Triangle Surface Research Articles

A semi-automatic method for block-structured hexahedral meshing of aortic dissections.

The article presents a semi-automatic approach to generating structured hexahedral meshes of patient-specific aortas ailed by aortic dissection. The condition manifests itself as a formation of two blood flow channels in the aorta, as a result of a tear in the inner layers of the aortic wall. Subsequently, the morphology of the aorta is greatly impacted, making the task of domain discretization highly challenging. The meshing algorithm presented herein is automatic for the individual lumina, whereas the tears require user interaction. Starting from an input (triangle) surface mesh, we construct an implicit surface representation as well as a topological skeleton, which provides a basis for the generation of a block-structure. Thereafter, the mesh generation is performed via transfinite maps. The meshes are structured and fully hexahedral, exhibit good quality and reliably match the original surface. As they are generated with computational fluid dynamics in mind, a fluid flow simulation is performed to verify their usefulness. Moreover, since the approach is based on valid block-structures, the meshes can be made very coarse (around 1000 elements for an entire aortic dissection domain), and thus promote using solvers based on the geometric multigrid method, which is typically reliant on the presence of a hierarchy of coarser meshes.

Lattice Boltzmann simulation of droplets accelerate shedding on an inverted triangular surface with wettability gradient

The droplet combining and shedding on a gradient-wetting inverted triangle surface is investigated using the lattice Boltzmann method based on the Shan-Chen pseudo-potential model. The impacts of the tip angle, wetting gradient, and Bond number are investigated. The study shows that the smaller the tip angle, the better for the droplets to merge and shed. The droplet combining and shedding process can be sped up by the triangular surface’s wetting gradient. As the wetting gradient increases, the droplet combining and shedding becomes easier. Applying a wetting gradient to speed drainage is better when the original surface is more hydrophilic. The combination and shedding of droplets on the wet surface are significantly influenced by the Bond number as well.

An integrated DEM code for tracing the entire regolith mass movement on asteroids

ABSTRACT This paper presents a general strategy for tracking the scale-span movement process of asteroid regolith materials. It achieves the tracking of the mass movement on the asteroid at a realistic scale, under conditions of high-resolution asteroid surface topography (submeter level) and actual regolith particle sizes. To overcome the memory exponential expansion caused by the enlarged computational domain, we improved the conventional cell-linked list method so that it can be applied to arbitrarily large computational domains around asteroids. An efficient contact detection algorithm for particles and polyhedral shape models of asteroids is presented, which avoids traversing all surface triangles and thus allows us to model high-resolution surface topography. A parallel algorithm based on Compute Unified Device Architecture for the gravitational field of the asteroid is presented. Leveraging heterogeneous computing features, further architectural optimization overlaps computations of the long-range and short-range interactions, resulting in an approaching doubling of computational efficiency compared to the code lacking architectural optimizations. Using the above strategy, a specific high-fidelity discrete element method code that integrates key mechanical models, including the irregular gravitational field, the interparticle and particle-surface interactions, and the coupled dynamics between the particles and the asteroid, is developed to track the asteroid regolith mass movement. As tests, we simulated the landslide of a sand pile on the asteroid’s surface during spin-up. The simulation results demonstrate that the code can track the mass movement of the regolith particles on the surface of the asteroid from local landslides to mass leakage with good accuracy.

RupMC: a ray-unit parallel marching cubes algorithm on CPU/GPU heterogeneous architectures

ABSTRACT The marching cubes (MC) algorithm is widely used for extracting isosurfaces from volume data and 3D visualizations because of its effectiveness and robustness but require extensive memory and computing time for large-scale applications. Additionally, MC isosurfaces lack topologic information, making them difficult to use in some geologic applications. To overcome these limitations, this study proposes an enhanced MC using CPU/GPU heterogeneous architecture called the ray-unit parallel MC (rupMC) algorithm. First, ray units form the basic voxel to determine how the surface intersects to reduce repeated computations and enhance efficiency. Then, rupMC uses multiple computing processes and threads on a CPU/GPU heterogeneous architecture to process points concurrently. Finally, the unique surface intersection indices are preserved to compose the surface triangles, and the topological surface information is directly embedded in the triangle compositions. Experiments on five stratum datasets of varying sizes demonstrated that, rupMC achieved approximately dozens of times faster than other serial MC and 4 times faster than a parallel DMC. rupMC demonstrated high scalability and adaptability to various CPUs/GPUs and datasets of various sizes. rupMC has remarkable capabilities for efficiently and feasibly extracting precise surface intersections and triangles, making it well-suited for large-scale and high-density applications.

