Interior Shape Research Articles

A STUDY ON CONVERGENCE MODELING OF CULTURAL ARTIFACT USING X-RAY COMPUTED TOMOGRAPHY AND THREE-DIMENSIONAL SCANNING TECHNOLOGIES

Abstract. Optical three-dimensional (3D) scanning technology is extensively used for digital recording and shape analysis of cultural heritage because it is simple to obtain precise surface shape and color information. In addition, X-ray computed tomography (X-ray CT) is used to record and analyze the internal shape of cultural heritage. However, while the 3D shape acquired by X-ray CT technology is excellent for visualizing the internal shape, expressing the high resolution of the surface shape is difficult. If the benefits of each technology are used to digitize the inside and outside of cultural heritage, the results of surface shape recording based on 3D scanning can be advanced, and various stereoscopic analysis can be performed. Therefore, an optimization modeling process that combines X-ray CT and optical surface scanning is required to record both internal and external shapes of cultural heritage. In this study, optimization modeling methodology was applied to cultural heritage by combining X-ray CT technology and optical 3D scanning technology. Based on the models obtained through both technologies, a mesh-based optimization convergence modeling methodology considering internal and external surface shapes and color is organized. Furthermore, because the X-ray CT data has a characteristic of a voxel base, it is determined that additional convergence methods, including internal voxel data, are required, and a voxel-based optimization model process is established concurrently. Following that, two convergence modeling methods were applied to each of the deer-shaped horn cup artifacts that had an interior shape. As a result, the 3D convergence model creation and mapping optimization process, which can reveal important internal and external information about artifacts such as surface color, fine shape, and internal structure, can be improved. This 3D convergence modeling methodology was able to supplement the two technologies while preserving the benefits of optical 3D scanning and X-ray CT technology. This is thought to contribute to the expansion of the digital recording process from a single technology to multiple technologies. The X-ray CT-based convergence modeling pipeline is expected to be an opportunity in promoting the revitalization of X-ray CT technology in the cultural heritage field because it can be used for a wide range of purposes such as shape analysis, preservation status evaluation, monitoring, restoration, and reproduction.

Extremal Solutions for Surface Energy Minimization: Bicubically Blended Coons Patches

A Coons patch is characterized by a finite set of boundary curves, which are dependent on the choice of blending functions. For a bicubically blended Coons patch (BBCP), the Hermite cubic polynomials (interpolants) are used as blending functions. A BBCP comprises information about its four corner points, including the curvature represented by eight tangent vectors, as well as the twisting behavior determined by the four twist vectors at these corner points. The interior shape of the BBCP depends not only on the tangent vectors at the corner points but on the twist vectors as well. The alteration in the twist vectors at the corner points can change the interior shape of the BBCP even for the same arrangement of tangent vectors at these corner points. In this study, we aim to determine the optimal twist vectors that would make the surface an extremal of the minimal energy functional. To achieve this, we obtain the constraints on the optimal twist vectors (MPDs) of the BBCP for the specified corner points by computing the extremal of the Dirichlet and quasi-harmonic functionals over the entire surface with respect to the twist vectors. These twist vectors can then be used to construct various quasi-minimal and quasi-harmonic BBCPs by varying corner points and tangent vectors. The optimization techniques involve minimizing a functional subject to certain constraints. The methods used to optimize twist vectors of BBCPs can have potential applications in various fields. They can be applied to fuzzy optimal control problems, allowing us to find the solution of complex and uncertain systems with fuzzy constraints. They provide us an opportunity to incorporate symmetry considerations for the partial differential equations associated with minimal surface equations, an outcome of zero-mean curvature for such surfaces. By exploring and utilizing the underlying symmetries, the optimization strategies can be further enhanced in terms of robustness and adaptability.

