Manifold Triangle Mesh Research Articles

3D Printed hair modeling from strand-level hairstyles

Recent advances in the design and fabrication of personalized figurines have made the creation of high-quality figurines possible for ordinary users with the facilities of 3D printing techniques. The hair plays an important role in gaining the realism of the figurines. Existing hair reconstruction methods suffer from the high demand for acquisition equipment, or the result is approximated very coarsely. Instead of creating hairs for figurines by scanning devices, we present a novel surface reconstruction method to generate a 3D printable hair model with geometric features from a strand-level hairstyle, thus converting the exiting digital hair database to a 3D printable database. Given a strand-level hair model, we filter the strands via bundle clustering, retain the main features, and reconstruct hair strands in two stages. First, our algorithm is the key to extracting the hair contour surface according to the structure of strands and calculating the normal for each vertex. Next, a close, manifold triangle mesh with geometric details and an embedded direction field is achieved with the Poisson surface reconstruction. We obtain closed-manifold hairstyles without user interactions, benefiting personalized figurine fabrication. We verify the feasibility of our method by exhibiting a wide range of examples.

Discrete conformal equivalence of polyhedral surfaces

This paper describes a numerical method for surface parameterization, yielding maps that are locally injective and discretely conformal in an exact sense. Unlike previous methods for discrete conformal parameterization, the method is guaranteed to work for any manifold triangle mesh, with no restrictions on triangulatiothat each task can be formulated as a convex problem where the triangulation is allowed to change---we complete the picture by introducing the machinery needed to actually construct a discrete conformal map. In particular, we introduce a new scheme for tracking correspondence between triangulations based on normal coordinates , and a new interpolation procedure based on layout in the light cone. Stress tests involving difficult cone configurations and near-degenerate triangulations indicate that the method is extremely robust in practice, and provides high-quality interpolation even on meshes with poor elements.

Cloth and Skin Deformation with a Triangle Mesh Based Convolutional Neural Network

AbstractWe introduce a triangle mesh based convolutional neural network. The proposed network structure can be used for problems where input and/or output are defined on a manifold triangle mesh with or without boundary. We demonstrate its applications in cloth upsampling, adding back details to Principal Component Analysis (PCA) compressed cloth, regressing clothing deformation from character poses, and regressing hand skin deformation from bones' joint angles. The data used for training in this work are generated from high resolution extended position based dynamics (XPBD) physics simulations with small time steps and high iteration counts and from an offline FEM simulator, but it can come from other sources. The inference time of our prototype implementation, depending on the mesh resolution and the network size, can provide between 4 to 134 times faster than a GPU based simulator. The inference also only needs to be done for meshes currently visible by the camera.

Constructing Intrinsic Delaunay Triangulations from the Dual of Geodesic Voronoi Diagrams

Intrinsic Delaunay triangulation (IDT) naturally generalizes Delaunay triangulation from R 2 to curved surfaces. Due to many favorable properties, the IDT whose vertex set includes all mesh vertices is of particular interest in polygonal mesh processing. To date, the only way for constructing such IDT is the edge-flipping algorithm, which iteratively flips non-Delaunay edges to become locally Delaunay. Although this algorithm is conceptually simple and guarantees to terminate in finite steps, it has no known time complexity and may also produce triangulations containing faces with only two edges. This article develops a new method to obtain proper IDTs on manifold triangle meshes. We first compute a geodesic Voronoi diagram (GVD) by taking all mesh vertices as generators and then find its dual graph. The sufficient condition for the dual graph to be a proper triangulation is that all Voronoi cells satisfy the so-called closed ball property. To guarantee the closed ball property everywhere, a certain sampling criterion is required. For Voronoi cells that violate the closed ball property, we fix them by computing topologically safe regions, in which auxiliary sites can be added without changing the topology of the Voronoi diagram beyond them. Given a mesh with n vertices, we prove that by adding at most O ( n ) auxiliary sites, the computed GVD satisfies the closed ball property, and hence its dual graph is a proper IDT. Our method has a theoretical worst-case time complexity O ( n 2 + tn log n ), where t is the number of obtuse angles in the mesh. Computational results show that it empirically runs in linear time on real-world models.

