Coordinates Of Vertices Research Articles

CATALOG-BASED REPRESENTATION OF 2D TRIANGULATIONS

Several Representations and Coding schemes have been proposed to represent efficiently 2D triangulations. In this paper, we propose a new practical approach to reduce the main memory space needed to represent an arbitrary triangulation, while maintaining constant time for some basic queries. This work focuses on the connectivity information of the triangulation, rather than the geometric information (vertex coordinates), since the combinatorial data represents the main part of the storage. The main idea is to gather triangles into patches, to reduce the number of pointers by eliminating the internal pointers in the patches and reducing the multiple references to vertices. To accomplish this, we define and use stable catalogs of patches that are closed under basic standard update operations such as insertion and deletion of vertices, and edge flips. We present some bounds and results concerning special catalogs, and some experimental results that exhibit the practical gain of such methods.

Versatile surface detail editing via Laplacian coordinates

This paper presents a versatile detail editing approach for triangular meshes based on filtering the Laplacian coordinates. More specifically, we first compute the Laplacian coordinates of the mesh vertices, then filter the Laplacian coordinates, and finally reconstruct the mesh from the filtered Laplacian coordinates by solving a linear least square system. The proposed detail editing method includes not only feature preserving smoothing but also enhancing. Furthermore, the proposed approach allows interactive editing of some user-specified frequencies and regions. Experimental results demonstrate that our method is much more versatile and faster than the existing methods.

Method for reconstruction of direction of gamma quanta registered by CsI calorimeter in E391 experiment

This study presents a new method for the reconstruction of the direction of γ quanta registered by a CsI calorimeter in the E391 experiment. A neural network in the form of a generalized basis function is used as the mathematical tool for reconstruction. The effective mass of the registered π0 mesons and z coordinate of the decay vertex was first reconstructed in E391 using the measured direction of the registered γ quanta. The reconstruction of these quantities increases the sensitivity of the E391 experiment by at least 35%.

THE ROLE OF BERYLLIUM IN BERYLLOSILICATE MINERAL STRUCTURES AND ZEOLITE FORMATION

Topological diagrams are constructed for all layered and framework beryllosilicates and for zeolites having related topological features. These diagrams are used to identify the secondary building units (SBU). The SBU are arranged in increasing order of ring dimension to establish a structural hierarchy for this chemical class. Vertex symbols (VS) and coordination sequences (CS) are determined for each unique tetrahedrally coordinated site in every crystal structure. The number sets, VS and CS, identify structural similarities in beryllosilicates and in natural and synthetic zeolites. The frequency of ring-size occurrence varies with Be content in both layered and framework beryllosilicates. Framework density (FD) is derived from structure diagrams, and topological density (TD) is derived from CS sums. Framework density and topological density are strongly correlated. The topological density is controlled by the Be content in tetrahedrally coordinated sites. This structural control could be used to design specific framework arrangements.

Compression of 3D Mesh Geometry and Vertex Attributes for Mobile Graphics

This paper presents a compression scheme for mesh geometry, which is suitable for mobile graphics. The main focus is to enable real-time decoding of compressed vertex positions while providing reasonable compression ratios. Our scheme is based on local quantization of vertex positions with mesh partitioning. To prevent visual seams along the partitioning boundaries, we constrain the locally quantized cells of all mesh partitions to have the same size and aligned local axes. We propose a mesh partitioning algorithm to minimize the size of locally quantized cells, which relates to the distortion of a restored mesh. Vertex coordinates are stored in main memory and transmitted to graphics hardware for rendering in the quantized form, saving memory space and system bus bandwidth. Decoding operation is combined with model geometry transformation, and the only overhead to restore vertex positions is one matrix multiplication for each mesh partition. In our experiments, a 32-bit floating point vertex coordinate is quantized into an 8-bit integer, which is the smallest data size supported in a mobile graphics library. With this setting, the distortions of the restored meshes are comparable to 11-bit global quantization of vertex coordinates. We also apply the proposed approach to compression of vertex attributes, such as vertex normals and texture coordinates, and show that gains similar to vertex geometry can be obtained through local quantization with mesh partitioning.

동작분석용 캐릭터 애니메이션 모델 제작에 관한 연구

In order to extract data modeled in Max, this study proposed an adequate character animation modeling method to be used in motion analysis using MaxScript. Using the script, we could extract the coordinates of vertices in a character model without going through a complicated process. When animation was performed by applying the method to a character model extracted through loading data obtained from captured tennis volley motions, it was performed normally. We extracted Biped materials with script, but expect to extract conveniently the coordinates not only of rackets, golf clubs and other gears necessary for motion analysis but also of stadiums, ballparks, and gymnasiums. Recently commercial 3D software is used often in biomechanics, but it is difficult to control what the users want such as the extraction of dynamic data. Moreover, it is even harder to approach computer programs out of interest in research on motion analysis programs. In this situation, we expect to approach them without difficulty using script or C Language as in our experiment.

