Triangle Soups Research Articles

1‐Lipschitz Neural Distance Fields

AbstractNeural implicit surfaces are a promising tool for geometry processing that represent a solid object as the zero level set of a neural network. Usually trained to approximate a signed distance function of the considered object, these methods exhibit great visual fidelity and quality near the surface, yet their properties tend to degrade with distance, making geometrical queries hard to perform without the help of complex range analysis techniques. Based on recent advancements in Lipschitz neural networks, we introduce a new method for approximating the signed distance function of a given object. As our neural function is made 1‐Lipschitz by construction, it cannot overestimate the distance, which guarantees robustness even far from the surface. Moreover, the 1‐Lipschitz constraint allows us to use a different loss function, called the hinge‐Kantorovitch‐Rubinstein loss, which pushes the gradient as close to unit‐norm as possible, thus reducing computation costs in iterative queries. As this loss function only needs a rough estimate of occupancy to be optimized, this means that the true distance function need not to be known. We are therefore able to compute neural implicit representations of even bad quality geometry such as noisy point clouds or triangle soups. We demonstrate that our methods is able to approximate the distance function of any closed or open surfaces or curves in the plane or in space, while still allowing sphere tracing or closest point projections to be performed robustly.

Cascading upper bounds for triangle soup Pompeiu‐Hausdorff distance

AbstractWe propose a new method to accurately approximate the Pompeiu‐Hausdorff distance from a triangle soup A to another triangle soup B up to a given tolerance. Based on lower and upper bound computations, we discard triangles from A that do not contain the maximizer of the distance to B and subdivide the others for further processing. In contrast to previous methods, we use four upper bounds instead of only one, three of which newly proposed by us. Many triangles are discarded using the simpler bounds, while the most difficult cases are dealt with by the other bounds. Exhaustive testing determines the best ordering of the four upper bounds. A collection of experiments shows that our method is faster than all previous accurate methods in the literature.

Coverage Axis++: Efficient Inner Point Selection for 3D Shape Skeletonization

AbstractWe introduce Coverage Axis++, a novel and efficient approach to 3D shape skeletonization. The current state‐of‐the‐art approaches for this task often rely on the watertightness of the input [LWS*15; PWG*19; PWG*19] or suffer from substantial computational costs [DLX*22; CD23], thereby limiting their practicality. To address this challenge, Coverage Axis++ proposes a heuristic algorithm to select skeletal points, offering a high‐accuracy approximation of the Medial Axis Transform (MAT) while significantly mitigating computational intensity for various shape representations. We introduce a simple yet effective strategy that considers shape coverage, uniformity, and centrality to derive skeletal points. The selection procedure enforces consistency with the shape structure while favoring the dominant medial balls, which thus introduces a compact underlying shape representation in terms of MAT. As a result, Coverage Axis++ allows for skeletonization for various shape representations (e.g., water‐tight meshes, triangle soups, point clouds), specification of the number of skeletal points, few hyperparameters, and highly efficient computation with improved reconstruction accuracy. Extensive experiments across a wide range of 3D shapes validate the efficiency and effectiveness of Coverage Axis++. Our codes are available at https://github.com/Frank-ZY-Dou/Coverage_Axis.

Feature‐Preserving Offset Mesh Generation from Topology‐Adapted Octrees

AbstractWe introduce a reliable method to generate offset meshes from input triangle meshes or triangle soups. Our method proceeds in two steps. The first step performs a Dual Contouring method on the offset surface, operating on an adaptive octree that is refined in areas where the offset topology is complex. Our approach substantially reduces memory consumption and runtime compared to isosurfacing methods operating on uniform grids. The second step improves the output Dual Contouring mesh with an offset‐aware remeshing algorithm to reduce the normal deviation between the mesh facets and the exact offset. This remeshing process reconstructs concave sharp features and approximates smooth shapes in convex areas up to a user‐defined precision. We show the effectiveness and versatility of our method by applying it to a wide range of input meshes. We also benchmark our method on the Thingi10k dataset: watertight and topologically 2‐manifold offset meshes are obtained for 100% of the cases.