Geometric Shape Characterisation Based on a Multi-Sweeping Paradigm

The characterisation of geometric shapes produces their concise description and is, therefore, important for subsequent analyses, for example in Computer Vision, Machine Learning, or shape matching. A new method for extracting characterisation vectors of 2D geometric shapes is proposed in this paper. The shape of interest, embedded into a raster space, is swept several times by sweep-lines having different slopes. The interior shape’s points, being in the middle of its boundary and laying on the actual sweep-line, are identified at each stage of the sweeping process. The midpoints are then connected iteratively into chains. The chains are filtered, vectorised, and normalised. The obtained polylines from the vectorisation step are used to design the shape’s characterisation vector for further application-specific analyses. The proposed method was verified on numerous shapes, where single- and multi-threaded implementations were compared. Finally, characterisation vectors, among which some were rotated and scaled, were determined for these shapes. The proposed method demonstrated a good rotation- and scaling-invariant identification of equal shapes.

Topology Optimization of Self-supporting Porous Structures Based on Triply Periodic Minimal Surfaces

With the advent of additive manufacturing (AM), topology optimization (TO) has become increasingly important in structural design. A key component of structural design is generating the interior shape of an object under predefined force conditions and specific constraints. Fabricating such models by layer-based AM suffers from the problem of adding and removing interior supporting structures, which can produce artifacts in the final product. In this paper, we propose an algorithm to design a self-supporting porous structure by integrating overhang constraints into the topology optimization framework. A minimum thickness constraint is also built into the optimization process to automatically enforce printability of the resulting structures. We utilize triply periodic minimal surfaces (TPMSs) to represent interior structures which can be analyzed, optimized and stored directly using analytical functions. We apply several acceleration methods including super element strategy, multigrid algorithm and GPU-based solver to handle models comprising of several million of elements efficiently. Numerical results indicate that the optimized interior structures obtained by our approach exhibit improved printability as they largely satisfy manufacturing requirements on overhang angles and minimal thicknesses.

Development and systematization of indoor noise reduction methods under a new vibrationacoustic coupling using energy density distribution

When the interior shape is determined, the frequency range to be reduced, which is a particular problem, is determined. Until now, there has been no noise reduction countermeasure method using information on resonant frequency such as strain and kinetic energy density. For the first time in this report, it is shown that noise reduction of the resonant frequency, existing in the problematic frequency, can be effectively obtained after reducing the plate thickness from the energy density distribution. The greatest advantage of this method is that, unlike conventional optimization methods, it is possible to take countermeasures interactively and extremely reasonably, and systematization to draw out its effectiveness will also be discussed.

From boundaries to bumps: When closed (extremal) contours are critical.

Invariants underlying shape inference are elusive: A variety of shapes can give rise to the same image, and a variety of images can be rendered from the same shape. The occluding contour is a rare exception: It has both image salience, in terms of isophotes, and surface meaning, in terms of surface normal. We relax the notion of occluding contour and, more accurately, the rim on the object that projects to it, to define closed extremal curves. This new shape descriptor is invariant over different renderings. It exists at the topological level, which guarantees an image-based counterpart. It surrounds bumps and dents, as well as common interior shape components, and formalizes the qualitative nature of bump perception. The invariants are biologically computable, unify shape inferences from shading and specular materials, and predict new phenomena in bump and dent perception. Most important, working at the topological level allows us to capture the elusive aspect of bump boundaries.

Multi-sided B-spline surfaces over curved, multi-connected domains

We propose a new surface representation, the Generalized B-spline (GBS) patch, that combines ribbon interpolants given in B-spline form. A GBS patch can connect to tensor-product B-spline surfaces with arbitrary Gm continuity. It supports ribbons not only along the perimeter loop, but also around holes in the interior of the patches.This is a follow-up paper of a recent publication (Várady et al., 2020) that described multi-sided Bézier surfaces over curved multi-sided domains. While the fundamental concept is retained, several new details have been elaborated. The weighting functions are modified to be products of B-spline and Bernstein basis functions, multiplied by rational terms. A new local parameterization method is introduced using harmonic functions, that handles periodic hole loops, as well. Interior shape control is adapted to the B-spline representation of the ribbons. Several examples illustrate the capabilities of the proposed scheme. Our implementation is based on a computationally efficient discretization.

