3D reconstruction of complex curved objects from line drawings

An active research topic in computer vision and graphics is developing algorithms that can reconstruct the 3D surface of curved objects from line drawings. There are a number of algorithms have been dedicated to solve this problem, but they can＇t solve this problem when the geometric structure of a curved object becomes complex. This paper proposes a novel approach to reconstructing a complex curved 3D object from single 2D line drawings. Our approach has three steps： （1） decomposing a complex line drawing into several simpler line drawings and transforming them into polyhedron; （2） reconstructing the 3D wireframe of curved object from these simpler line drawings and generating the curved faces; （3） combining the 3D objects into the complete objects. A number of examples are given to demonstrate the ability of our approach to successfully perform reconstruction of curved objects which are more complex than previous methods.

Jackson type theorems on complex curves

Let Γ be a closed smooth Jordan curve in the complex plane. In this paper, with the help of a class of fundamental functions of Hermite interpolation, the author introduces a continuous function interpolation which uniformly approximates to f(z) ∈ C(Γ ) with the same order of approximation as that in Jackson Theorem 1 on real interval [1, 1]. The accuracy of the order of approximation is proved. Using the method different from the early works, the author studies simultaneous approximation to function and its derivatives and the desired results analogues to that in Jackson Theorem 2 on real interval [1, 1] are obtained.

On almost complex curves and Hopf hypersurfaces in the nearly Kahler six-sphere

We study the almost complex curves and Hopf hypersurfaces in the nearly Khler S6(1),and their relations.For Hopf hypersurfaces,we give a classification theorem under some additional conditions.For compact almost complex curves,we obtain some interesting global results with respect to Gaussian curvature,area and the genus.

Frequency-dependent viscoelasticity effects on the wave attenuation performance of multi-layered periodic foundations

In this paper,layered periodic foundations(LPFs)are numerically examined for their responses to longitudinal and transverse modes in the time and frequency domains.Three different unit-cells,i.e.,2-layer,4-layer,and 6-layer unit-cells,comprising concrete/rubber,concrete/rubber/steel/rubber,and concrete/rubber/steel/rubber/lead/rubber materials,respectively,are taken into account.Also,the viscoelasticity behavior of the rubber is modeled with two factors,i.e.,a frequency-independent(FI)loss factor and a linear frequency-dependent(FD)loss factor.Following the extraction of the complex dispersion curves and the identification of the band gaps(BGs),the simulations of wave transmission in the time and frequency domains are performed using the COMSOL software.Subsequent parametric studies evaluate the effects of the rubber viscoelasticity models on the dispersion curves and the wave transmission for the longitudinal and transverse modes.The results show that considering the rubber viscoelasticity enhances the wave attenuation performance.Moreover,the transverse-mode damping is more sensitive to the viscoelasticity model than its longitudinal counterpart.The 6-layer unit-cell LPF exhibits the lowest BG,ranging from 4.8 Hz to 6.5 Hz.

Curved and Stepped Breakwater Wall

-This paper introduces the main points of design and operation features of a curved combinative breakwater wall which can not only resist storm surge but also roll wave back and which has the functions of seawall, tide protection, anti-wave, land development, traffic and tourism. The new kind of breakwater optimized by wave model test has been utilized in the seawall in the coast regulation project in Zhanjiang City, and good results have been achieved.

Weakly Disk-busting Curves in the Boundary of a Compression Body

Let V be a nontrivial compression body which is not simple. An essential simple closed curve J in ?;V is called weakly disk-busting if ?;V-J has only one compressing disk up to isotopy. In this paper, we give an upper bound of the diameter of the image of boundaries of essential disks in V under any projection determined by a weakly disk-busting curve. Moreover, we give a sufficient condition for the handle additions to be boundary irreducible.

UNSTEADY INTERACTION OF SHOCK WAVE DIFFRACTING AROUND A CIRCULAR CYLINDER IN AIR

The reflection and diffraction of a planar shock wave around a circular cylinder are a typical problem of the complex nonlinear shock wave phenomena in literature.It has long been studied experimentally,analytically as well as numerically.Takayama in 1987 obtained clear experimental pictures ofisopycnics in shock tube under the condi- tion that the impinging shock wave propagates as far as 3 diameters away from the cylinder.To know more complete- ly the whole unsteady process,it is desirable to get experimental results in a region which is more than 10 diameters away from the cylinder.This is what has been done in this paper by using the pulsed laser holographic interferometry for several shock Mach numbers of the impinging shock. Results for several moments are shown,giving more know- ledge about the whole unsteady flow field.This is useful for a reliable and complete understanding of the changing force acting on the cylinder,and provides interesting data to check the performance of many recently developed high resolution numerical methods for unsteady shock wave calculation.

