Subdivision Schemes for Thin Plate Splines

Thin plate splines are a well known entity of geometric design. They are defined as the minimizer of a variational problem whose differential operators approximate a simple notion of bending energy. Therefore, thin plate splines approximate surfaces with minimal bending energy and they are widely considered as the standard "fair" surface model. Such surfaces are desired for many modeling and design applications.
Traditionally, the way to construct such surfaces is to solve the associated variational problem using finite elements or by using analytic solutions based on radial basis functions. This paper presents a novel approach for defining and computing thin plate splines using subdivision methods. We present two methods for the construction of thin plate splines based on subdivision: A globally supported subdivision scheme which exactly minimizes the energy functional as well as a family of strictly local subdivision schemes which only utilize a small, finite number of distinct subdivision rules and approximately solve the variational problem. A tradeoff between the accuracy of the approximation and the locality of the subdivision scheme is used to pick a particular member of this family of subdivision schemes.
Later, we show applications of these approximating subdivision schemes to scattered data interpolation and the design of fair surfaces. In particular we suggest an efficient methodology for finding control points for the local subdivision scheme that will lead to an interpolating limit surface and demonstrate how the schemes can be used for the effective and efficient design of fair surfaces.     

Interactive Visualization of Flood and Heavy Rain Simulations

In this paper, we present a real‐time technique to visualize large‐scale adaptive height fields with C ‐continuous surface reconstruction. Grid‐based shallow water simulation is an indispensable tool for interactive flood management applications. Height fields defined on adaptive grids are often the only viable option to store and process the massive simulation data. Their visualization requires the reconstruction of a continuous surface from the spatially discrete simulation data. For regular grids, fast linear and cubic interpolation are commonly used for surface reconstruction. For adaptive grids, however, there exists no higher‐order interpolation technique fast enough for interactive applications. Our proposed technique bridges the gap between fast linear and expensive higher‐order interpolation for adaptive surface reconstruction. During reconstruction, no matter if regular or adaptive, discretization and interpolation artifacts can occur, which domain experts consider misleading and unaesthetic. We take into account boundary conditions to eliminate these artifacts, which include water climbing uphill, diving towards walls, and leaking through thin objects. We apply realistic water shading with visual cues for depth perception and add waves and foam synthesized from the simulation data to emphasize flow directions. The versatility and performance of our technique are demonstrated in various real‐world scenarios. A survey conducted with domain experts of different backgrounds and concerned citizens proves the usefulness and effectiveness of our technique.     

Geometrically nonlinear analysis of rectangular mindlin plates using the finite strip method

A general finite strip method of analysis is presented for the geometrically nonlinear analysis of laterally loaded, rectangular, isotropic plates. The analysis is based on the use of Mindlin plate theory and therefore includes the effects of transverse shear deformation. The nonlinearity is introduced via the strain-displacement equations and correspondingly the analysis pertains to problems involving moderate displacements but small rotations. The principle of minimum potential energy is used in the development of the strip and the complete plate stiffness equations and the latter equations are solved using the Newton-Raphson method. In numerical applications a particular type of finite strip is used in which all five reference quantities (three displacements and two rotations) are represented by cubic polynomial interpolation across the strip whilst the ends of the strip are simply supported for bending/shearing behaviour and immovable for membrane behaviour. These applications are concerned with uniformly loaded plates of both thin and moderately-thick geometry and detailed presentation is given of both displacement- and force-type quantities.     

A hybrid displacement plate element for bending and stability analysis

A hybrid displacement plate element is derived from a modified energy functional based on a variational principle. The higher order curvature terms which generate high energy densities are filtered out by using independent interpolation of curvatures and moments. The inter-element compatibility requirements are relaxed by including element discontinuities in the variational formulation. The accuracy of the element is shown to be excellent in both plate bending and buckling analysis.     