Automatic construction of watertight manifold triangle meshes from scanned point clouds using matched umbrella facets

ABSTRACTGeneration of watertight manifold triangle meshes from scanned point clouds has emerged as a key task in computer-aided design and inspection. An effective algorithm is presented in this paper, targeting the automatic creation of such triangle meshes from unorganized, scanned data points. The algorithm builds on the initial version of the Umbrella Facet Matching (UFM) algorithm developed by the authors. The mesh generation process starts with Delaunay triangulation of the given point cloud to determine the Delaunay triangle set at each data point. The algorithm then seeks to iteratively generate, in parallel, the local 2-dimensional manifold triangle mesh, resembling the shape of an open umbrella, at each data point from its Delaunay triangle set that fully overlaps with its neighboring umbrellas. Particularly, a four-level inheritance priority queuing mechanism is introduced to enhance the prioritization and ordering of the Delaunay triangles at each data point in order to facilitate the iterativ...

Discrete geodesic graph (DGG) for computing geodesic distances on polyhedral surfaces

We present a new graph-based method, called discrete geodesic graph (DGG), to compute discrete geodesics in a divide-and-conquer manner. Let M be a manifold triangle mesh with n vertices and ε>0 the given accuracy parameter. Assume the vertices are uniformly distributed on the input mesh. We show that the DGG associated to M has O(nε) edges and the shortest path distances on the graph approximate geodesic distances on M with relative error O(ε). Computational results show that the actual error is less than 0.6ε on common models. Taking advantage of DGG's unique features, we develop a DGG-tailored label-correcting algorithm that computes geodesic distances in empirically linear time. With DGG, we can guarantee the computed distances are true distance metrics, which is highly desired in many applications. We observe that DGG significantly outperforms saddle vertex graph (SVG) – another graph based method for discrete geodesics – in terms of graph size, accuracy control and runtime performance.

Progressive Compression of 3D Mesh Geometry Using Sparse Approximations from Redundant Frame Dictionaries

The proliferation of sophisticated techniques for 3D model acquisition and graphic design in recent years is resulting in a rapid increase in the number and complexity of 3D models being produced. At the same time, the need for exchanging 3D models is also rising due to new computing paradigms (e.g., cloud computing) and an increase in collaborative applications and online social networks. This has created a need for efficient compression techniques for 3D models, which are progressive, allow high quality or even lossless reconstruction, and minimize the amount of transferred data. Most of the research on 3D model compression to date has focused on the compression of triangular surface meshes, as this is the most common representation for 3D objects. In particular, progressive compression techniques for 3D mesh models have become very popular in recent years, as they allow a mesh to be reconstructed from coarse to fine levels of detail at the decoder while the bitstream of data is still being received. Currently the best-performing progressive compression techniques seem to be those that use transform coding ideas borrowed from traditional signal and image processing. The fundamental assumption behind such techniques is that the input data can be represented as some sparse linear combination of atoms taken from a representative dictionary of atoms that constitute the new representation domain. Traditionally, these dictionaries have been chosen to be orthogonal bases; however, recent research into alternative signal representations has shown that overcomplete dictionaries, or frames, may be able to produce even sparser representations than orthogonal bases can. In the field of 3D mesh compression, the idea of using redundant representations has only just started to surface. The main challenge here is currently the creation of a good overcomplete dictionary, particularly for mesh models with irregular connectivity that needs to be preserved. In light of this, the main objective of the work in this thesis is to develop a new method for constructing a frame, which can be applied to a manifold triangle mesh directly (i.e., with no requirement for a prior remeshing to a more regular domain) and can be used to obtain sparse approximations of the mesh geometry in a progressive compression scenario. This is the main contribution of this thesis. The frames that we propose are constructed from the unit-norm eigenvectors of a combinatorial mesh Laplacian matrix, plus a large number of redundant linear combinations of these eigenvectors. A sparse synthesis of the input mesh geometry is achieved by selecting atoms from the frame using the Matching Pursuit algorithm. The proposed frames can be applied directly to a manifold mesh with arbitrary topology and connectivity type, as long as the mesh can be represented as a connected graph. Our experimental results for a variety of different mesh models indicate that, for a given reconstruction quality, a sparser approximation of the input mesh geometry can be obtained with the proposed…

Knot Optimization for Biharmonic B-splines on Manifold Triangle Meshes.