Airflow-acoustic interactions in speech production research

Speech production involves air traveling from a reservoir (the lungs) through various ducts (the bronchi and trachea, the vocal and nasal tracts), past various structures at which sounds can be generated by the flow of air. Some structures (e.g., the vocal folds or the tongue tip) can be positioned so as to self-oscillate, generating quasi-periodic sound; some (e.g., the lips or the tongue tip) can be positioned to create a constriction small enough to generate turbulence, and thus turbulence noise. These sounds excite the resonances of the tract. They can also interact, as when the sound generated by vocal fold vibration modulates the turbulent jet formed at a downstream constriction. It would seem to be straightforward to predict the sound that propagates through the tract and is radiated externally, except that the tract changes shape continually; the walls of the tract vary in compliance, from hard (e.g., teeth) to yielding (e.g., cheeks); and in spite of co-opting many types of medical imaging, it is very difficult to measure the interior shape of the tract accurately and without disturbing either the speech or the speaker. Some acousto-fluidic interactions that occur during speech, and the ways they have been modeled, are discussed.

Image Zooming Based on Two Classes of C1-Continuous Coons Patches Construction with Shape Parameters over Triangular Domain

Image interpolation is important in image zooming. To improve the quality of image zooming, in this work, we proposed a class of rational quadratic trigonometric Hermite functions with two shape parameters and two classes of C 1 -continuous Coons patches constructions over a triangular domain by improved side–side method and side–vertex method. Altering the values of shape parameters can adjust the interior shape of the triangular Coons patch without influencing the function values and partial derivatives of the boundaries. In order to deal with the problem of well-posedness in image zooming, we discussed symmetrical sufficient conditions for region control of shape parameters in the improved side–side method and side–vertex method. Some examples demonstrate the proposed methods are effective in surface design and digital image zooming. C 1 -continuous Coons patches constructed by the proposed methods can interpolate to scattered 3D data. By up-sampling to the constructed interpolation surface, high-resolution images can be obtained. Image zooming experiment and analysis show that compared to bilinear, bicubic, iterative curvature-based interpolation (ICBI), novel edge orientation adaptive interpolation scheme for resolution enhancement of still images (NEDI), super-resolution using iterative Wiener filter based on nonlocal means (SR-NLM) and rational ball cubic B-spline (RBC), the proposed method can improve peak signal to noise ratio (PSNR) and structural similarity index (SSIM). Edge detection using Prewitt operator shows that the proposed method can better preserve sharp edges and textures in image zooming. The proposed methods can also improve the visual effect of the image, therefore it is efficient in computation for image zooming.

Multi-sided Bézier surfaces over curved, multi-connected domains

A new multi-sided, control point based surface formulation is proposed, extending the principles of the Generalized Bézier patch published by Várady et al. (2016). The surface is constructed from side interpolants given in Bézier form. The boundary curves may have different degrees, and the cross-derivatives can ensure arbitrary G-continuity with adjacent patches. The representation is capable of handling boundary curves with high curvature variations and concave angles. The surfaces are C∞-continuous and may have holes in their interior.The most distinctive feature of the patch is that it is defined over a planar domain with curved boundaries that mimic the shape of the 3D boundary curves. Local parameters, derived from harmonic barycentric coordinates, are associated with each side of the domain. The control points are multiplied by Bernstein functions and additional rational terms that provide the same degree of freedom for shape design as their quadrilateral counterparts.The paper introduces the full construction of Curved Domain (CD) Bézier patches including domain generation, parameterization, basis functions, and methods for additional interior shape control. Specific problems related to CD surfaces are also discussed with many examples that demonstrate the peculiarity and usefulness of the scheme.

Exterior Shape Factors From Interior Shape Factors

Shape factors for steady heat conduction enable quick and highly simplified calculations of heat transfer rates within bodies having a combination of isothermal and adiabatic boundary conditions. Many shape factors have been tabulated, and most undergraduate heat transfer books cover their derivation and use. However, the analytical determination of shape factors for any but the simplest configurations can quickly come to involve complicated mathematics, and, for that reason, it is desirable to extend the available results as far as possible. In this paper, we show that known shape factors for the interior of two-dimensional objects are identical to the corresponding shape factors for the exterior of those objects. The canonical case of the interior and exterior of a disk is examined first. Then, conformal mapping is used to relate known configurations for squares and rectangles to the solutions for the disk. Both a geometrical and a mathematical argument are introduced to show that shape factors are invariant under conformal mapping. Finally, the general case is demonstrated using Green's functions. In addition, the “Yin-Yang” phenomenon for conduction shape factors is explained as a rotation of the unit disk prior to conformal mapping.