Robust Segmentation of Multiple Intersecting Manifolds from Unoriented Noisy Point Clouds

We present a method for extracting complex manifolds with an arbitrary number of (self‐) intersections from unoriented point clouds containing large amounts of noise. Manifolds are formed in a three‐step process. First, small flat neighbourhoods of all possible orientations are created around all points. Next, neighbourhoods are assembled into larger quasi‐flat patches, whose overlaps give the global connectivity structure of the point cloud. Finally, curved manifolds are extracted from the patch connectivity graph via a multiple‐source flood fill. The manifolds can be reconstructed into meshed surfaces using standard existing surface reconstruction methods. We demonstrate the speed and robustness of our method on several point clouds, with applications in point cloud segmentation, denoising and medial surface reconstruction.     

Quadrilateral finite elements for analysis of thick and thin plates

We discuss two quadrilateral plate elements applicable in the analysis of both thick and thin plates. The elements are based on Reissner-Mindlin plate theory and an enhanced displacement interpolation, which enables the consistent loading vector to be constructed. The constraint on the constant shear strain is enforced explicitly thus eliminating the shear locking phenomena in the analysis of thin plates. As a by-product of this work, we take a new look at a well-known discrete Kirchhoff plate element.     

薄板的几何非线性求积元分析

针对薄板非线性迭代计算量很大的问题,依据von Kárman薄板非线性理论构造能量泛函,并用数值积分和数值微分进行离散,得到非线性方程组,从而利用求积元法(Quadrature Element Method,QEM)求解薄板的中等挠度的弯曲和非线性屈曲问题,得到可信的结果.算例表明:在处理薄板几何非线性问题上,QEM计算效率很高,应用潜力很大.     

Image Interpolation by Pixel-Level Data-Dependent Triangulation

We present a novel image interpolation algorithm. The algorithm can be used in arbitrary resolution enhancement, arbitrary rotation and other applications of still images in continuous space. High‐resolution images are interpolated from the pixel‐level data‐dependent triangulation of lower‐resolution images. It is simpler than other methods and is adaptable to a variety of image manipulations. Experimental results show that the new “mesh image” algorithm is as fast as the bilinear interpolation method. We assess the interpolated images' quality visually and also by the MSE measure which shows our method generates results comparable in quality to slower established methods. We also implement our method in graphics card hardware using OpenGL which leads to real‐time high‐quality image reconstruction. These features give it the potential to be used in gaming and image‐processing applications.     

Sensor applications of thin‐film devices originating in display technologies

Thin‐film devices are widely utilized for flat‐panel displays, and the essential advantages of the thin‐film devices are generally large‐area production, various‐material substrate, layered structure, etc. Appropriate applications are flat‐panel displays, and other applications where the abovementioned advantages are available and the disadvantages are acceptable are sensor applications. Moreover, if the sensor devices can be made by thin‐film devices that have been already utilized for flat‐panel displays, they can be made without additional cost. Therefore, thin‐film devices are again promising for sensor applications especially for interactive displays. We are investigating sensor applications of thin‐film devices. Particular in this journal paper, we review sensor applications of thin‐film devices originating in display technologies. The various sensors are visible‐light sensor, infrared‐light sensor, temperature sensor, magnetic‐field sensor, etc. Many research results from many research organizations as well as our research laboratory are introduced.     

Generating Design Suggestions under Tight Constraints with Gradient‐based Probabilistic Programming

We present a system for generating suggestions from highly‐constrained, continuous design spaces. We formulate suggestion as sampling from a probability distribution; constraints are represented as factors that concentrate probability mass around sub‐manifolds of the design space. These sampling problems are intractable using typical random walk MCMC techniques, so we adopt Hamiltonian Monte Carlo (HMC), a gradient‐based MCMC method. We implement HMC in a high‐performance probabilistic programming language, and we evaluate its ability to efficiently generate suggestions for two different, highly‐constrained example applications: vector art coloring and designing stable stacking structures.     

