Triangle Surface Research Articles

Interactive hepatic parenchymal transection simulation with haptic feedback

BackgroundLiver resection involves surgical removal of a portion of the liver. It is used to treat liver tumors and liver injuries. The complexity and high-risk nature of this surgery prevents novice doctors from practicing it on real patients. Virtual surgery simulation was developed to simulate surgical procedures to enable medical professionals to be trained without requiring a patient, a cadaver, or an animal. Therefore, there is a strong need for the development of a liver resection surgery simulation system. We propose a real-time simulation system that provides realistic visual and tactile feedback for hepatic parenchymal transection. MethodsThe tetrahedron structure and cluster-based shape matching are used for physical model construction, topology update of a three-dimensional liver model soft deformation simulation, and haptic rendering acceleration. During the liver parenchyma separation simulation, a tetrahedral mesh is used for surface triangle subdivision and surface generation of the surgical wound. The shape-matching cluster is separated via component detection on an undirected graph constructed using the tetrahedral mesh. ResultsIn our system, cluster-based shape matching is implemented on a GPU, whereas haptic rendering and topology updates are implemented on a CPU. Experimental results show that haptic rendering can be performed at a high frequency (>900Hz), whereas mesh skinning and graphics rendering can be performed at 45fps. The topology update can be executed at an interactive rate (>10Hz) on a single CPU thread. ConclusionsWe propose an interactive hepatic parenchymal transection simulation method based on a tetrahedral structure. The tetrahedral mesh simultaneously supports physical model construction, topology update, and haptic rendering acceleration.

Robust conformal adaptive meshing of complex textile composites unit cells

A methodology to create conformal tetrahedral meshes of realistic woven unit cells for mesoscale analysis is presented. A voxel representation is used and the quadrangle surface mesh of the yarns is smoothed by a constrained surface division technique associated with a control of the yarn volume. The jagged effect is removed and, as the connectivity is unchanged, a conformal surface mesh is obtained. Simultaneously, a triangle surface mesh, free of intersections, is created. A first tetrahedral mesh is performed using an inner grid and an unstructured mesh generator. In a final step, mesh adaptation or coarsening is carried out to reduce drastically the computational cost of the finite element analysis. The approach is very robust and complex woven unit cells with a high number of yarns into contact can be meshed at an accurate yarn volume ratio compared to the voxel model.

RXMesh

We propose a new static high-performance mesh data structure for triangle surface meshes on the GPU. Our data structure is carefully designed for parallel execution while capturing mesh locality and confining data access, as much as possible, within the GPU's fast "shared memory." We achieve this by subdividing the mesh into patches and representing these patches compactly using a matrix-based representation. Our patching technique is decorated with ribbons , thin mesh strips around patches that eliminate the need to communicate between different computation thread blocks, resulting in consistent high throughput. We call our data structure RXMesh : Ribbon-matriX Mesh. We hide the complexity of our data structure behind a flexible but powerful programming model that helps deliver high performance by inducing load balance even in highly irregular input meshes. We show the efficacy of our programming model on common geometry processing applications---mesh smoothing and filtering, geodesic distance, and vertex normal computation. For evaluation, we benchmark our data structure against well-optimized GPU and (single and multi-core) CPU data structures and show significant speedups.

Morphological simplification of asphaltic mixture components for micromechanical simulation using finite element method

AbstractIn micromechanical simulations of asphalt mixtures, complex shapes of asphalt mortar and coarse aggregates require numerous elements in the finite element (FE) representation. This makes simulation time‐consuming with a high risk of failure. To conduct simulations with acceptable accuracy and low computational cost, an approach is proposed to simplify the geometry of mixture microstructures with error assessment due to simplification. The methodology comprises four main steps, as follows: (1) coarse aggregates in a specimen are three‐dimensionally reconstructed to conduct surface triangulation; (2) surface triangles are then clustered with a predefined fitting accuracy using the least square method; (3) coarse aggregates are simplified as polyhedrons based on triangle clusters, and the asphalt mortar is then reconstructed using Boolean operations; and (4) the simulation error caused by simplification is assessed based on FE interpolation theory to ensure the reliability of the simulation. Two samples were prepared and then reconstructed for the simulation of a cyclic indirect tensile test. The volume difference for more than 95% aggregates was less than 5% for the two specimens. The difference of stress and strain curves of original and simplified models of the two specimens ranged from 2% to 4%, which indicates that the simulation solutions of the simplified and original microstructures were very close. Furthermore, computational time was significantly reduced due to the simplification of the aggregates. This method facilitates the reliable and highly efficient simulation of asphalt mixtures using the FE method.