Geometry Acquisition and 3D Modelling of a Wind Tower using a 3D Laser Scanning Technology

This work aims at acquiring the interior shape of wind towers by means of a 3D laser scanning system (LSS). Typically, wind towers are made of structural steel sheets and their fabrication consists of rolling and welding of abutted rolled sheets. This task is typically carried out by welding robots moving through the tower structure. In this study, the developed setup consists of a camera and a circular laser module mounted on the welding robot’s arm traveling through the tower with a constant velocity. The deployed system assists in examining the tower’s interior surface, making it possible to obtain its 3D profile. It will therefore be beneficial for monitoring the geometric changes which occur during the welding process. Encouraging results have been achieved in the characterization of the tower’s geometry, contributing to the assessment of the robustness and accuracy of the deployed 3D LSS.

Emotion and Sustainable Residential Interior Shape

Focusing on inhabitant‟s climate comfort causes the neglect of personal and aesthetic factors that have effects on emotions and psychological comfort. Blindly adhering to sustainable design principles regardless of the basic architectural design parameters cause similar interior spaces in today‟s housing of Iran. Interior space form is one the main design factors that has some effects on inhabitant‟s emotions. It is a correlation research to study inhabitant‟s emotions towards sustainable interior space by focusing on interior form. It illustrates that form can consider as an influential factor in creating and improving sustainable conditions according to inhabitant‟s emotions.

Continuous optimization of interior carving in 3D fabrication

In this paper we propose an optimization framework for interior carving of 3D fabricated shapes. Interior carving is an important technique widely used in industrial and artistic designs to achieve functional purposes by hollowing interior shapes in objects. We formulate such functional purpose as the objective function of an optimization problem whose solution indicates the optimal interior shape. In contrast to previous volumetric methods, we directly represent the boundary of the interior shape as a triangular mesh. We use Eulerian semiderivative to relate the time derivative of the object function to a virtual velocity field and iteratively evolve the interior shape guided by the velocity field with surface tracking. In each iteration, we compute the velocity field guaranteeing the decrease of objective function by solving a linear programming problem. We demonstrate this general framework in a novel application of designing objects floating in fluid and two previously investigated applications, and print various optimized objects to verify its effectiveness.

Point-based medialness for 2D shape description and identification

We propose a perception-based medial point description of a natural form (2D: static or in articulated movement) as a framework for a shape representation which can then be efficiently used in biological species identification and matching tasks. Medialness is defined by adapting and refining a definition first proposed in the cognitive science literature when studying the visual attention of human subjects presented with articulated biological 2D forms in movement, such as horses, dogs and humans (walking, running). In particular, special loci of high medialness for the interior of a form in movement, referred to as “hot spots”, prove most attractive to the human perceptual system. We propose an algorithmic process to identify such hot spots. In this article we distinguish exterior from interior shape representation. We further augment hot spots with extremities of medialness ridges identifying significant concavities (from outside) and convexities (from inside). Our representation is strongly footed in results from cognitive psychology, but also inspired by know-how in art and animation, and the algorithmic part is influenced by techniques from more traditional computer vision. A robust shape matching algorithm is designed that finds the most relevant targets from a database of templates by comparing feature points in a scale, rotation and translation invariant way. The performance of our method has been tested on several databases. The robustness of the algorithm is further tested by perturbing the data-set at different levels.