Smooth Shape‐Aware Functions with Controlled Extrema

Functions that optimize Laplacian‐based energies have become popular in geometry processing, e.g. for shape deformation, smoothing, multiscale kernel construction and interpolation. Minimizers of Dirichlet energies, or solutions of Laplace equations, are harmonic functions that enjoy the maximum principle, ensuring no spurious local extrema in the interior of the solved domain occur. However, these functions are only C⁰ at the constrained points, which often causes smoothness problems. For this reason, many applications optimize higher‐order Laplacian energies such as biharmonic or triharmonic. Their minimizers exhibit increasing orders of continuity but lose the maximum principle and show oscillations. In this work, we identify characteristic artifacts caused by spurious local extrema, and provide a framework for minimizing quadratic energies on manifolds while constraining the solution to obey the maximum principle in the solved region. Our framework allows the user to specify locations and values of desired local maxima and minima, while preventing any other local extrema. We demonstrate our method on the smoothness energies corresponding to popular polyharmonic functions and show its usefulness for fast handle‐based shape deformation, controllable color diffusion, and topologically‐constrained data smoothing.     

A simple selectively integrated torsion—Flexure coupled tapered beam element with transverse shear deformation

A tapered beam element with torsional flexibility and transverse shear deformation is developed for use in swept plate studies. Recently established guidelines for selective reduced integration allow the use of independent interpolation functions for the transverse deflection $\text{w}$, rotation ψ and torsional rotation θ to obtain an element that does not lock in extremely thin situations encountered in thin beam/plate analysis. The element is tested for free vibration and for the static case of a severely swept cantilever plate of high aspect-ratio subjected to uniform distributed load. The results indicate very good performance of the element.     

Multi-view face identification and pose estimation using B-spline interpolation

The available face views in the training set are mostly limited. In this paper, we present a view interpolation method using nonlinear B-spline on face manifolds. Two models, the inner–outer ellipse model and the moment of inertia model, are developed to estimate the pose orientation. We use the limited view-pose face images to form the pose eigen space. Then, based on these nonlinear manifolds we form a B-spline for each individual. Identification is to compute the shortest Euclidean distance from a given test view to the nearest point within one of these B-splines. Once the test view is classified as a familiar individual in the training set, not only can the individual be identified, but also the pose angle can be estimated. Experimental results show that B-spline interpolation can achieve a recognition rate of 95%.     

Elastic Curves as Solutions of Riemannian and Sub-Riemannian Control Problems

We consider the nonlinear dynamic interpolation problem on Riemannian manifolds and, in particular, on connected and compact Lie groups. Basically we force the dynamic variables of a control system to pass through specific points in the configuration space, while minimizing a certain energy function, by a suitable choice of the controls. The energy function we consider depends on the velocity and acceleration along trajectories. The solution curves can be seen as generalizations of the classical splines in tension for the Euclidean space. The relations with sub-Riemannian optimal control problems are explained. Date received: June 2, 1999. Date revised: November 25, 1999.     

Experiences developing architectures for realizing thin‐client diagram editing tools

Diagram‐centric applications such as software design tools, project planning tools and business process modelling tools are usually ‘thick‐client’ applications running as stand‐alone desktop applications. There are several advantages to providing such design tools as Web‐based or even PDA‐ and mobile‐phone‐based applications. These include ease of access and upgrade, provision of collaborative work support and Web‐based integration with other applications. However, building such thin‐client diagram editing tools is very challenging. We have developed several thin‐client diagram editing applications realized as a set of plug‐in extensions to a meta‐tool for visual design environment development. In this paper, we discuss key user interaction and software architecture issues, illustrate examples of interacting with our thin‐client diagram editing tools, describe our design and implementation approaches, and present the results of several different evaluations of the resultant applications. Our experiences will be useful for those interested in developing their own thin‐client diagram editing architectures and applications. Copyright © 2007 John Wiley & Sons, Ltd.     