CREATING CONTEXTUAL VIEW OF CMMS ASSETS USING GEOSPATIAL 2D/3D DATA

Abstract. Computerized maintenance management systems (CMMS) aim to assist administration and maintenance agents in their asset maintenance tasks (e.g., building, network, air conditioning, faucets maintenance). In this context, geospatial data can help to have a better understanding of the assets they represent by providing additional information: spatial, thematic, temporal, or inter-object relationships. Using such information often leads to interoperability issues as different domains describe them with different data models, like Building Information Modeling (using the Industry Foundation Classes format) and Geographic Information System (using the CityGML format). Spatial information, and particularly 2D or 3D geometry, are stored using heterogeneous representations (e.g., triangle soup, boundary representation, sweep volume, composite solids). Visualization and navigation in the information provided by multiple data sources remain a problem, as there is a need to understand the domains, languages, and models used to describe them. Furthermore, there is a need for solutions to integrate geometric data to manage and visualize existing 2D or 3D representations of assets in geospatial data stores while being able to retrieve additional information using semantic data stores. We propose, in this paper, a methodology to integrate heterogeneous geospatial data in the same viewer by transforming geometric data to a standardized format while keeping a link to sources, in order to navigate in the context of an asset by visualizing its spatial and thematic information.

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.

Geodesic Distance Computation via Virtual Source Propagation

AbstractWe present a highly practical, efficient, and versatile approach for computing approximate geodesic distances. The method is designed to operate on triangle meshes and a set of point sources on the surface. We also show extensions for all kinds of geometric input including inconsistent triangle soups and point clouds, as well as other source types, such as lines. The algorithm is based on the propagation of virtual sources and hence easy to implement. We extensively evaluate our method on about 10000 meshes taken from the Thingi10k and the Tet Meshing in the Wild data sets. Our approach clearly outperforms previous approximate methods in terms of runtime efficiency and accuracy. Through careful implementation and cache optimization, we achieve runtimes comparable to other elementary mesh operations (e.g. smoothing, curvature estimation) such that geodesic distances become a “first‐class citizen” in the toolbox of geometric operations. Our method can be parallelized and we observe up to 6× speed‐up on the CPU and 20× on the GPU. We present a number of mesh processing tasks easily implemented on the basis of fast geodesic distances. The source code of our method is provided as a C++ library under the MIT license.

Fast tetrahedral meshing in the wild

We propose a new tetrahedral meshing method, fTetWild, to convert triangle soups into high-quality tetrahedral meshes. Our method builds on the TetWild algorithm, replacing the rational triangle insertion with a new incremental approach to construct and optimize the output mesh, interleaving triangle insertion and mesh optimization. Our approach makes it possible to maintain a valid floating-point tetrahedral mesh at all algorithmic stages, eliminating the need for costly constructions with rational numbers used by TetWild, while maintaining full robustness and similar output quality. This allows us to improve on TetWild in two ways. First, our algorithm is significantly faster, with running time comparable to less robust Delaunay-based tetrahedralization algorithms. Second, our algorithm is guaranteed to produce a valid tetrahedral mesh with floating-point vertex coordinates, while TetWild produces a valid mesh with rational coordinates which is not guaranteed to be valid after floating-point conversion. As a trade-off, our algorithm no longer guarantees that all input triangles are present in the output mesh, but in practice, as confirmed by our tests on the Thingi10k dataset, the algorithm always succeeds in inserting all input triangles.

Fast texture mapping for triangle soups using electrostatic monopole field lines

We present an efficient approach for the parameterization of triangle soups. Our technique tackles the problem by first approximating the triangle soup by a watertight 2-manifold offset mesh proxy. By establishing point correspondences between the triangle soup and the shape proxy by tracing electrostatic field lines in time O(kn) instead of O(kn2), we can transfer properties computed on the surface, such as UV-coordinates even for large input meshes. The technique can process large triangle soups by replacing the computational intensive physical calculations by approximations developed initially for large-scale physical simulations. Thus, it is possible to decrease the time complexity of the initial charge distribution algorithm from O(n3) to O(n). We demonstrate our method on a multitude of challenging triangle soups and focus on the transfer of UV-coordinates during our experiments. An intensive run-time analysis and a comparison of our results to state of the art techniques in standard modeling tools concludes our study.

