A parametric maize leaf model quantifying morphology and geometry via 3D triangle mesh

The problem of Constructive Solid Geometry (CSG) tree reconstruction from 3D point clouds or 3D triangle meshes is hard to solve. At first, the input data set (point cloud, triangle soup or triangle mesh) has to be segmented and geometric primitives (spheres, cylinders, ...) have to be fitted to each subset. Then, the size- and shape optimal CSG tree has to be extracted. We propose a pipeline for CSG reconstruction consisting of multiple stages: A primitive extraction step, which uses deep learning for primitive detection, a clustered variant of RANSAC for parameter fitting, and a Genetic Algorithm (GA) for convex polytope generation. It directly transforms 3D point clouds or triangle meshes into solid primitives. The filtered primitive set is then used as input for a GA-based CSG extraction stage. We evaluate two different CSG extraction methodologies and furthermore compare our pipeline to current state-of-the-art methods.Keywords3D computer visionCSG tree recoveryDeep learningEvolutionary algorithmsFittingRANSACSegmentation

Efficient algorithms for compressing three-dimensional (3D) triangle meshes have been widely developed in recent years, but most of them are designed to deal with manifold meshes. A progressive geometry-driven 3D triangle meshes algorithm is proposed in this work which can be easily extended to non-manifold mesh compression and polygon mesh compression. Different from connectivity-driven algorithms; our method starts with the geometry; it encodes the geometry data into a symbol sequence consisting of only three kinds of symbols. Edge collapse and vertex unification operator are used to encode the connectivity, and the symbol sequences can be further encoded by arithmetic coding.

Execution of automatically generated programs for accurate robotic machining requires the generated trajectories to be not only accurate with respect to the work piece, but also that the trajectories are continuous differentiable (C1) while avoiding unnecessary large curvatures leading to large accelerations that could compromise machining quality or speed. A widely used work piece representation is 3D triangle meshes as they can be easily generated in any CAD representations and from surface scans, and they are also very suitable for robotics applications. However, they lack the C1 property across the triangle edges. In this paper, a new method for generating C1 surfaces based on 3D triangle meshes is presented. It will be shown by an example that the method is as good as existing methods with respect to the accuracy of the generated surface, and that the problem with large curvatures is much smaller than for existing methods. Moreover, the difficult input specification of derivatives at the vertices is avoided with this method.

In computer graphics, various processing operations are applied to 3D triangle meshes and these processes often involve distortions, which affect the visual quality of surface geometry. In this context, perceptual quality assessment of 3D triangle meshes has become a crucial issue. In this paper, we propose a new objective quality metric for assessing the visual difference between a reference mesh and a corresponding distorted mesh. Our analysis indicates that the overall quality of a distorted mesh is sensitive to the distortion distribution. The proposed metric is based on a spatial pooling strategy and statistical descriptors of the distortion distribution. We generate a perceptual distortion map for vertices in the reference mesh while taking into account the visual masking effect of the human visual system. The proposed metric extracts statistical descriptors from the distortion map as the feature vector to represent the overall mesh quality. With the feature vector as input, we adopt a support vector regression model to predict the mesh quality score.We validate the performance of our method with three publicly available databases, and the comparison with state-of-the-art metrics demonstrates the superiority of our method. Experimental results show that our proposed method achieves a high correlation between objective assessment and subjective scores.

Triangle meshes are a crucial and powerful data type for three-dimensional (3D) shapes, extensively studied in the fields of computer vision and computer graphics. In this paper, we delve into the challenge of analyzing deforming 3D triangle meshes using deep neural networks. While existing methods extend graph-based deep learning to 3D triangle meshes using graph convolution, the lack of effective graph convolutional structures and pooling operations limits the learning capacity of their networks. We propose a variational autoencoder structure that integrates graph convolutional residual blocks with multilayer pooling to explore the latent space of 3D shapes for generation. This framework introduces graph convolutional residual blocks to address the issue of gradient vanishing in deep networks. By employing multilayer pooling and unpooling structures based on triangle mesh simplification, gradually reducing the spatial dimensions of the input, the model can extract more general features. This enables it to handle denser mesh models effectively. Extensive experiments demonstrate that our generalized framework can learn reasonable representations of deformable shape collections with minimal training examples. It produces competitive results across various applications, including shape generation and interpolation, requiring fewer training samples and outperforming state-of-the-art techniques.