Partial Differential Equations for Zooming,Deinterlacing and Dejittering

In this paper, for imaging applications, we introduce partial differential equations (PDEs), which allow for correcting displacement errors, for dejittering, and for deinterlacing, respectively, in multi-channel data. These equations are derived via semi-groups for non-convex energy functionals. As a particular example, for gray valued data, we find the mean curvature equation and the corresponding non-convex energy functional. As a further application for correction of displacement errors we study image interpolation, in particular zooming, of digital color images. For actual image zooming, the solutions of the proposed PDEs are projected onto a space of functions satisfying interpolation constraints. A comparison of the test results with standard and state-of-the-art interpolation algorithms shows the competitiveness of this approach.     

Analysis of plates by finite strip method

New finite strips are developed for the analysis of plates. Based on Reissner's plate theory, the effect of shear deformation is included in the formulation. To eliminate artificial hardening, the shape functions for the strips are so chosen that there is no mismatched term along the interpolation functions for the interpolation parameters. Numerical examples are reported to demonstrate that the strips can work equally well in thick as well as thin plates.     

A simple displacement-based 3-node triangular element for linear and geometrically nonlinear analysis of laminated composite plates

A simple displacement-based 3-node, 18-degree-of-freedom flat triangular plate/shell element LDT18 is proposed in this paper for linear and geometrically nonlinear finite element analysis of thin and thick laminated composite plates. The presented element is based on the first-order shear deformation theory (FSDT), and the total Lagrangian approach is employed to formulate the element for geometrically nonlinear analysis. The deflection and rotation functions of the element boundary are obtained from the Timoshenko’s laminated composite beam functions, hence convergence to the thin plate solution can be achieved theoretically and shear-locking problem is avoided naturally. The plane displacement interpolation functions of the Airman’s triangular membrane element with drilling degrees of freedom are taken as the in-plane displacements of the element. Numerical examples demonstrate that the present element is accurate and efficient for linear and geometrically nonlinear analysis of thin to moderately thick laminated composite plates.     

Elastic Principal Graphs and Manifolds and their Practical Applications

Principal manifolds serve as useful tool for many practical applications. These manifolds are defined as lines or surfaces passing through “the middle” of data distribution. We propose an algorithm for fast construction of grid approximations of principal manifolds with given topology. It is based on analogy of principal manifold and elastic membrane. First advantage of this method is a form of the functional to be minimized which becomes quadratic at the step of the vertices position refinement. This makes the algorithm very effective, especially for parallel implementations. Another advantage is that the same algorithmic kernel is applied to construct principal manifolds of different dimensions and topologies. We demonstrate how flexibility of the approach allows numerous adaptive strategies like principal graph constructing, etc. The algorithm is implemented as a C++ package elmap and as a part of stand-alone data visualization tool VidaExpert, available on the web. We describe the approach and provide several examples of its application with speed performance characteristics.     

Single‐layered retardation films with negative wavelength dispersion birefringence made from liquid‐crystalline monomers

Organic light‐emitting diode displays have a cathode composed of a layer of highly reflective metal. Reflection of external light from this layer can be suppressed with a broadband quarter‐wave plate. Although various types of quarter‐wave plate retardation films have been prepared by copolymerizing, mixing, or laminating multiple polymers, ideal wavelength dispersion has not been achieved with thin retardation films because of their relatively low birefringence and the complexity of the procedure required manufacturing them. In this study, we developed (i) new liquid‐crystalline monomers with negative wavelength dispersion birefringence that we used to obtain thin, single‐layered retardation films suitable for coating and (ii) retardation films with different molecular alignments. We found that the monomers showed high solubility and high regularity of molecular alignment, with less damage to the substrate and alignment films. We also investigated the wavelength dispersion and thermal stability of the films. We succeeded in developing retardation films that had a homeotropic alignment or a hybrid alignment with negative wavelength dispersion. These alignments can be used to obtain antireflection films with an improved viewing angle for organic light‐emitting diode displays or next‐generation thin displays.