Polygonal mesh watermarking using Laplacian coordinates

AbstractWe propose a watermarking algorithm for polygonal meshes based on the modification of the Laplacian coordinates. More specifically, we first compute the Laplacian coordinates (x,y,z) of the mesh vertices, then construct the histogram of the lengths of the (x,y,z) vectors, and finally, insert the watermark by altering the shape of that histogram. The watermark extraction is carried out blindly, with no reference to the host model. The proposed method is more robust than several existing high capacity watermarking algorithms. In particular, it is able to resist attacks such as translations, rotations, uniform scaling and vertex reordering, due to the invariance of the histogram of the Laplacian vector lengths under such transformations. Compared to the existing robust watermarking methods, our experiments show that the proposed method can better resist common mesh editing attacks, due to the good behaviour of the Laplacian coordinates under such operations.

Making 3D Object Surfaces Smoother:

Interpolating subdivision schemes let users adjust coordinates of a 3D object's initial vertices, generate new vertices, and replace the original mesh with more and smaller polygons to make the object's surface smoother. Two new schemes for triangular meshes extend and combine existing schemes to improve the process and its results.

ALFLARSENITE: STRUCTURE AND RELATIONSHIP TO OTHER Be-Si AND ZEOLITE FRAMEWORK STRUCTURES

Alflarsenite, ideally NaCa 2 Be 3 Si 4 O 13 (OH)·2H 2 O, is a new zeolite species from the Tuften larvikite quarry, Tvedalen, Larvik, Vestfold, south Norway. The crystal structure has been solved in space group P 2 1 , with unit-cell parameters refined from single-crystal data: a 7.1222(4), b 19.8378(11), c 9.8071(5) A, β 111.287(1)°, V 1291.1(2) A 3 and Z = 4. The crystal structure, a zeolite framework, was refined to R 1 = 0.046 for 3283 observed reflections. The Be–Si framework of tetrahedra has cages containing the Na and Ca atoms and H 2 O groups. The framework has Cmcm space-group symmetry; the addition of Na and Ca cations reduces the symmetry to space group Cmc 2 1 , whereas taking into consideration the H 2 O groups, the structure reduces in symmetry to monoclinic P 2 1 . Topological diagrams were constructed for all framework beryllium silicates and for zeolites that have topological features similar to alflarsenite. These diagrams are used to identify the secondary building units (SBU), 5–1 and spiro –5, and to extract vertex symbols and coordination sequences for each topologically unique site having tetrahedral coordination. The SBUs and coordination-sequence numbers show structural similarities to bikitaite and the synthetic zeolites CAS and NSI. All four structures have slabs composed of alternating chains of 5- and 8-connected rings. The cross-linkage of these slabs varies in each structure.

Simulation of tau neutrino interaction in an emulsion track detector

Simulation of the interactions between tau neutrinos ντ and the material of the emulsion track detector using Geant4 software is described. The purpose of the work is to generate artificial events and to estimate, on their basis, the reconstruction accuracy for the geometric parameters (vertex coordinates, impact parameters, and track kink angles) and distributions of these parameters used in the selection criteria of the OPERA experiment.

Convex regular-faced polyhedra indecomposable by any plane to regular-faced polyhedra

A convex polyhedron with regular faces or with faces decomposable by two regular polygons is called indecomposable if any section plane dissects this polyhedron into two parts so that at least one of the faces of these two parts is an irregular polygon. In this article, the precise values of coordinates of vertices of such indecomposable convex polyhedra are calculated in the case when some of the faces consist of two regular polygons. The algebraic models of other indecomposable polyhedra are already constructed. So, for any indecomposable convex polyhedron, we give here the explicit values of the coordinates of such vertices and describe such isometries of the space, that the collection of orbits of these vertices under action of the group generated by these isometries coincides with the set of all vertices of this polyhedron.

Progressive Lossless Mesh Compression Via Incremental Parametric Refinement

AbstractIn this paper, we propose a novel progressive lossless mesh compression algorithm based on Incremental Parametric Refinement, where the connectivity is uncontrolled in a first step, yielding visually pleasing meshes at each resolution level while saving connectivity information compared to previous approaches. The algorithm starts with a coarse version of the original mesh, which is further refined by means of a novel refinement scheme. The mesh refinement is driven by a geometric criterion, in spirit with surface reconstruction algorithms, aiming at generating uniform meshes. The vertices coordinates are also quantized and transmitted in a progressive way, following a geometric criterion, efficiently allocating the bit budget. With this assumption, the generated intermediate meshes tend to exhibit a uniform sampling. The potential discrepancy between the resulting connectivity and the original one is corrected at the end of the algorithm. We provide a proof‐of‐concept implementation, yielding very competitive results compared to previous works in terms of rate/distortion trade‐off.