The Effects of Temperature Variation with Surface Triangle Grating on Silicon Thin-Film Solar Cell Array Efficiency

AbstractThis paper examines the effect of temperature variation on the surface triangular grating of the surface plasmon polariton (SPP) on the effectiveness of the entire array of silicon thin-film solar cells. Thin-film solar cells’ optical and electrical characteristics are examined using the electromagnetic and semiconductor models. The 3D Multiphysics simulator is used to present this study. The MATLAB/SIMULINK model based on mathematical formulas is developed to simulate the entire array of solar cells with thin films. This approach is suggested for quickly simulating the thin-film array. The presented model was applied on thin-film solar cells with and without SPP depending on the complete cell parameters from the COMSOL Multiphysics model. The triangle’s SPPs accomplish a 14.76% efficiency increase of 1.07% over a solar cell without SPPs.

BPM: Blended Piecewise Möbius Maps

AbstractWe propose a novel Möbius interpolator that takes as an input a discrete map between the vertices of two planar triangle meshes, and outputs a continuous map on the input domain. The output map interpolates the discrete map, is continuous between triangles, and has low quasi‐conformal distortion when the input map is discrete conformal. Our map leads to considerably smoother texture transfer compared to the alternatives, even on very coarse triangulations. Furthermore, our approach has a closed‐form expression, is local, applicable to any discrete map, and leads to smooth results even for extreme deformations. Finally, by working with local intrinsic coordinates, our approach is easily generalizable to discrete maps between a surface triangle mesh and a planar mesh, i.e., a planar parameterization. We compare our method with existing approaches, and demonstrate better texture transfer results, and lower quasi‐conformal errors.

A Hermite Surface Triangle Modeling Method Considering High-Precision Fitting of 3D Printing Models

Three-dimensional printing is a layer-by-layer stacking process. It can realize complex models that cannot be manufactured by traditional manufacturing technology. The most common model currently used for 3D printing is the STL model. It uses planar triangles to simplify the CAD model. This approach makes it difficult to fit complex surface shapes with high accuracy. The fitting result usually suffers from loss of local features of the model, poor fitting accuracy, or redundant data due to face piece subdivision, which will cause problems such as poor manufacturing accuracy or difficult data processing. To this end, this paper proposes a method for constructing Hermite surface models considering high-precision fitting of 3D printing models. The mapping relationship between different surface triangles and the same base triangle is established by analyzing the characteristics of Hermite surface triangles in AMF format files and using the radial variation property. By constructing a cubic surface model with general parameters and combining the vertex and tangent vector information, a cubic Hermite curve and surface triangle model are obtained. A sampling mapping point solution method is proposed, which transforms the volume integration problem between models into the summation problem of sampling point height difference. Considering the mean deviation and variance in multiple directions of the sampling points, a method for calculating and evaluating the model fitting error is constructed. Finally, the effectiveness of the proposed method is verified by rabbit and turbine.