A generic energy‐conserving discrete element modeling strategy for concave particles represented by surface triangular meshes

AbstractA generic energy‐conserving linear normal contact model for concave particles in the discrete element method (DEM) is presented in this article. It is derived based on a recently enhanced general energy‐conserving contact theory for arbitrarily shaped particles. A set of more effective evaluation schemes required in the model are also given, which shows that only the intersection boundary between two contact shapes, instead of their contact region or surfaces, is required to be explicitly obtained, thereby substantially improving both efficiency and applicability of the proposed contact model over the previous version. A surface triangular mesh is used to represent any 3D concave particle. The computational issues associated with the contact of two surface triangulated 3D shapes, including the contact detection, the determination of intersection boundary segments, the computation of contact features and parallelization, critical time step, and friction and damping treatment for multiple contacts are described in detail. Two sets of numerical examples involving various concave 3D shapes with a large number of surface triangles are presented to demonstrate either the superb energy‐conserving property of the proposed model model, or its effectiveness, robustness, and universal nature for wider and more complex problems.

Exact and efficient polyhedral envelope containment check

We introduce a new technique to check containment of a triangle within an envelope built around a given triangle mesh. While existing methods conservatively check containment within a Euclidean envelope, our approach makes use of a non-Euclidean envelope where containment can be checked both exactly and efficiently. Exactness is crucial to address major robustness issues in existing geometry processing algorithms, which we demonstrate by integrating our technique in two surface triangle remeshing algorithms and a volumetric tetrahedral meshing algorithm. We provide a quantitative comparison of our method and alternative algorithms, showing that our solution, in addition to being exact, is also more efficient. Indeed, while containment within large envelopes can be checked in a comparable time, we show that our algorithm outperforms alternative methods when the envelope becomes thin.

Reliable estimation of membrane curvature for cryo-electron tomography.

Curvature is a fundamental morphological descriptor of cellular membranes. Cryo-electron tomography (cryo-ET) is particularly well-suited to visualize and analyze membrane morphology in a close-to-native state and molecular resolution. However, current curvature estimation methods cannot be applied directly to membrane segmentations in cryo-ET, as these methods cannot cope with some of the artifacts introduced during image acquisition and membrane segmentation, such as quantization noise and open borders. Here, we developed and implemented a Python package for membrane curvature estimation from tomogram segmentations, which we named PyCurv. From a membrane segmentation, a signed surface (triangle mesh) is first extracted. The triangle mesh is then represented by a graph, which facilitates finding neighboring triangles and the calculation of geodesic distances necessary for local curvature estimation. PyCurv estimates curvature based on tensor voting. Beside curvatures, this algorithm also provides robust estimations of surface normals and principal directions. We tested PyCurv and three well-established methods on benchmark surfaces and biological data. This revealed the superior performance of PyCurv not only for cryo-ET, but also for data generated by other techniques such as light microscopy and magnetic resonance imaging. Altogether, PyCurv is a versatile open-source software to reliably estimate curvature of membranes and other surfaces in a wide variety of applications.