Anthropometric specification of child crash dummy pelves through statistical analysis of skeletal geometry

The pelves of the child dummies of the widely used Hybrid-III family are based on minimal data from children. Because an accurate pelvis design is critical for realistic assessments of belt restraint interactions, an analysis of medical imaging data was conducted to develop guidance for improved pelvis design. Three-dimensional polygonal meshes of the bony pelvis were generated from computed tomography (CT) data from 81 children from ages 5 to 11. After aligning to a uniform anatomical coordinate system, the meshes were resampled to create a quadrilateral mesh with 12,960 vertices for each pelvis. A principal components analysis was conducted with the mesh vertex coordinates and the locations of 31 landmarks. Over 99% of the variance in size and shape was accounted for by the first 40 components. A three-dimensional model representing the target for a new dummy pelvis was developed using bispinous breadth as the predictor variable. To obtain the appropriate geometry for the six-year-old (6YO) and 10YO Hybrid-III dummies, a regression analysis was conducted using a large sample of child anthropometry data from a previous study to obtain a target dimension for bispinous breadth, using the design stature for each dummy as input. A separate regression analysis was conducted to predict principal component scores from bispinous breadth. Reconstructing a pelvis model from the principal components scores predicted for the target bispinous breadth values yielded a three-dimensional design target for the each dummy. The new pelvis target is similar in overall size to the current pelvis components, but the location of the anterior-superior iliac spine is markedly lower, which has important implications for belt interaction.

Magnetic Basement Depth Inversion in the Space Domain

We present a total-field anomaly inversion method to determine both the basement relief and the magnetization direction (inclination and declination) of a 2D sedimentary basin presuming negligible sediment magnetization. Our method assumes that the magnetic intensity contrast is constant and known. We use a nonspectral approach based on approximating the vertical cross section of the sedimentary basin by a polygon, whose uppermost vertices are forced to coincide with the basin outcrop, which are presumably known. For fixed values of the x coordinates our method estimates the z coordinates of the unknown polygon vertices. To obtain the magnetization direction we assume that besides the total-field anomaly, information about the basement’s outcrops at the basin borders and the basement depths at a few points is available. To obtain stable depth-to-basement estimates we impose overall smoothness and positivity constraints on the parameter estimates. Tests on synthetic data showed that the simultaneous estimation of the irregular basement relief and the magnetization direction yields good estimates for the relief despite the mild instability in the magnetization direction. The inversion of aeromagnetic data from the onshore Almada Basin, Brazil, revealed a shallow, eastward-dipping basement basin.

Robust Watermarking of 3D Polygonal Meshes

This paper presents an algorithm for the robust watermarking of 3D polygonal mesh models. The proposed algorithm embeds the watermark into a 2D image extracted from the 3D model, rather than directly embedding it into 3D geometry. The proposed embedding domain, i.e., the 2D image, is devised to be robust against the attacks like mesh simplification which severely modifies the vertices and connectivity while preserving the appearance of the model. The watermark-embedded model is obtained by using a simple vertex perturbation algorithm without iterative optimization. Two exemplary watermark applications using the proposed methods are also presented: one is to embed several bits into 3D models and the other is to detect only the existence of a watermark. The experimental results show that the proposed algorithm is robust against similarity transform, mesh simplification, additive Gaussian noise, quantization of vertex coordinates and mesh smoothing, and that its computational complexity is lower than that of the conventional methods.

Arithmetic relations in the set covering polyhedron of circulant clutters

Fil: Aguilera, Nestor Edgardo. Consejo Nacional de Investigaciones Cientificas y Tecnicas. Centro Cientifico Tecnologico Conicet - Santa Fe. Instituto de Matematica Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matematica Aplicada del Litoral; Argentina