Recursive computation of the multipole expansions of layer potential integrals over simplices for efficient fast multipole accelerated boundary elements

In boundary element methods (BEM) in R3, matrix elements and right hand sides are typically computed via analytical or numerical quadrature of the layer potential multiplied by some function over line, triangle and tetrahedral volume elements. When the problem size gets large, the resulting linear systems are often solved iteratively via Krylov subspace methods, with fast multipole methods (FMM) used to accelerate the matrix vector products needed. When FMM acceleration is used, most entries of the matrix never need be computed explicitly - they are only needed in terms of their contribution to the multipole expansion coefficients. We propose a new fast method - Quadrature to Expansion (Q2X) - for the analytical generation of the multipole expansion coefficients produced by the integral expressions for single and double layers on surface triangles; charge distributions over line segments and over tetrahedra in the volume; so that the overall method is well integrated into the FMM, with controlled error. The method is based on the O(1) per moment cost recursive computation of the moments. The method is developed for boundary element methods involving the Laplace Green's function in R3. The derived recursions are first compared against classical quadrature algorithms, and then integrated into FMM accelerated boundary element and vortex element methods. Numerical tests are presented and discussed.

Controlled Release of Felodipine from 3D-Printed Tablets with Constant Surface Area: Influence of Surface Geometry.

In this study, 3D-printed tablets with a constant surface area were designed and fabricated using polylactic acid (PLA) in the outer compartment and polyvinyl alcohol and felodipine (FDP) in the inner compartment. The influences of different surface geometries of the inner compartment, namely, round, hexagon, square, and triangle, on drug release from 3D-printed tablets were also studied. The morphology and porosity of the inner compartment were determined using scanning electron microscopy and synchrotron radiation X-ray tomographic microscopy, respectively. Additionally, drug content and drug release were also evaluated. The results revealed that the round-shaped geometry seemed to have the greatest total surface area of the inner compartment, followed by square-shaped, hexagon-shaped, and triangle-shaped geometries. FDP-loaded 3D-printed tablets with triangle and hexagon surface geometries had the slowest drug release (about 80% within 24 h). In the round-shaped and square-shaped 3D-printed tablets, complete drug release was observed within 12 h. Furthermore, the drug release from triangle-shaped 3D-printed tablets with double the volume of the inner compartment was faster than that of a smaller volume. This was due to the fact that a larger tablet volume increased the surface area contacting the medium, resulting in a faster drug release. The findings indicated that the surface geometry of 3D-printed tablets with a constant surface area affected drug release. This study suggests that 3D printing technology may be used to develop oral solid dosage forms suitable for customized therapeutic treatments.

A vectorized spherical convolutional network for recognizing 3D mesh models with unknown rotation