Fast winding numbers for soups and clouds

Inside-outside determination is a basic building block for higher-level geometry processing operations. Generalized winding numbers provide a robust answer for triangle meshes, regardless of defects such as self-intersections, holes or degeneracies. In this paper, we further generalize the winding number to point clouds. Previous methods for evaluating the winding number are slow for completely disconnected surfaces, such as triangle soups or-in the extreme case- point clouds. We propose a tree-based algorithm to reduce the asymptotic complexity of generalized winding number computation, while closely approximating the exact value. Armed with a fast evaluation, we demonstrate the winding number in a variety of new applications: voxelization, signing distances, generating 3D printer paths, defect-tolerant mesh booleans and point set surfaces.

Tetrahedral meshing in the wild

We propose a novel tetrahedral meshing technique that is unconditionally robust, requires no user interaction, and can directly convert a triangle soup into an analysis-ready volumetric mesh. The approach is based on several core principles: (1) initial mesh construction based on a fully robust, yet efficient, filtered exact computation (2) explicit (automatic or user-defined) tolerancing of the mesh relative to the surface input (3) iterative mesh improvement with guarantees, at every step, of the output validity. The quality of the resulting mesh is a direct function of the target mesh size and allowed tolerance: increasing allowed deviation from the initial mesh and decreasing the target edge length both lead to higher mesh quality. Our approach enables "black-box" analysis, i.e. it allows to automatically solve partial differential equations on geometrical models available in the wild, offering a robustness and reliability comparable to, e.g., image processing algorithms, opening the door to automatic, large scale processing of real-world geometric data.

Drowning in triangle soup: the quest for a better 3-D printing file format

File formats for additive manufacturing are lagging behind the capabilities of 3-D printing technology itself, and no one is doing anything about it.

Automatic portal generation for 3D audio – from triangle soup to a portal system

The purpose of this paper is to investigate an algorithm for generating an automatic portal system. This has been accomplished based on a given set of triangles. The proposed solution was designed to enhance the performance of a sound beam-tracing engine. This solution can also be used for other areas where portal systems are applicable. The provided technical solution emphasizes the beam tracing engine's requirements. Our approach is based on the work of Haumont et al. (with additional improvements), resulting in improved scene segmentation and lower computational complexity. We examined voxelization techniques and their properties, and have adjusted these to fit the requirements of a beam-tracing engine. As a result of our investigation, a new method for finding portal placement has been developed by adjusting the orientation of the found portals to fit the neighboring scene walls. In addition, we replaced Haumont et al.'s prevoxelization step, which is used for erasing geometrical details (for example, thin walls). This was done by smoothing the distance field that, in effect, eliminated incorrectly positioned portals. The results of our work remove the requirement for walls that separate rooms to have a particular thickness. We also describe a method for building a structure that accelerates real-time queries for determining the area where a given point is located. All of the presented techniques allow for the use of larger sized voxels, which increases performance and reduces memory requirements (not only during the preprocessing phase but also during real-time usage). The proposed solutions were tested using scenarios with scenes of varying complexity.

Coupled segmentation and similarity detection for architectural models

Recent shape retrieval and interactive modeling algorithms enable the re-use of existing models in many applications. However, most of those techniques require a pre-labeled model with some semantic information. We introduce a fully automatic approach to simultaneously segment and detect similarities within an existing 3D architectural model. Our framework approaches the segmentation problem as a weighted minimum set cover over an input triangle soup, and maximizes the repetition of similar segments to find a best set of unique component types and instances. The solution for this set-cover formulation starts with a search space reduction to eliminate unlikely combinations of triangles, and continues with a combinatorial optimization within each disjoint subspace that outputs the components and their types. We show the discovered components of a variety of architectural models obtained from public databases. We demonstrate experiments testing the robustness of our algorithm, in terms of threshold sensitivity, vertex displacement, and triangulation variations of the original model. In addition, we compare our components with those of competing approaches and evaluate our results against user-based segmentations. We have processed a database of 50 buildings, with various structures and over 200K polygons per building, with a segmentation time averaging up to 4 minutes.