3D 변형가능 형상 모델 기반 3D 얼굴 모델링

3D 얼굴 모델링은 33공간에서 얼굴을 자유롭게 회전 시켜 다양한 얼굴 자세를 표현하고 조명 효과도 적절하게 모델링 할 수 있으므로, 얼굴 자세, 조명, 표정 등의 표현에 있어서 2D 얼굴 모델링에 비해 보다 정교하며 사실감이 뛰어나 얼굴 인식, 게임, 아바타 등에서 많은 요구가 존재한다. 본 논문에서는 3D 변형 가능 형상 모델에 기반을 둔 3D 얼굴 모델링 방법을 제안한다. 제안된 3D 얼굴 모델링 방법은 먼저 3D 스캐너를 통하여 획득한 3D 얼굴 스캔 데이터를 이용하여 3D 얼굴 변형 가능 형상 모델을 구축한다. 다음, 3D 얼굴 모델링을 하고자 하는 얼굴의 2D 이미지 시퀀스로부터, 해당 얼굴의 특징점들을 검출하고 이들을 매칭하여, 매칭된 특징점들로부터 인수분해 기반 SfM 기법을 이용하여 해당 특징점의 3D 버텍스 좌표 값을 구한다. 이후, 구한 3D 버텍스들을 3D 변형 가능 형상 모델에 정합하여 해당 얼굴의 3D 형상 모델을 얻는다. 또한, 2D 얼굴 이미지 시퀀스들로부터 뷰 독립적인 2D 원통 좌표 텍스쳐 맵을 구하고 이를 이용하여 3D 형상 모델을 렌더링 함으로써, 최종적으로 3B 얼굴 모델을 완성한다. 제안된 3D 얼굴 모델링 방법에 의한 3D 얼굴 모델 생성 과정을 통해서, 본 논문에서 제안한 3D 얼굴 모델링 방법이 기존의 얼굴 모델링 방법들에 비해 상대적으로 빠르고 비교적 정교하게 수행됨을 볼 수 있었다. Since 3D face can be rotated freely in 3D space and illumination effects can be modeled properly, 3D face modeling Is more precise and realistic in face pose, illumination, and expression than 2D face modeling. Thus, 3D modeling is necessitated much in face recognition, game, avatar, and etc. In this paper, we propose a 3D face modeling method based on 3D morphable shape modeling. The proposed 3D modeling method first constructs a 3D morphable shape model out of 3D face scan data obtained using a 3D scanner Next, the proposed method extracts and matches feature points of the face from 2D image sequence containing a face to be modeled, and then estimates 3D vertex coordinates of the feature points using a factorization based SfM technique. Then, the proposed method obtains a 3D shape model of the face to be modeled by fitting the 3D vertices to the constructed 3D morphable shape model. Also, the proposed method makes a cylindrical texture map using 2D face image sequence. Finally, the proposed method builds a 3D face model by rendering the 3D face shape model with the cylindrical texture map. Through building processes of 3D face model by the proposed method, it is shown that the proposed method is relatively easy, fast and precise than the previous 3D face model methods.

Reversible Data-Hiding Scheme for 2-D Vector Maps Based on Difference Expansion

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> Reversible watermarking is suitable for hiding data in 2-D vector maps because the distortions induced by data embedding can be removed after extracting the hidden bits. In this paper, two reversible data-hiding schemes are explored based on the idea of difference expansion. The first scheme takes the coordinates of vertices as the cover data and hides data by modifying the differences between the adjacent coordinates. The scheme achieves high capacity in the maps with highly correlated coordinates. Instead of the raw coordinates, the second scheme adopts the manhattan distances between neighbor vertices as the cover data. A set of invertible integer mappings is defined to extract manhattan distances from coordinates and the hidden data are embedded by modifying the differences between the adjacent distances. For those maps where distances exhibit high correlation, this scheme shows better performance than the former one, both in capacity and invisibility. Three different maps with distinct features are used for the experiments. The results indicate that two proposed schemes suit different types of maps, respectively, according to the correlation of the selected cover data. Both schemes are strictly reversible. In addition, they can be slightly robust for low amplitude distortions by selecting higher digits for data hiding. The potential applications of proposed schemes may include map data authentication, secret communication, etc. </para>

The heat equation to generate planar grids

An algorithm for the generation of quadrilateral grids on planar domains is presented. This algorithm is given by an iterative procedure, where, starting from an initial grid on the domain under consideration, the coordinates of the grid vertices are iteratively adjusted by using a local discrete variational approach. This procedure resembles the explicit difference scheme for a perturbed heat equation, where the perturbation can be dropped for convex domains. Experimental results on benchmark domains are presented, and show an interesting behavior of the proposed method.

LENGTH, AREA AND VOLUME COMPUTATION IN HOMOGENEOUS COORDINATES

Many problems solved in computer graphics, computer vision, visualization etc. require fast and robust computation of an area of a triangle or volume of a tetrahedron. These very often used algorithms are well known and robust if vertices coordinates of triangles or tetrahedrons are given in Euclidean coordinates. The homogeneous coordinates are often used for the representation of geometric transformations. They enable us to represent translation, rotation, scaling and projection operations in a unique way and handle them properly. Today's graphics hardware based on GPU offers very high computational power using pixel shaders and fragment shaders not only for graphical elements processing, but also for general computation using GPU as well. This paper presents simple methods for the area of a triangle and the volume of a tetrahedron computation if vertices are given in homogeneous coordinates without the need to use the division operation for vertices coordinates transformation from the homogeneous coordinates to the Euclidean coordinates. Area or volume computation is transferred to the cross product computation that is fast, simple, and robust and can be supported in hardware or implemented on GPU that uses vector operations with homogeneous coordinates natively. The presented formula can be used directly for Euclidean representation just setting w equal to 1.