Wrap&Zip decompression of the connectivity of triangle meshes compressed with Edgebreaker

Abstract. The 3D triangle mesh is widely used to represent indoor space. One of widely used methods of generating 3D triangle mesh data of indoor space is the construction from the point cloud collected using LIDAR. However, there are many problems in using generated triangle mesh data as a geometric representation of the indoor space. First, the number of triangles forming the triangle mesh is very large, which results in a bottleneck of the performance for storage and management. Second, no consideration on the properties of indoor space has been done by the previous work on mesh simplification for indoor geometric representation. Third, there is no research to construct indoor spatial standard data from triangle mesh data. For resolving these problems, we propose the a method for generating triangular mesh data for indoor geometric representation based in the observations mentioned above. First this method removes unnecessary objects and reduces the number of surfaces from the original fine-grained triangular mesh data using the properties of indoor space. Second, it also produces indoor geometric data in IndoorGML – an OGC standard for indoor spatial data model. In experimental studies, we present a case study of indoor triangle mesh data from real world and compare results with raw data.

This article presents a new computational framework for constructing 3D self-supporting surfaces with isotropic stress. Inspired by the self-supporting property of catenary and the fact that catenoid (the surface of revolution of the catenary curve) is a minimal surface, we discover the relation between 3D self-supporting surfaces and 4D minimal hypersurfaces (which are 3-manifolds). Lifting the problem into 4D allows us to convert gravitational forces into tensions and reformulate the equilibrium problem to total potential energy minimization, which can be solved using a variational method. We prove that the hyper-generatrix of a 4D minimal hyper-surface of revolution is a 3D self-supporting surface, implying that constructing a 3D self-supporting surface is equivalent to volume minimization. We show that the energy functional is simply the surface’s gravitational potential energy, which in turn can be converted into a surface reconstruction problem with mean curvature constraint. Armed with our theoretical findings, we develop an iterative algorithm to construct 3D self-supporting surfaces from triangle meshes. Our method guarantees convergence and can produce near-regular triangle meshes, thanks to a local mesh refinement strategy similar to centroidal Voronoi tessellation. It also allows users to tune the geometry via specifying either the zero potential surface or its desired volume. We also develop a finite element method to verify the equilibrium condition on 3D triangle meshes. The existing thrust network analysis methods discretize both geometry and material by approximating the continuous stress field through uniaxial singular stresses, making them an ideal tool for analysis and design of beam structures. In contrast, our method works on piecewise linear surfaces with continuous material. Moreover, our method does not require the 3D-to-2D projection, therefore it also works for both height and non-height fields.

We introduce an automatic technique for mapping onto a 3D triangle mesh, approximating the shape of a real 3D object, a high resolution texture synthesized from several pictures taken simultaneously by real cameras sur­ rounding the object. We create a texture atlas by first unwrapping the 3D mesh to form a set of 2D patches with no distortion (i.e., the angles and relative sizes of the 3D triangles are preserved in the atlas), and then mixing the color information from the input images, through another three steps: step no. 2 packs the 2D patches so that the bounding canvas of the set is as small as possible; step no. 3 assigns at most one triangle to each canvas pixel; finally, in step no. 4, the color of each pixel is calculated as a smoothly varying weighted average of the corresponding pixels from several input photographs. Our method is especially good for the creation of realistic 3D models without the need of having graphic artists retouch the texture.

3D triangle meshes are extremely used to model discrete surfaces, and almost always represented with two tables: one for geometry and another for connectivity. While the raw size of a triangle mesh is of around 200 bits per vertex, by coding cleverly (and separately) those two distinct kinds of information it is possible to achieve compression ratios of 15:1 or more. Different techniques must be used depending on whether single-rate vs. progressive bitstreams are sought; and, in the latter case, on whether or not hierarchically nested meshes are desirable during reconstruction.