Modal function transformation for isometric 3D shape representation

Isometric deformations complicate 3D shape representation and recognition. Therefore, proper modeling is in need. In this paper, we propose a novel modal function transformation framework for shape information abstraction. Key to our approach is to generalize the notion of pairwise shape matching by comparing their modal functions. By choosing intrinsic embedding basis (e.g. eigenfunction of Laplace–Beltrami Operator (LBO)) properly on each shape, we get a compact function space that is suitable for informative inference. To characterize the interior shape structure, a special inner function is devised. Then, the largest spectra of the inner functions are adopted as our modal feature. On this basis, we discuss the properties of the modal feature. For performance evaluation, non-rigid object recognition experiments are carried out on several popular shape matching benchmarks. The final results show that the proposed approach works well with significant accuracy improvement against the LBO based methods. Besides, the performance of our method is comparable with state-of-the-art results.

Vortex Ventilation in the Laboratory Environment

Assured containment at low airflow has long eluded the users of ventilated enclosures including chemical fume hoods used throughout industry. It is proposed that containment will be enhanced in a hood that has a particular interior shape that causes a natural vortex to occur. The sustained vortex improves the containment of contaminants within the enclosure at low airflow. This hypothesis was tested using the ASHRAE 110 tracer gas test. A known volume of tracer gas was emitted in the hood. A MIRAN SapphIRe infrared spectrometer was used to measure the concentration of tracer gas that escapes the enclosure. The design of the experiment included a written operating procedure, data collection plan, and statistical analysis of the data. A chemical fume hood of traditional design was tested. The hood interior was then reconstructed to enhance the development of a vortex inside the enclosure. The hood was retested using the same method to compare the performance of the traditional interior shape with the enhanced vortex shape. In every aspect, the vortex hood showed significant improvement over the traditional hood design. Use of the Hood Index characterizing the dilution of gas in an air stream as a logarithmic function indicates a causal relationship between containment and volumetric airflow through an enclosure. Use of the vortex effect for ventilated enclosures can provide better protection for the user and lower operating cost for the owner.[Supplementary materials are available for this article. Go to the publisher's online edition of Journal of Occupational and Environmental Hygiene for the following free supplemental resource: a data collection spreadsheet, data analysis, and data collection procedure.]

CAD of the shoe interior shape

CAD of the shoe interior shape

Support Vector Shape: A Classifier-Based Shape Representation

We introduce a novel implicit representation for 2D and 3D shapes based on Support Vector Machine (SVM) theory. Each shape is represented by an analytic decision function obtained by training SVM, with a Radial Basis Function (RBF) kernel so that the interior shape points are given higher values. This empowers support vector shape (SVS) with multifold advantages. First, the representation uses a sparse subset of feature points determined by the support vectors, which significantly improves the discriminative power against noise, fragmentation, and other artifacts that often come with the data. Second, the use of the RBF kernel provides scale, rotation, and translation invariant features, and allows any shape to be represented accurately regardless of its complexity. Finally, the decision function can be used to select reliable feature points. These features are described using gradients computed from highly consistent decision functions instead from conventional edges. Our experiments demonstrate promising results.

The Structure of Galaxies: II. Fitting Functions and Scaling Relations for Ellipticals

AbstractSurface photometry of 311 ellipticals from the 2MASS imaging database is analyzed with respect to the two most common fitting functions: the r1/4 law and the Sérsic r1/n model. The advantages and disadvantages of each fitting function are examined. In particular, the r1/4 law performs well in the middle regions, but is inadequate for the core (inner 5 kpc) and the outer regions (beyond the half-light radius) which do not have r1/4 shapes. It is found that the Sérsic r1/n model produces good fits to the core regions of ellipticals (r<rhalf), but is an inadequate function for the entire profile of an elliptical from core to halo due to competing effects on the Sérsic n index and the fact that the interior shape of an elliptical is only weakly correlated with its halo shape. In addition, there are a wide range of Sérsic parameters that will equally describe the shape of the outer profile, degrading the Sérsic model's usefulness as a describer of the entire profile. Empirically determined parameters, such as half-light radius and total luminosity, have less scatter than fitting function variables. The scaling relations for ellipticals are often non-linear, but for ellipticals brighter than MJ < −23 the following structural relations are found: L ∝ r0.8±0.1, L ∝ Σ−0.5±0.1, and Σ ∝ r−1.5±0.1.