目的3维目标分类是视觉领域的一个基本问题，3维目标的旋转变化给分类带来极大挑战。同时不规则3维网格模型难以运用传统2维卷积网络提取特征。针对这两个问题，提出一种基于矢量型球面卷积网络的分类方法，用于识别未知旋转的3维网格模型。方法 使用矢量型神经元作为网络的基础神经元，并提出一种新型矢量层间的卷积方式。首先，将3维模型规范化并映射到单位球上，获取球面的信号表示；然后，使用矢量型分类网络和重建网络学习等变的3维模型特征；最后，使用分类网络完成3维模型分类。结果 经过消融实验对比，使用本文提出的球面卷积模块和矢量卷积层，并在训练时加入重建模块。对原本未旋转（no rotation，NR）数据集进行任意旋转（arbitrary rotation，AR），并设定NR/AR，AR/AR，NR/NR共3种训练/测试策略的分类任务，其中NR/AR任务衡量模型识别未知旋转的能力。在刚性数据集ModelNet40上，相比基于球面卷积网络（spherical convolutional neural network，SCNN）的分类方法，在3种任务上分别提高了7.7%，1.8%，3.1%。为验证本文方法在识别非刚性3维网格目标的优越性，在非刚性数据集SHREC15（shape retrieval contest 2015）上，相比SCNN，本文方法在3种任务上分别提高了8.8%，4.5%，5.0%。结论 本文提出一种将矢量型网络运用在3维目标分类的思路，使用光线投射法获得分布在球面空间的特征，便于使用统一的球面卷积算子进行处理；设计一种球面残差模块避免梯度消失；使用矢量型神经元并设计矢量层之间的卷积方式以保证网络的等变性，使得识别任意旋转的3维模型时更加准确。;Objective The 3D meshes are concerned of spatial information-demonstrated surface triangles，which can optimize surface information than other related representations like voxel or point cloud. The 3D shape analysis is still to be resolved in relevant to mesh representation on two aspects：1）the irregular data structure of the mesh model is challenged for feature extraction using traditional 2D convolutional networks，and 2）the 3D rotation transformation is challenged for object recognition as well. The emerging convolutional neural networks（CNNs）have been developing dramatically in the context of 2D vision like classification，segmentation，detection，as well as 3D objects-oriented applications. Current CNNbased 3D mesh classification is developed from two aspects：1）the 3D object is transferred to 2D images and the following 2D-based CNN methods are used，and 2）convolution methods are designed on 3D mesh data. However，it is still challenged to recognize rotated objects due to traditional CNN-equivariant-lacked pooling operation. The lack of rotation equivariance can be improved on the basis of two networks which are vectorized and equivariant networks. The vectorized network，known as capsule network，has shown its potentials in learning spatial transformation on 2D images，but convolutionconstrained method is required to be applied on 3D mesh further. To apply the vectorized neural network to 3D mesh data and preserve rotation equivariance，we develop a vectorized spherical neural network-derived method for 3D mesh classification. Method Our method can be segmented into three categories as mentioned below：First，the 3D mesh model is preprocessed to signals on the sphere. We normalize the 3D mesh into a unit sphere and get the spherical signals on the unit sphere using the ray casting scheme. The obtained spherical signals are nearly equivalent 3D shape representations and can be further processed by spherical convolution methods. The aims of processing 3D mesh to spherical signals are 1）to utilize the spherical signals-defined equivariant spherical convolution operators，and 2）to design vectorized neurons in a coordinated manner. Second，the autoencoder-structured model is used to learn the feature of the spherical signal. The model is composed of two sub-networks：i）a vectorized spherical convolutional neural network（VSCNN）to encode the equivariant feature and classify the 3D object，and ii）a multilayer perceptron decoder to decode the extracted feature back to sphere signal. The VSCNN is based on two kinds of spherical residual convolution block and the vector convolution layer. To train deeper networks and resist overfitting，we develop two spherical convolution modules which are S2 convolution block and SO(3) convolution block，and the primary vectorized neurons are obtained after that. The vector convolution layer is used to learn high-level vectorized features derived from the lower layer. The vector convolutional layer can be used to transfer the primary vectorized neurons to get high-level ones. A deep vectorized network can be constructed through the vector convolutional layer-based stacking. To guarantee the rotation-equivariant spherical vector neurons can be learned well during convolution，we use the SO(3) convolution operator to predict the high-level neurons. The VSCNN and the network-reconstructed are trained simultaneously. Third，the VSCNN-based 3D object classification is demonstrated. For validation，we use VSCNN to clarify the category information of the 3D model only. Result The ModelNet40 and SHREC15 of two 3D datasets are verified for the effectiveness of the proposed method. Our model is trained on the non-rotated（NR） and arbitrarily rotated（AR）training set，and it is tested on the non-rotated and rotated test set as well. The robustness of the model is demonstrated to rotation. For the rigid data set ModelNet40，the accuracy of rotation-unidentified targets can be reached to 85. 2%，surpassing the baseline method by 7. 7%. The comparative analysis shows that our method proposed can surpass most of multi-view and point cloud methods compared to other related 3D data representations. The NR/NR result can show its optimization ability in comparison with the benchmarks. At the same time，to identify non-rigid threedimensional grid targets，we carry out a rotation classification experiment on the non-rigid data set SHREC15，and the accuracy rate can be reached to 90. 4%，surpassing the baseline method by 8. 8%. Conclusion We develop a 3D object classification method for rotated mesh. The robustness to 3D rotation can be optimized in terms of vectorized neurons and the equivariant vector convolution layer. The 3D models-rotated recognition is facilitated excluding rotation augmentation， and it shows the learning ability for vectorized networks-based transformation.