Biharmonic B-splines, proposed by Feng and Warren, are an elegant generalization of univariate B-splines to planar and curved domains with fully irregular knot configuration. Despite the theoretic breakthrough, certain technical difficulties are imperative, including the necessity of Voronoi tessellation, the lack of analytical formulation of bases on general manifolds, expensive basis re-computation during knot refinement/removal, being applicable for simple domains only (e.g., such as euclidean planes, spherical and cylindrical domains, and tori). To ameliorate, this paper articulates a new biharmonic B-spline computing paradigm with a simple formulation. We prove that biharmonic B-splines have an equivalent representation, which is solely based on a linear combination of Green's functions of the bi-Laplacian operator. Consequently, without explicitly computing their bases, biharmonic B-splines can bypass the Voronoi partitioning and the discretization of bi-Laplacian, enable the computational utilities on any compact 2-manifold. The new representation also facilitates optimization-driven knot selection for constructing biharmonic B-splines on manifold triangle meshes. We develop algorithms for spline evaluation, data interpolation and hierarchical data decomposition. Our results demonstrate that biharmonic B-splines, as a new type of spline functions with theoretic and application appeal, afford progressive update of fully irregular knots, free of singularity, without the need of explicit parameterization, making it ideal for a host of graphics tasks on manifolds.

EBits: Compact stream of mesh refinements for remote visualization

We focus on applications where a remote client needs to visualize or process a complex, manifold triangle mesh, M, but only in a relatively small, user controlled, Region of Interest (RoI) at a time. The client first downloads a coarse base mesh, pre-computed on the server via a series of simplification passes on M, one per Level of Detail (LoD), each pass identifying an independent set of triangles, collapsing them, and, for each collapse, storing, in a Vertex Expansion Record (VER), the information needed to reverse the collapse. On each client initiated RoI modification request, the server pushes to the client a selected subset of these VERs, which, when decoded and applied to refine the mesh locally, ensure that the portion in the RoI is always at full resolution. The eBits approach proposed here offers state of the art compression ratios (using less than 2.5 bits per new full resolution RoI triangle when the RoI has more than 2000 vertices to transmit the connectivity for the selective refinements) and fine-grain control (allowing the user to adjust the RoI by small increments). The effectiveness of eBits results from several novel ideas and novel variations of previous solutions. We represent the VERs using persistent labels so that they can be applied in different orders within a given LoD. The server maintains a shadow copy of the client’s mesh. To avoid sending IDs identifying which vertices should be expanded, we either transmit, for each new vertex, a compact encoding of its death tag ​–the LoD at which it will be expanded if it lies in the RoI–or transmit vertex masks for the RoI and its neighboring vertices. We also propose a three-step simplification that reduces the overall transmission cost by increasing both the simplification effectiveness and the regularity of the valences in the resulting meshes.

POMAR: Compression of progressive oriented meshes accessible randomly

This paper presents a new random accessible and progressive lossless manifold triangle mesh compression algorithm named POMAR. It allows to extract different parts of the input mesh at different levels of detail during the decompression. A smooth transition without artefacts is generated between adjacent regions decompressed at different levels of detail. Our approach allows selective decompression with low delay and compares favourably to previous random accessible and progressive schemes in terms of compression rates.

LR

We propose LR ( Laced Ring )---a simple data structure for representing the connectivity of manifold triangle meshes. LR provides the option to store on average either 1.08 references per triangle or 26.2 bits per triangle. Its construction, from an input mesh that supports constant-time adjacency queries, has linear space and time complexity, and involves ordering most vertices along a nearly-Hamiltonian cycle. LR is best suited for applications that process meshes with fixed connectivity, as any changes to the connectivity require the data structure to be rebuilt. We provide an implementation of the set of standard random-access, constant-time operators for traversing a mesh, and show that LR often saves both space and traversal time over competing representations.