An efficient method to integrate polynomials over polytopes and curved solids

In this paper, we present an efficient approach to compute the integral of monomials and polynomials over polyhedra and regions defined by parametric curved boundary surfaces. We use Euler's theorem for homogeneous functions in combination with Stokes's theorem to reduce the integration of a monomial over a three-dimensional solid to its boundary. If the solid is a polytope, through a recursive application of these theorems, the integral is further reduced to just the evaluation of the monomial and its derivatives at the vertices of the polytope. The present approach is simpler than existing techniques that rely on repeated use of the divergence theorem, which require the antiderivative of the monomials and the projection of these functions onto hyperplanes. For convex and nonconvex polytopes, our approach does not introduce any approximation for the integration of monomials. For curved solid regions bounded by surfaces that admit a parameterization, the same approach yields simplified formulas to compute the integral of any homogeneous function, including monomials. For surfaces parameterized by polynomial surfaces (such as Bézier surface triangles and B-spline patches), the method yields machine-precision accuracy for the volumetric integration of monomials with an appropriate quadrature rule. Numerical examples over regions bounded by polynomial surfaces and rational surfaces are presented to establish the accuracy and efficiency of the method.

Improved tribological performance of AISI 316L stainless steel by a combined surface treatment: Surface texturing by selective laser melting and plasma nitriding

Surface texturing, which depends on the formation of different patterns on materials, is used to improve the tribological performance of materials. Therefore, the effects of different surface textures fabricated by selective laser melting (SLM) and plasma nitriding on the friction and wear properties of AISI 316L stainless steel were investigated in this study. AISI 316L samples with hexagonal, random, ellipse, triangle, square and the new model (ellipse+triangle) surface textures (patterns) were produced by SLM and they were plasma nitrided at 400 °C for 2 h. Tribological behavior of them was determined by a pin-on-disc type tribo-tester under dry and simulated body fluid (SBF) conditions. XRD, SEM, microhardness tester and 3D surface profilometer were used for characterizations. The results showed that the surface textures and their area density were highly effective on the friction and wear properties and the increasing area density provided better wear resistance. Ellipse geometric pattern had the lowest friction coefficient and wear rate because it trapped wear debris and provided a smooth stress transition in comparison to the sharp-edged textures by enabling hydrodynamic benefit. Plasma nitriding led to decrease friction coefficient and wear rate for all surface textures since it produced a hard compound layer. Also, the best results were obtained from SBF because solid-solid contact was prevented and wear debris was removed by solution.

Computer graphics simulation of natural mummification by desiccation

AbstractOrganic bodies are subject to internal processes after death, causing significant structural, and optical changes. Mummification by desiccation leads to volume shrinkage, skin wrinkling, and discoloration. We propose a method to simulate the process of mummification by desiccation and its effects on the corpse's morphology and appearance. The mummifying body is represented by a layered model consisting of a tetrahedral mesh, representing the volume, plus a high resolution triangle surface mesh representing the skin. The finite element method is used to solve the moisture diffusion and the resulting volume deformations. Skin wrinkling is achieved using position based dynamics. In order to model a visually believable reproduction of the skin coloration changes due to mummification, a skin shading approach is used that considers moisture content, hemoglobin content, and oxygen saturation. The main focus of the work in this article is to recreate the appearance changes of mummification by desiccation, which, to the best of our knowledge, has not been attempted before in computer graphics to this level of realism. The suggested approach is able to model changes in the internal structure and the surface appearance of the body which resemble the postmortem processes of natural mummification by desiccation.

Enhanced PEEC Model Based on Automatic Voronoi Decomposition of Triangular Meshes

We present an enhanced partial element equivalent circuit (PEEC) model based on Voronoi decomposition of triangular meshes. A complex geometry is accurately represented by many surface triangles, while keeping the number of elements in the corresponding equivalent circuit far less than the number of triangles. To do this, the triangular geometry is automatically decomposed into surface partitions using Voronoi's algorithm. These partitions describe capacitance cells, while inductance elements are set between all neighboring partition pairs. The inductance ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</i> ) and capacitance ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">C</i> ) matrix calculations are done independently using solvers based on quasi-static electric and magnetic full-wave method of moments (MoM). To get the current and charge distribution over the triangles, the MoM results during <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LC</i> evaluation are combined with the results of modified nodal analysis. We validated our method against the standard PEEC and MoM results as well as measured data. Then, we used our method to simulate conducted emission for a real automotive LED brake-light module.