Stable Evaluation of 3D Zernike Moments for Surface Meshes

The 3D Zernike polynomials form an orthonormal basis of the unit ball. The associated 3D Zernike moments have been successfully applied for 3D shape recognition; they are popular in structural biology for comparing protein structures and properties. Many algorithms have been proposed for computing those moments, starting from a voxel-based representation or from a surface based geometric mesh of the shape. As the order of the 3D Zernike moments increases, however, those algorithms suffer from decrease in computational efficiency and more importantly from numerical accuracy. In this paper, new algorithms are proposed to compute the 3D Zernike moments of a homogeneous shape defined by an unstructured triangulation of its surface that remove those numerical inaccuracies. These algorithms rely on the analytical integration of the moments on tetrahedra defined by the surface triangles and a central point and on a set of novel recurrent relationships between the corresponding integrals. The mathematical basis and implementation details of the algorithms are presented and their numerical stability is evaluated.

Reticular chemistry for the rational design of mechanically robust mesoporous merged-net metal-organic frameworks

Reticular chemistry for the rational design of mechanically robust mesoporous merged-net metal-organic frameworks

Morphometrics of Xenopus laevis Kept as Laboratory Animals.

Morphometric data that provide information on body conditions can be used to monitor the health and well-being of animals. In laboratory animals, they can help to evaluate the stress due to experiments or treatments, following the 3R principles. The aim of the present study was to obtain morphometric data of male and female African clawed frogs, Xenopus laevis, as the bases for body condition evaluations. Adult frogs (n = 198) were weighed and standardized photographs were taken. The photographs were used to determine several measurements (length, cranial width, caudal width, thigh width). In addition, a triangle was drawn to outline each frog’s simplified body form, and the triangle surface was calculated. In conclusion, the triangle surface drawn on the dorsal plane of each frog correlated with the body weight of the females. There were significant differences between the body weights and sizes of male and female frogs, with males being smaller (p < 0.001). Based on the morphometric data, females could be assigned to five groups in which an assessment of the animal’s well-being is feasible.

Enhanced strategy for adaptive Cartesian grid generation with arbitrarily complex 3D geometry

This article presents an enhanced strategy for generating Cartesian grids for arbitrary complex three-dimensional (3D) geometry. It addresses the major challenges, including data structures managing surface triangles and Cartesian cells, background Cartesian generation, intersection cell determination, and adaptive mesh refinement. To overcome the problem of inefficiency, we developed a robust method for determining intersecting cells based on the k-dimensional tree data structure combined with the fast 3D-Cartesian box-triangle overlap testing algorithm. Furthermore, the minimum distance query algorithm based on the k-dimensional tree was enhanced to improve the query efficiency by reducing the number of backtrackings. The correctness and efficiency of the proposed strategy were evaluated and verified by 3D tests on different configurations. The results show that in terms of mesh generation, the CPUtime∕cell was nearly 5.33–5.54×10−6 s; in terms of the minimum distance query, the query efficiency of the improved backtracking method improved by up to 870.9 times compared with the traversal method. Meshing experiments of several complicated configurations demonstrated that the proposed algorithms were accurate, robust, and efficient. At last, an example was examined, and the result demonstrates that the mesh generation strategy developed in this study meets the actual flow field calculation requirements.

Cutting Simulation in Unity 3D Using Position Based Dynamics with Various Refinement Levels

Augmented and Virtual Reality-based surgical simulations have become some of the fastest-developing areas, due to the recent technological advances and changes, in surgical education. Cutting simulation is a crucial part of the virtual surgery simulation in which an incision operation is performed. It is a complex process that includes three main tasks: soft body simulation, collision detection and handling, and topological deformation of the soft body. In this paper, considering the content developer’s convenience, the deformable object simulation, using position-based dynamics (PBD), was applied in the Unity 3D environment. The proposed algorithm for fast collision detection and handling between the cutting tool and the deformable object uses a sweep surface. In case of incision, the algorithm updates the mesh topology by deleting intersected triangles, re-triangulation, and refinement. In the refinement part, the boundary edges threshold was used to match the resolution of new triangles to the existing mesh triangles. Additionally, current research is focused on triangle surface meshes, which help to reduce the computational costs of the topology modifications. It was found that the algorithm can successfully handle arbitrary cuts, keeping the framerate within interactive and, in some cases, in the real-time.

