that σ/δ represents an effective index to identify the degree of building damage.

Fast and accurate surface normal integration on non-rectangular domains

The integration of surface normals for the purpose of computing the shape of a surface in 3D space is a classic problem in computer vision. However,even nowadays it is still a challenging task to devise a method that is flexible enough to work on non-trivial computational domains with high accuracy, robustness,and computational efficiency. By uniting a classic approach for surface normal integration with modern computational techniques, we construct a solver that fulfils these requirements. Building upon the Poisson integration model, we use an iterative Krylov subspace solver as a core step in tackling the task. While such a method can be very efficient, it may only show its full potential when combined with suitable numerical preconditioning and problem-specific initialisation. We perform a thorough numerical study in order to identify an appropriate preconditioner for this purpose.To provide suitable initialisation, we compute this initial state using a recently developed fast marching integrator. Detailed numerical experiments illustrate the benefits of this novel combination. In addition, we show on real-world photometric stereo datasets that the developed numerical framework is flexible enough to tackle modern computer vision applications.

Stroke-Based Surface Reconstruction

In this paper,we present a surface reconstruction via 2D strokes and a vector field on the strokes based on a two-step method.In the first step,from sparse strokes drawn by artists and a given vector field on the strokes,we propose a nonlinear vector interpolation combining total variation(TV)and H1 regularization with a curl-free constraint for obtaining a dense vector field.In the second step,a height map is obtained by integrating the dense vector field in the first step.Jump discontinuities in surface and discontinuities of surface gradients can be well reconstructed without any surface distortion.We also provide a fast and efficient algorithm for solving the proposed functionals.Since vectors on the strokes are interpreted as a projection of surface gradients onto the plane,different types of strokes are easily devised to generate geometrically crucial structures such as ridge,valley,jump,bump,and dip on the surface.The stroke types help users to create a surface which they intuitively imagine from 2D strokes.We compare our results with conventional methods via many examples.

Dynkin diagrams of rank 20 on supersingular K3 surfaces

We classify normal supersingular K 3 surfaces Y with total Milnor number 20 in characteristic p,where p is an odd prime that does not divide the discriminant of the Dynkin type of the rational double points on Y.This paper appeared in preprint form in the home page of the first author in the year 2005.

New design of a compact aero-robotic drilling end effector: An experimental analysis

This paper presents the development of a normal adjustment cell (NAC) in aero-robotic drilling to improve the quality of vertical drilling, by using an intelligent double-eccentric disk normal adjustment mechanism (2-EDNA), a spherical plain bearing and a floating compress module with sensors. After the surface normal vector is calculated based on the laser sensors' feedback, the 2-EDNA concept is conceived specifically to address the deviation of the spindle from the surface normal at the drilling point. Following the angle calculation, depending on the actual initial position, two precise eccentric disks (PEDs) with an identical eccentric radius are used to rotate with the appropriate angles using two high-resolution DC servomotors. The two PEDs will carry the spindle to coincide with the surface normal, keeping the vertex of the drill bit still to avoid repeated adjustment and position compensation. A series of experiments was conducted on an aeronautical drilling robot platform with a precise NAC. The effect of normal adjustment on bore diameter, drilling force, burr size, drilling heat, and tool wear was analyzed. The results validate that using the NAC in robotic drilling results in greatly improved vertical drilling quality and is attainable in terms of intelligence and accuracy. (C) 2015 The Authors. Production and hosting by Elsevier Ltd. on behalf of Chinese Society of Aeronautics and Astronautics.

The Effect of Particle Shape on the Structure and Rheological Properties of Carbon-based Particle Suspensions

The structure and rheological properties of carbon-based particle suspensions, i.e., carbon black（CB）, multi-wall carbon nanotube（MWNT）, graphene and hollow carbon sphere（HCS） suspended in polydimethylsiloxane（PDMS）, are investigated. In order to study the effect of particle shape on the structure and rheological properties of suspensions, the content of surface oxygen-containing functional groups of carbon-based particles is controlled to be similar. Original spherical-like CB（fractal filler）, rod-like MWNT and sheet-like graphene form large agglomerates in PDMS, while spherical HCS particles disperse relatively well in PDMS. The dispersion state of carbon-based particles affects the critical concentration of forming a rheological percolation network. Under weak shear, negative normal stress differences（ΔN） are observed in CB, MWNT and graphene suspensions, while ΔN is nearly zero for HCS suspensions. It is concluded that the vorticity alignment of CB, MWNT and graphene agglomerates under shear results in the negative ΔN. However, no obvious structural change is observed in HCS suspension under weak shear, and accordingly, the ΔN is almost zero.