Connectedness of curve complex of surface

For a closed orientable surface Sg of genus not smaller than 2,C(Sg) is the curve complex on S g whose vertices consist of the isotopy classes of nontrivial circles on Sg. It has been showed that any two vertices in C(Sg) can be connected by an edge path,and C(Sg) has an infinite diameter. We show that for 0 ≤i≤3g-5,two i-simplices can be connected by an(i +1)-path in C(Sg),and the diameter of C(Sg) under such a distance is infinite.

Subsurface 1-distance of the Handlebody

For a handlebody H w ith dH = 5, let F belong S be an essential connected subsurface of S. Let C（S） be the curve complex of S, AC（F） be the arc and curve complex of F , D（H） belong C（S） be the disk complex of H and πf（D （H ） ） belong AC（F） be the image of D （H） in AC （F）. We introduce the definition of subsurface 1-distance between the 1-simplices of AC（F） and show that under some hypothesis, πF（D（H） ） comes within subsurface 1-distance at most 4 of every 1-simplex of AC （F）.

Spanning Pre-disks in a Compression Body

A properly embedded essential planar surface P（not a disk） in a compression body V is called a spanning pre-disk with respect to J, if one boundary component of P is lying in ?;V and all other boundary components of P are lying in?;V and coplanar with J. In this paper, we show that the number of boundary components of spanning pre-disks in a compression body is unbounded. But the number of a maximal collection of spanning pre-disks is bounded.

Distance of Edges in the Curve Complex of a Surface

Let S be a closed orientable surface of genus g ≥ 2,and C（S）the curve complex of S.In the paper,we introduce the concepts of 2-path between edges in C（S）,which can be regarded as an analogue to the edge path between vertices in C（S）.We show that C（S）is 2P-connected,and the 2-diameter of C（S）is infinite.

Sufficient Conditions for Amalgamated 3-Manifolds to be ∂-Irreducible

In this paper,the authors give some sufficient conditions for an amalgamated 3-manifold along a compact connected surface F with boundary to be ∂-irreducible in terms of distances between some kinds of vertex subsets of the curve complex and the arc complex of F.

Local rigidity of the Teichmüller space with the Thurston metric

We show that every R-linear surjective isometry between the cotangent spaces to the Teichmüller space equipped with the Thurston norm is induced by some isometry between the underlying hyperbolic surfaces.This is an analogue of Royden's theorem concerning the Teichmüller norm.

Associative Cones and Integrable Systems

Abstract We identify R^7 as the pure imaginary part of octonions. Then the multiplication in octonions gives a natural almost complex structure for the unit sphere S^6. It is known that a cone over a surface M in S^6 is an associative submanifold of R^7 if and only if M is almost complex in S^6. In this paper, we show that the Gauss-Codazzi equation for almost complex curves in S^6 are the equation for primitive maps associated to the 6-symmetric space G2/T^2, and use this to explain some of the known results. Moreover, the equation for S^1-symmetric almost complex curves in S^6 is the periodic Toda lattice, and a discussion of periodic solutions is given.

Non degenerating Dehn fillings on genus two Heegaard splittings of knots' complements

It is Thurston's result that for a hyperbolic knot K in S^3, almost all Dehn fillings on its complement result in hyperbolic 3-manifolds except some exceptional cases. So almost all produced 3-manifolds have the same geometry. It is known that its complement in S^3, denoted by E(K), admits a Heegaard splitting. Then it is expected that there is a similar result on Heegaard distance for Dehn fillings. In this paper, Dehn fillings on genus two Heegaard splittings are studied. More precisely, we prove that if the distance of a given genus two Heegaard splitting of E(K) is at least 3, then for any two degenerating slopes on ?E(K), there is a universal bound of their distance in the curve complex of ?E(K).

On reducible Heegaard splittings

Let Ⅴ∪S W be a reducible Heegaard splitting of genus g = g（S） ≥ 2. For a maximal prime connected sum decomposition of Ⅴ∪S W, let q denote the number of the genus 1 Heegaard splittings of S2 × S1 in the decomposition, and p the number of all other prime factors in the decomposition. The main result of the present paper is to describe the relation of p, q and dim（Cy ∩ Cw）.