Neural dual contouring

We introduce neural dual contouring (NDC), a new data-driven approach to mesh reconstruction based on dual contouring (DC). Like traditional DC, it produces exactly one vertex per grid cell and one quad for each grid edge intersection, a natural and efficient structure for reproducing sharp features. However, rather than computing vertex locations and edge crossings with hand-crafted functions that depend directly on difficult-to-obtain surface gradients, NDC uses a neural network to predict them. As a result, NDC can be trained to produce meshes from signed or unsigned distance fields, binary voxel grids, or point clouds (with or without normals); and it can produce open surfaces in cases where the input represents a sheet or partial surface. During experiments with five prominent datasets, we find that NDC, when trained on one of the datasets, generalizes well to the others. Furthermore, NDC provides better surface reconstruction accuracy, feature preservation, output complexity, triangle quality, and inference time in comparison to previous learned (e.g., neural marching cubes, convolutional occupancy networks) and traditional (e.g., Poisson) methods. Code and data are available at https://github.com/czq142857/NDC.

Alpha wrapping with an offset

Given an input 3D geometry such as a triangle soup or a point set, we address the problem of generating a watertight and orientable surface triangle mesh that strictly encloses the input. The output mesh is obtained by greedily refining and carving a 3D Delaunay triangulation on an offset surface of the input, while carving with empty balls of radius alpha. The proposed algorithm is controlled via two user-defined parameters: alpha and offset. Alpha controls the size of cavities or holes that cannot be traversed during carving, while offset controls the distance between the vertices of the output mesh and the input. Our algorithm is guaranteed to terminate and to yield a valid and strictly enclosing mesh, even for defect-laden inputs. Genericity is achieved using an abstract interface probing the input, enabling any geometry to be used, provided a few basic geometric queries can be answered. We benchmark the algorithm on large public datasets such as Thingi10k, and compare it to state-of-the-art approaches in terms of robustness, approximation, output complexity, speed, and peak memory consumption. Our implementation is available through the CGAL library.

Development of Square and Triangle Surface Area Pocket Books as Learning Media for Junior High Schools

This study was conducted at SMP Negeri 8 Lhokseumawe about the development of rectangular and triangular pocket books against the background of the lack of availability of textbooks in schools, coupled with inadequate learning media that supports students to study independently, thus causing low learning motivation of students. and learning outcomes have not increased. The aims of this study: (1) To determine the validity of the development of rectangular and triangular surface area pocket books as learning media for junior high schools, (2) to determine the feasibility of developing square and triangular surface area pocket books as learning media for junior high schools, (3) to find out responses teachers and students on the development of rectangular and triangular surface area pocket books as learning media for junior high schools. The design of this research is research and development called Research and Development (R D) using the Borg and Gall model modified into 7 stages according to Sugiyono. Data collection techniques using validation sheets and questionnaires. The results obtained from the validation of media experts obtained a percentage of 91.48% and material experts obtained a percentage of 83.52% with a very valid category. The results of the feasibility of pocket books obtained a percentage of 84.69% with a very decent category, and teacher responses to pocket books obtained a percentage of 89.52% in a very good category, and students' responses to pocket books obtained a percentage of 80% in a good category. So it can be concluded that pocket books can be well received at SMP Negeri 8 Lhokseumawe. Recommendations from the research are expected to schools, institutions related to educational practitioners to conduct trials on a broad group so that the level of effectiveness can be known to support learning.

