A Low Distortion Mesh Parameterization Mapping Method Based on Proxy Function and Combined Newton

To address the issues of low efficiencies and serious mapping distortions in current mesh parameterization methods, we present a low distortion mesh parameterization mapping method based on proxy function and combined Newton’s method in this paper. First, the proposed method calculates visual blind areas and distortion prone areas of a 3D mesh model, and generates a model slit. Afterwards, the method performs the Tutte mapping on the cut three-dimensional mesh model, measures the mapping distortion of the model, and outputs a distortion metric function and distortion values. Finally, the method sets iteration parameters, establishes a reference mesh, and finds the optimal coordinate points to get a convergent mesh model. When calculating mapping distortions, Dirichlet energy function is used to measure the isometric mapping distortion, and MIPS energy function is used to measure the conformal mapping distortion. To find the minimum value of the mapping distortion metric function, we use an optimal solution method combining proxy functions and combined Newton’s method. The experimental data show that the proposed method has high execution efficiency, fast descending speed of mapping distortion energy and stable optimal value convergence quality. When a texture mapping is performed, the texture is evenly colored, close laid and uniformly lined, which meets the standards in practical applications.

Abnormal Bone Morphology in Charcot-Marie-Tooth Disease

Background: Although long suspected, it has yet to be shown whether the foot and ankle deformities of Charcot-Marie-Tooth disease (CMT) are generally associated with abnormalities in osseous shape. Computed tomography (CT) was used to quantify morphologic differences of the calcaneus, talus, and navicular in CMT compared with healthy controls. Methods: Weightbearing CT scans of 21 patients (27 feet) with CMT were compared to those of 20 healthy controls. Calcaneal measurements included radius of curvature, sagittal posterior tuberosity-posterior facet angle, and tuberosity coronal rotation. Talar measurements included axial and sagittal body-neck declination angle, and coronal talar head rotation. Surface-mesh model analysis of the hindfoot was performed comparing the average of the CMT cohort to the controls using a CT analysis software (Disior Bonelogic 2.0). Means were compared with a t test ( P < .05). Results: CMT patients had significantly less talar sagittal declination vs controls (17.8 vs 25.1 degrees; P < .05). Similarly, CMT patients had less talar head coronal rotation vs controls (30.8 vs 42.5 degrees; P < .001). The calcaneal radius of curvature in CMT patients was significantly smaller than controls (822.8 vs 2143.5 mm; P < .05). CMT sagittal posterior tuberosity–posterior facet angle was also significantly different from that of controls (60.3 vs 67.9 degrees respectively; P < .001). Surface-mesh model analysis demonstrated the largest differences in morphology at the navicular tuberosity, medial talar head, sustentaculum tali, and anterior process of the calcaneus. Conclusion: This is the first study to quantify the morphologic differences in hindfoot osteology seen in CMT patients. Patients identified with osseous changes of the calcaneus, especially a smaller axial radius of curvature, may benefit from a 3-dimensional osteotomy for correction.

Detection of periodic displacements of shell structures with edges using spline surfaces, meshes and point clouds

This research paper tackles the problem of determining displacements of complex-shaped shell structures, measured periodically using laser scanning. Point clouds obtained during different measurement epochs can be compared with each other directly or they can be converted into continuous models in the form of a triangle mesh or smooth patches (spline functions). The accuracy of the direct comparison of point clouds depends on the scanning density, while the accuracy of comparing the point cloud to the model depends on approximation errors that are formed during its creation. Modelling using triangle meshes flattens the local structure of the object compared to the spline model. However, if the shell has edges in its structure, their exact representation by spline models is impossible due to the undulations of functions along them. Edges can also be distorted by the mesh model by their chamfering with transverse triangles. These types of surface modelling errors can lead to the generation of pseudo-deformation of the structure, which is difficult to distinguish from real deformation. In order to assess the possibility of correct determination of deformation using the above-mentioned methods, laser scanning of a complex shell structure in two epochs was performed. Then, modelling and comparison of the results of periodic measurements were carried out. As a result of the research, advantages and disadvantages of each method were identified. It was noticed that none of the methods made it possible to correctly represent all deformations while suppressing pseudo-deformation. However, the combination of their best qualities made it possible to determine the actual deformation of the structure.