Modeling Complex Deformations of the Sigmoid Colon Between External Beam Radiation Therapy and Brachytherapy Images of Cervical Cancer

In this study, we investigated registration methods for estimating the large interfractional sigmoid deformations that occur between external beam radiation therapy (EBRT) and brachytherapy (BT) for cervical cancer. Sixty-three patients were retrospectively analyzed. The sigmoid colon was delineated on 2 computed tomography images acquired during EBRT (without applicator) and BT (with applicator) for each patient. Five registration approaches were compared to propagate the contour of the sigmoid from BT to EBRT anatomies: rigid registration, commercial hybrid (ANAtomically CONstrained Deformation Algorithm), controlling ROI surface projection of RayStation, and the classical and constrained symmetrical thin-plate spline robust point matching (sTPS-RPM) methods. Deformation of the sigmoid due to insertion of the BT applicator was reported. Registration performance was compared by using the Dice similarity coefficient (DSC), distance to agreement, and Hausdorff distance. The 2 sTPS-RPM methods were compared by using surface triangle quality criteria between deformed surfaces. Using the deformable approaches, the BT dose of the sigmoid was deformed toward the EBRT anatomy. The displacement and discrepancy between the deformable methods to propagate the planned D1cm3 and D2cm3 of the sigmoid from BT to EBRT anatomies were reported for 55 patients. Large and complex deformations of the sigmoid were observed for each patient. Rigid registration resulted in poor sigmoid alignment with a mean DSC of 0.26. Using the contour to drive the deformation, ANAtomically CONstrained Deformation Algorithm was able to slightly improve the alignment of the sigmoid with a mean DSC of 0.57. Using only the sigmoid surface as controlling ROI, the mean DSC was improved to 0.79. The classical and constrained sTPS-RPM methods provided mean DSCs of 0.95 and 0.96, respectively, with an average inverse consistency error <1 mm. The constrained sTPS-RPM provided more realistic deformations and better surface topology of the deformed sigmoids. The planned mean (range) D1cm3 and D2cm3 of the sigmoid were 13.4 Gy (1-24.1) and 12.2 Gy (1-21.5) on the BT anatomy, respectively. Using the constrained sTPS-RPM to deform the sigmoid from BT to EBRT anatomies, these hotspots had a mean (range) displacement of 27.1 mm (6.8-81). Large deformations of the sigmoid were observed between the EBRT and BT anatomies, suggesting that the D1cm3 and D2cm3 of the sigmoid would unlikely to be at the same position throughout treatment. The proposed constrained sTPS-RPM seems to be the preferred approach to manage the large deformation due to BT applicator insertion. Such an approach could be used to map the EBRT dose to the BT anatomy for personalized BT planning optimization.

Design of Navigation System for Liver Surgery Guided by Augmented Reality

The traditional surgical navigation system combining preoperative CT and intraoperative ultrasound is widely used in open hepatectomy, but the problem of this system is that there are some errors in terms of the precision of the time and the space during the surgery. In order to solve the above problems, this paper introduces augmented reality technology into the surgical navigation system. In order to accurately describe the biomechanical characteristics of the liver and let the navigation system perform more accurately, this paper uses Tetgen to perform tetrahedral partition on the triangle mesh data obtained after the three-dimensional CT was reconstructed, and then the surface mesh data and the internal tetrahedral data were obtained and they were used to describe a whole liver model. The surface triangle mesh data is used to render graphics and describe the surface topology change, and the internal tetrahedral data combined with mass-spring theory is used to simulate deformation. Subsequently, the ex vivo pig liver was used to experimentally verify the accuracy of gravity deformation of the liver model, and the results show that the error was mainly distributed between −2mm and −2.5mm. At the same time, this paper uses the NDI Polaris infrared tracking system to carry out precision experiments on the augmented reality module, and the measured error is 1.55± 0.29mm. Finally, various modules of the system are integrated to finish the experiment in which the ring-shaped lesions are cut from the ex vivo pig liver with the aid of augmented reality. The experimental error is 0± 1.26mm, and with the assistance of the general purpose graphics processing unit (GPGPU), the refresh rate is above 200FPS. The results prove that the liver surgery navigation system proposed in this paper is excellent in terms of real-time performance and accuracy, which can help doctors accurately locate the tumor during surgery and perform ideal resection.