Study on Acoustic Emission Characteristics of Self-Compacting Concrete under Uniaxial Compression Test

To study the relationship between acoustic emission characteristic parameters of self-compacting concrete(SCC) and its destruction evolution, under uniaxial compression, acoustic emission(AE) tests are performed on C30 selfcompacting concrete test blocks that are preserved for 7 days and 28 days, the corresponding relationship among energy, amplitude, ring count and different failure stages of the specimens are analyzed by AE experiment, and the spatial distribution of AE in each stage is described by introducing location map. The test shows that there are two rules for the failure of SCC specimens cured for 7 days and 28 days: (1) The first failure law is divided into four stages according to the percentage of the stress value reaching the limit stress: Initial stage: above 10%, the compaction time of test block cured for 28 days is relatively low; Elastic failure stage: 30%–35%, the cumulative value of each parameter increases linearly, and the cumulative value of the amplitude is the largest; Crack stable propagation stage: 35%–90%, there is a moment that causes local stress concentration in both test blocks; Active stage: above 90%, the cumulative value of the parameter rises sharply, then continues to load the test block instability and damage. (2) The second failure law is divided into five stages according to the percentage of the stress value reaching the limit stress: Initial stage: 15%–20%, the cumulative value of each parameter increases with time; Elastic failure stage: 20%–40%, the cumulative value of the parameter continues to grow, but the growth curve is approximately parallel; Crack stable propagation stage: 40%–60%, all parameters increased sharply and the increase reached the peak of the whole process; A stable state: 60–80%, the emission characteristic parameter will become zero, and the stable state of the 28 days curing test block is lagging; Active stage: above 90%, the number of signals increased sharply, but the energy and amplitude are low, and the later test block is completely fractured. (3) In the process of failure, the test block of SCC will form an inverted triangle or landslide failure surface, and the part above the failure surface is prone to failure, and there is a tendency to leave the test block. (4) Under uniaxial compression, the penetration of SCC cracks is mostly shear penetration.

TriSurfaceImmersion: Computing volume fractions and signed distances from triangulated surfaces immersed in unstructured meshes

We propose a numerical method that enables the calculation of volume fractions from triangulated surfaces immersed in unstructured meshes. First, the signed distances are calculated geometrically near the triangulated surface. For this purpose, the computational complexity has been reduced by using an octree space subdivision. Second, an approximate solution of the Laplace equation is used to propagate the inside/outside information from the surface into the solution domain. Finally, volume fractions are computed from the signed distances in the vicinity of the surface. The volume fraction calculation utilizes either geometrical intersections or a polynomial approximation based on signed distances. An adaptive tetrahedral decomposition of polyhedral cells ensures a high absolute accuracy. The proposed method extends the admissible shape of the fluid interface (surface) to triangulated surfaces that can be open or closed, disjoint, and model objects of technical geometrical complexity.Current results demonstrate the effectiveness of the proposed algorithm for two-phase flow simulations of wetting phenomena, but the algorithm has broad applicability. For example, the calculation of volume fractions is crucial for achieving numerically stable simulations of surface tension-driven two-phase flows with the unstructured Volume-of-Fluid method. The method is applicable as a discrete phase-indicator model for the unstructured hybrid Level Set/Front Tracking method.The implementation is available on GitLab [27]. Program summaryProgram Title: argo/triSurfaceImmersionCPC Library link to program files:https://doi.org/10.17632/7g72xrcgjp.1Developer's repository link:https://gitlab.com/leia-methods/argoLicensing provisions: GPLv3Programming language: C++Nature of problem: Computing volume fractions and signed distances from triangulated surfaces immersed in unstructured meshes.Solution method: First, the algorithm computes minimal signed distances between mesh points (cell centers and cell corner-points) and the triangulated surface, in the close vicinity of the surface. The sign is computed with respect to the surface normal orientation. Afterwards, the sign is propagated throughout the unstructured volume mesh by an approximate solution of a diffusion equation. The bulk cells' volume fractions are set, and interface cells are identified based on the signed distances. Volume fractions in cells intersected by the triangulated surface mesh are either computed by geometric intersections between surface triangles and a cell or by an approximation of the volume fraction approximation from signed distances, coupled with tetrahedral cell decomposition and refinement.Additional comments including restrictions and unusual features: The volume mesh can consist of cells of arbitrary shape. The surface mesh normal vectors need to be oriented consistently.