Local Dynamic Updating Method of Orebody Model Based on Mesh Reconstruction and Mesh Deformation

In this paper, to update the orebody model based on the given interpreted geological information, we present a local dynamic updating method of the orebody model that allows the interactive construction of the constraint deformation conditions and the dynamic updating of the mesh model. The rules for constructing deformation constraints based on the control polylines are discussed. Because only part of the model is updated, the updated mesh is effective and the overall quality is satisfactory. Our main contribution is that we propose a local dynamic updating method for the orebody model based on mesh reconstruction and mesh deformation. This method can automatically update a given 3D orebody model based on a set of unordered geological interpretation lines. Moreover, we implement a deformation neighborhood region search method based on the specified ring radius and a local constrained mesh deformation algorithm for the orebody model. Finally, we test the method and show the model update results with real geological datasets, which proves that this method is effective for the local updating of orebody models.

An energy, momentum and angular momentum conserving scheme for a regularization model of incompressible flow

We introduce a new regularization model for incompressible fluid flow, which is a regularization of the EMAC (energy, momentum, and angular momentum conserving) formulation of the Navier-Stokes equations (NSE) that we call EMAC-Reg. The EMAC formulation has proved to be a useful formulation because it conserves energy, momentum and angular momentum even when the divergence constraint is only weakly enforced. However, it is still a NSE formulation and so cannot resolve higher Reynolds number flows without very fine meshes. By carefully introducing regularization into the EMAC formulation, we create a model more suitable for coarser mesh computations but that still conserves the same quantities as EMAC, i.e., energy, momentum, and angular momentum. We show that EMAC-Reg, when semi-discretized with a finite element spatial discretization is well-posed and optimally accurate. Numerical results are provided that show EMAC-Reg is a robust coarse mesh model.

An efficient data masking method for encrypted 3D mesh model

The industrial 3D mesh model (3DMM) plays a significant part in engineering and computer aided designing field. Thus, protecting copyright of 3DMM is one of the major research problems that require significant attention. Further, the industries started outsourcing its 3DMM to cloud computing (CC) environment. For preserving privacy, the 3DMM are encrypted and stored on cloud computing environment. Thus, building efficient data masking of encrypted 3DMM is considered to be efficient solution for masking information of 3DMM. First, using the secret key, the original 3DMM is encrypted. Second without procuring any prior information of original 3DMM it is conceivable mask information on encrypted 3D mesh models. Third, the original 3DMM are reconstructed by extracting masked information. The existing masking methods are not efficient in providing high information masking capacity in reversible manner and are not robust. For overcoming research issues, this work models an efficient data masking (EDM) method that is reversible nature. Experiment outcome shows the EDM for 3DMM attain better performance in terms of peak signal-to-noise ratio (PSNR) and root mean squared error (RMSE) over existing data masking methods. Thus, the EDM model brings good tradeoffs between achieving high data masking capacity with good reconstruction quality of 3DMM.

A simplified algorithm for 3D mesh model considering the influence of edge features

Aiming at the problem that most of the existing grid simplification algorithms for 3D models can not deal with a large number of boundary or non-popular grid models, this paper proposes a grid simplification algorithm for 3D models based on traditional algorithms. The algorithm mainly studies the geometric features of the model, considering the calculation methods and characteristics of edge shrinkage, and introduces the edge feature factors on the basis of the traditional algorithm, that is, the triangular area and side length factors of local area are introduced in the calculation of folding cost. In addition, the gaussian curvature characteristics of the 3D model are also included. Experimental results show that the proposed algorithm can keep the detail features of the mesh model well, and greatly reflect the quality and effect of mesh simplification after simplification.

Automatic Reconstruction of Building Façade Model from Photogrammetric Mesh Model

Three-dimensional (3D) building façade model reconstruction is of great significance in urban applications and real-world visualization. This paper presents a newly developed method for automatically generating a 3D regular building façade model from the photogrammetric mesh model. To this end, the contour is tracked on irregular triangulation, and then the local contour tree method based on the topological relationship is employed to represent the topological structure of the photogrammetric mesh model. Subsequently, the segmented contour groups are found by analyzing the topological relationship of the contours, and the original mesh model is divided into various components from bottom to top through the iteration process. After that, each component is iteratively and robustly abstracted into cuboids. Finally, the parameters of each cuboid are adjusted to be close to the original mesh model, and a lightweight polygonal mesh model is taken from the adjusted cuboid. Typical buildings and a whole scene of photogrammetric mesh models are exploited to assess the proposed method quantitatively and qualitatively. The obtained results reveal that the proposed method can derive a regular façade model from a photogrammetric mesh model with a certain accuracy.