Partitioned Shadow Volumes

AbstractReal‐time shadows remain a challenging problem in computer graphics. In this context, shadow algorithms generally rely either on shadow mapping or shadow volumes. This paper rediscovers an old class of algorithms that build a binary space partition over the shadow volumes. For almost 20 years, such methods have received little attention as they have been considered lacking of both robustness and efficiency. We show that these issues can be overcome, leading to a simple and robust shadow algorithm. Hence we demonstrate that this kind of approach can reach a high level of performance. Our algorithm uses a new partitioning strategy which avoids any polygon clipping. It relies on a Ternary Object Partitioning tree, a new data structure used to find if an image point is shadowed. Our method works on a triangle soup and its memory footprint is fixed. Our experiments show that it is efficient and robust, including for finely tessellated models.

Occluder Simplification Using Planar Sections

AbstractWe present a method for extreme occluder simplification. We take a triangle soup as input, and produce a small set of polygons with closely matching occlusion properties. In contrast to methods that optimize the original geometry, our algorithm has very few requirements for the input— specifically, the input does not need to be a watertight, two‐manifold mesh. This robustness is achieved by working on a well‐behaved, discretized representation of the input instead of the original, potentially badly structured geometry. We first formulate the algorithm for individual occluders, and further introduce a hierarchy for handling large, complex scenes.

The POP Buffer: Rapid Progressive Clustering by Geometry Quantization

AbstractWithin this paper, we present a novel, straightforward progressive encoding scheme for general triangle soups, which is particularly well‐suited for mobile and Web‐based environments due to its minimal requirements on the client's hardware and software. Our rapid encoding method uses a hierarchy of quantization to effectively reorder the original primitive data into several nested levels of detail. The resulting stateless buffer can progressively be transferred as‐is to the GPU, where clustering is efficiently performed in parallel during rendering. We combine our approach with a crack‐free mesh partitioning scheme to obtain a straightforward method for fast streaming and basic view‐dependent LOD control.

Robust diameter-based thickness estimation of 3D objects

We propose a robust thickness estimation approach for 3D objects based on the Shape Diameter Function (SDF). Our method first applies a modified strategy to estimate the local diameter with increased accuracy. We then compute a scale-dependent robust thickness estimate from a point cloud, constructed using this local diameter estimation and a variant of a robust distance function. The robustness of our method is benchmarked against several operations such as remeshing, geometric noise and artifacts common in triangle soups. The experimental results show a more stable local thickness estimation than the original SDF, and consistent segmentation results on defect-laden inputs.

Fitting polynomial surfaces to triangular meshes with Voronoi squared distance minimization

This paper introduces Voronoi squared distance minimization (VSDM), an algorithm that fits a surface to an input mesh. VSDM minimizes an objective function that corresponds to a Voronoi-based approximation of the overall squared distance function between the surface and the input mesh (SDM). This objective function is a generalization of the one minimized by centroidal Voronoi tessellation, and can be minimized by a quasi-Newton solver. VSDM naturally adapts the orientation of the mesh elements to best approximate the input, without estimating any differential quantities. Therefore, it can be applied to triangle soups or surfaces with degenerate triangles, topological noise and sharp features. Applications of fitting quad meshes and polynomial surfaces to input triangular meshes are demonstrated.

An efficient alias-free shadow algorithm for opaque and transparent objects using per-triangle shadow volumes

This paper presents a novel method for generating pixel-accurate shadows from point light-sources in real-time. The new method is able to quickly cull pixels that are not in shadow and to trivially accept large chunks of pixels thanks mainly to using the whole triangle shadow volume as a primitive, instead of rendering the shadow quads independently as in the classic Shadow-Volume algorithm. Our CUDA implementation outperforms z-fail consistently and surpasses z-pass at high resolutions, although these latter two are hardware accelerated, while inheriting none of the robustness issues associated with these methods. Another, perhaps even more important property of our algorithm, is that it requires no pre-processing or identification of silhouette edges and so robustly and efficiently handles arbitrary triangle soups. In terms of view sample test and set operations performed, we show that our algorithm can be an order of magnitude more efficient than z-pass when rendering a game-scene at multi-sampled HD resolutions. We go on to show that the algorithm can be trivially modified to support textured, semitransparent and colored semi-transparent shadow-casters and that it can be combined with either depth-peeling or stochastic transparency to also support transparent shadow receivers. Compared to recent alias-free shadow-map algorithms, our method has a very small memory footprint, does not suffer from load-balancing issues, and handles omni-directional lights without modification. It is easily incorporated into any deferred rendering pipeline and combines many of the strengths of shadow maps and shadow volumes.