Mandoline

Although geometry arising "in the wild" most often comes in the form of a surface representation, a plethora of geometrical and physical applications require the construction of volumetric embeddings either of the geometry itself or the domain surrounding it. Cartesian cut-cell-based mesh generation provides an attractive solution in which volumetric elements are constructed from the intersection of the input surface geometry with a uniform or adaptive hexahedral grid. This choice, especially common in computational fluid dynamics, has the potential to efficiently generate accurate, surface-conforming cells; unfortunately, current solutions are often slow, fragile, or cannot handle many common topological situations. We therefore propose a novel, robust cut-cell construction technique for triangle surface meshes that explicitly computes the precise geometry of the intersection cells, even on meshes that are open or non-manifold. Its fundamental geometric primitive is the intersection of an arbitrary segment with an axis-aligned plane. Beginning from the set of intersection points between triangle mesh edges and grid planes, our bottom-up approach robustly determines cut-edges, cut-faces, and finally cut-cells, in a manner designed to guarantee topological correctness. We demonstrate its effectiveness and speed on a wide range of input meshes and grid resolutions, and make the code available as open source.

A greedy region growing algorithm for anisotropic stretch adaptive triangulation of geometry images

The geometry image representation is a remeshing of an irregular triangle surface mesh onto a rectangular grid of points and facilitates the processing of surface geometry. Its connectivity is commonly generated by splitting each rectangular quad of grid points along the shorter diagonal. However, this simple approach typically yields skinny triangles on the surface when the underlying local surface metric tensor eigenvalues differ significantly. Sequences of such triangles can appear like jaggedness.This paper presents a greedy, region growing algorithm for anisotropic triangulation of geometry images obtained by geometric stretch parametrization. The algorithm compensates for the local stretch anisotropy and variations in the principal directions of the metric tensor by minimizing the total length of the new edges of triangles added to the grown region. The surface reconstructed is more faithful to the original surface than the ones reconstructed by quad-splitting connectivity and recognized triangulation approaches for point clouds.

Prediction errors in surface segmentation are reflected in the visual mismatch negativity, independently of task and surface features.

The visual system quickly registers perceptual regularities in the environment and responds to violations in these patterns. Errors of perceptual prediction are associated with electrocortical modulation, including the visual mismatch negativity (vMMN) and P2 event-related potential. One relatively unexplored question is whether these prediction error signals can encode higher-level properties such as surface segmentation, or whether they are limited to lower-level perceptual features. Using a roving standard paradigm, a triangle surface appeared either behind (featuring amodal contours) or in front of (featuring real contours) a second surface with hole-like windows. A surface layout appeared for two to five repetitions before switching to the other "deviant" layout; lighting and orientation of stimuli varied across presentations while remaining isoluminant. Observers responded when they detected a rare "pinched" triangle, which occasionally appeared. Cortical activity-reflected in mismatch responses affecting the P2-N2 and P300 amplitudes-was sensitive to a change in stimulus layout, when surfaces shifted position in depth, following several repetitions. Specifically, layout deviants led to a more negative P2-N2 complex at posterior electrodes, and greater P300 positivity at central sites. Independently of these signals of a deviant surface layout, further modulations of the P2 encoded differences between layouts and detection of the rare target stimulus. Comparison of the effect of preceding layout repetitions on this prediction error signal suggests that it is all or none and not graded with respect to the number of previous repetitions. We show that within the visual domain, unnoticed and task-irrelevant changes in visual surface segmentation leads to observable electrophysiological signals of prediction error that are dissociable from stimulus-specific encoding and lower-level perceptual processing.

Laplacian-based 3D mesh simplification with feature preservation

We propose a novel Laplacian-based algorithm that simplifies triangle surface meshes and can provide different preservation ratios of geometric features. Our efficient and fast algorithm uses a 3D mesh model as input and initially detects geometric features by using a Laplacian-based shape descriptor (L-descriptor). The algorithm further performs an optimized clustering approach that combines a Laplacian operator with K-means clustering algorithm to perform vertex classification. Moreover, we introduce a Laplacian weighted cost function based on L-descriptor to perform feature weighting and error statistics comparison, which are further used to change the deletion order of the model elements and preserve the saliency features. Our algorithm can provide different preservation ratios of geometric features and may be extended to handle arbitrary mesh topologies. Our experiments on a variety of 3D surface meshes demonstrate the advantages of our algorithm in terms of improving accuracy and applicability, and preserving saliency geometric features.