Shape Analysis Using the Auto Diffusion Function

AbstractScalar functions defined on manifold triangle meshes is a starting point for many geometry processing algorithms such as mesh parametrization, skeletonization, and segmentation. In this paper, we propose the Auto Diffusion Function (ADF) which is a linear combination of the eigenfunctions of the Laplace‐Beltrami operator in a way that has a simple physical interpretation. The ADF of a given 3D object has a number of further desirable properties: Its extrema are generally at the tips of features of a given object, its gradients and level sets follow or encircle features, respectively, it is controlled by a single parameter which can be interpreted as feature scale, and, finally, the ADF is invariant to rigid and isometric deformations.We describe the ADF and its properties in detail and compare it to other choices of scalar functions on manifolds. As an example of an application, we present a pose invariant, hierarchical skeletonization and segmentation algorithm which makes direct use of the ADF.

Biorthogonal Loop-Subdivision Wavelets

We present a biorthogonal wavelet construction for Loop subdivision, based on the lifting scheme. Our wavelet transform uses scaling functions that are recursively defined by Loop subdivision for arbitrary manifold triangle meshes. We orthogonalize our wavelets with respect to local scaling functions. This way, the wavelet analysis computes locally a least squares fit when reducing the resolution and converting geometric detail into sparse wavelet coefficients. The contribution of our approach is local computation of both, wavelet analysis and synthesis in linear time. We provide numerical examples supporting the stability of our scheme.

REPAIRING NON-MANIFOLD TRIANGLE MESHES USING SIMULATED ANNEALING

In the field of reverse engineering one often faces the problem of repairing triangulations with holes, intersecting triangles, Mobius-band-like structures or other artifacts. In this paper we present a novel approach for generating manifold triangle meshes from such incomplete or imperfect triangulations. Even for heavily damaged triangulations, representing closed surfaces with arbitrary genus, our algorithm results in correct manifold triangle meshes. The algorithm is based on a randomized optimization technique from probability calculus called simulated annealing.

SwingWrapper

We focus on the lossy compression of manifold triangle meshes. Our SwingWrapper approach partitions the surface of an original mesh M into simply connected regions, called triangloids . From these, we generate a new mesh M ′ . Each triangle of M ′ is an approximation of a triangloid of M . By construction, the connectivity of M ′ is fairly regular and can be compressed to less than a bit per triangle using EdgeBreaker or one of the other recently developed schemes. The locations of the vertices of M ′ are compactly encoded with our new prediction technique, which uses a single correction parameter per vertex. SwingWrapper strives to reach a user-defined output file size rather than to guarantee a given error bound. For a variety of popular models, a rate of 0.4 bits/triangle yields an L 2 distortion of about 0.01% of the bounding box diagonal. The proposed solution may also be used to encode crude meshes for adaptive transmission or for controlling subdivision surfaces.

ShieldTester: Cell‐to‐Cell Visibility Test for Surface Occluders

Abstract We present a novel Cell‐To‐Cell Visibility (C2CV) algorithm, which given two polyhedra, AandBand a connectedand oriented manifold triangle mesh, S offers a simple, fast and conservative test for detecting when A and B areoccluded from each other by S. Previously disclosed C2CV algorithms either relied on costly occlusion fusion orwere restricted to convex or “apparently convex” occluders, which makes them inappropriate for scenes wherepotential occluders are arbitrary triangulated surfaces, such as the body of a car or a portion of a terrain. Thesimplicity of our C2CV algorithm, named ShieldTester, stems from a new Occlusion Theorem, introduced herewhich permits to establish occlusion by computing the intersection of S with a single ray from a vertex ofAtoa vertex ofB. ShieldTester may be used to establish that pairs of cells in a subdivision of space are hidden fromeach other by a relatively large surface occluder, so that when the viewer is in one cell, the objects in the othercell need not be displayed.Categories and Subject Descriptors (according to ACM CCS): I.3.3 [Computer Graphics]: Computational Geometryand Object Modeling: Occlussion Culling, Visibility Test, Triangle Meshes