Recently, Basic patterns with excellent body fitness and automation availability are required to be developed in order to automate the patterns of women's clothes. In this study, this reference points, reference lines and segments were fixed onto 3D scan data for the lower body the women in their twenties, they were directly spread out to be 2D flat pattern to facilitate development into the design of slacks adhered closely to the human body such as special and highly-functional clothes, and then slacks 2D pattern was developed for the purpose of seeking scientific approach to the development into basic form slacks and 3d emotional pattern. For conversion of 3D pattern into 2D flat pattern, reference points and segments were created by using Rapid Form of 3D shape analysis software, and triangle mesh of the body surface of the created shape was developed with Auto CAD 2005. The correspondence between slacks and human body was examined by the fixation of major reference lines. Specially, the wearing characteristics of slacks were considered by the fixation of side lines in consideration of posture. As a result of using the way of development to constantly maintain the length while 3D triangle mesh is converted into 2D flat mesh, the shape was shown to be excellently reproduced, and the area of flat pattern was increased compared to the shape of parting plane. Also, the sunk-in curve like the brief line of front crotch length needed a cutting line when it was closely adhered, when mesh was overlapped, and the pattern area was smaller compared to the actual shape.

Many three-dimensional (3D) games possess sophisticated gaming worlds and most of such worlds are constructed via a 3D triangle mesh, including landform, buildings, vegetation and other static objects. Some games focusing on natural outdoor environments, such as many RPG (Role-playing game) and MOBA (Multiplayer Online Battle Arena) games, adopt the height filed to demonstrate a landform, while some games focusing on indoor types, such as many FPS (First Person Shooting), TPS (Third Personal Shooting Game) and ACT (Action Game), build basic indoor environments via a constructive solid geometry (CGD) technology. Since the unprecedented success of Minecraft in 2009, the voxel has become another feasible manner to construct a gaming world.

Digital watermarking can be used as data hiding technique to interleave cover content with auxiliary information before transmitting and storing applications. While image and video watermarking has been widely studied, much less attention has been paid to its application in 3D mesh models. This is principally due to their intrinsic irregular sampling nature. This paper proposes a high-capacity watermarking scheme for the purpose of inserting meta-data into 3D triangle meshes. Our proposal can be applied to meshes with arbitrary topology by using irregular wavelet-based analysis. The watermark is embedded in an appropriate resolution level by quantizing the norms of wavelet coefficient vectors. To ensure robustness to similarity transformation, a robust synchronization (indexing) mechanism is performed on the 3D model after irregular wavelet analysis. Experimental results show that our watermarking framework is robust to common geometric attacks and can provide relatively high data embedding rate whereas keep a relative lower distortion.

We show how to continuously map a texture onto a 3D triangle mesh when some of the mesh vertices are constrained to have given (u,v) coordinates. This problem arises frequently in interactive texture mapping applications and, to the best of our knowledge, a complete and efficient solution is not available. Our techniques always guarantee a solution by introducing extra (Steiner) vertices in the triangulation if needed. We show how to apply our methods to texture mapping in multi-resolution scenarios and image warping and morphing.

This paper proposes a 3D facial mesh detection algorithm based on the geometric saliency of surface. Specifically, the geometric saliency of each vertex on 3D triangle mesh is measured by the combination of Gaussian-weighted curvature and spin-image correlation. Salient vertices with similar properties are clustered into regions on the saliency map, and represented as nodes by the graph model. To detect a 3D facial mesh, initialization and registration steps are applied to match each triangle in the graph model with a reference graph, corresponding to a 3D reference facial mesh. Furthermore, the match error between the graph model of the testing 3D mesh and the reference facial mesh is computed to classify face and non-face meshes. Experimental results demonstrate that the proposed algorithm is effective to detect 3D facial meshes and robust to facial expressions and geometric noises.