Higher-Order Mesh Generation Using Linear Meshes [EM Programmer's Notebook

A simple method for generating highorder, 3D surface meshes is presented. The higher-order meshes are suitable for investigating higherorder convergence in electromagnetic analysis codes. The mesh-generation algorithm uses two linear meshes: a coarse mesh and a refinement of the coarse mesh. The method is applied to both quadrilateral and triangle surface meshes. Mesh generation is validated by computing the discretization error for various meshes. Finally, integral equation error convergence of plane wave scattering from a conducting sphere is investigated in terms of mesh order and basis order. A reference implementation of the algorithms is made available.

Mean value coordinates for quad cages in 3D

Space coordinates offer an elegant, scalable and versatile framework to propagate (multi-)scalar functions from the boundary vertices of a 3-manifold, often called a cage , within its volume. These generalizations of the barycentric coordinate system have progressively expanded the range of eligible cages to triangle and planar polygon surface meshes with arbitrary topology, concave regions and a spatially-varying sampling ratio, while preserving a smooth diffusion of the prescribed on-surface functions. In spite of their potential for major computer graphics applications such as freeform deformation or volume texturing, current space coordinate systems have only found a moderate impact in applications. This follows from the constraint of having only triangles in the cage most of the time, while many application scenarios favor arbitrary (non-planar) quad meshes for their ability to align the surface structure with features and to naturally cope with anisotropic sampling. In order to use space coordinates with arbitrary quad cages currently, one must triangulate them, which results in large propagation distortion. Instead, we propose a generalization of a popular coordinate system - Mean Value Coordinates - to quad and tri-quad cages, bridging the gap between high-quality coarse meshing and volume diffusion through space coordinates. Our method can process non-planar quads, comes with a closed-form solution free from global optimization and reproduces the expected behavior of Mean Value Coordinates, namely smoothness within the cage volume and continuity everywhere. As a result, we show how these coordinates compare favorably to classical space coordinates on triangulated quad cages, in particular for freeform deformation.

A transfer-operator-based relation between Laplace eigenfunctions and zeros of Selberg zeta functions

Over the last few years Pohl (partly jointly with coauthors) has developed dual ‘slow/fast’ transfer operator approaches to automorphic functions, resonances, and Selberg zeta functions for a certain class of hyperbolic surfaces$\unicode[STIX]{x1D6E4}\backslash \mathbb{H}$with cusps and all finite-dimensional unitary representations$\unicode[STIX]{x1D712}$of$\unicode[STIX]{x1D6E4}$. The eigenfunctions with eigenvalue 1 of the fast transfer operators determine the zeros of the Selberg zeta function for$(\unicode[STIX]{x1D6E4},\unicode[STIX]{x1D712})$. Further, if$\unicode[STIX]{x1D6E4}$is cofinite and$\unicode[STIX]{x1D712}$is the trivial one-dimensional representation then highly regular eigenfunctions with eigenvalue 1 of the slow transfer operators characterize Maass cusp forms for$\unicode[STIX]{x1D6E4}$. Conjecturally, this characterization extends to more general automorphic functions as well as to residues at resonances. In this article we study, without relying on Selberg theory, the relation between the eigenspaces of these two types of transfer operators for any Hecke triangle surface$\unicode[STIX]{x1D6E4}\backslash \mathbb{H}$of finite or infinite area and any finite-dimensional unitary representation$\unicode[STIX]{x1D712}$of the Hecke triangle group $\unicode[STIX]{x1D6E4}$. In particular, we provide explicit isomorphisms between relevant subspaces. This solves a conjecture by Möller and Pohl, characterizes some of the zeros of the Selberg zeta functions independently of the Selberg trace formula, and supports the previously mentioned conjectures.