Controlled Metamorphosis Between Skeleton‐Driven Animated Polyhedral Meshes of Arbitrary Topologies

Enabling animators to smoothly transform between animated meshes of differing topologies is a long‐standing problem in geometric modelling and computer animation. In this paper, we propose a new hybrid approach built upon the advantages of scalar field‐based models (often called implicit surfaces) which can easily change their topology by changing their defining scalar field. Given two meshes, animated by their rigging‐skeletons, we associate each mesh with its own approximating implicit surface. This implicit surface moves synchronously with the mesh. The shape‐metamorphosis process is performed in several steps: first, we collapse the two meshes to their corresponding approximating implicit surfaces, then we transform between the two implicit surfaces and finally we inverse transition from the resulting metamorphosed implicit surface to the target mesh. The examples presented in this paper demonstrating the results of the proposed technique were implemented using an in‐house plug‐in for Maya?.     

A Semi‐Lagrangian Closest Point Method for Deforming Surfaces

We present an Eulerian method for the real‐time simulation of intrinsic fluid dynamics effects on deforming surfaces. Our method is based on a novel semi‐Lagrangian closest point method for the solution of partial differential equations on animated triangle meshes. We describe this method and demonstrate its use to compute and visualize flow and wave propagation along such meshes at high resolution and speed. Underlying our technique is the efficient conversion of an animated triangle mesh into a time‐dependent implicit representation based on closest surface points. The proposed technique is unconditionally stable with respect to the surface deformation and, in contrast to comparable Lagrangian techniques, its precision does not depend on the level of detail of the surface triangulation.     

Feature Preserving Mesh Generation from 3D Point Clouds

We address the problem of generating quality surface triangle meshes from 3D point clouds sampled on piecewise smooth surfaces. Using a feature detection process based on the covariance matrices of Voronoi cells, we first extract from the point cloud a set of sharp features. Our algorithm also runs on the input point cloud a reconstruction process, such as Poisson reconstruction, providing an implicit surface. A feature preserving variant of a Delaunay refinement process is then used to generate a mesh approximating the implicit surface and containing a faithful representation of the extracted sharp edges. Such a mesh provides an enhanced trade‐off between accuracy and mesh complexity. The whole process is robust to noise and made versatile through a small set of parameters which govern the mesh sizing, approximation error and shape of the elements. We demonstrate the effectiveness of our method on a variety of models including laser scanned datasets ranging from indoor to outdoor scenes.     

High Performance GPU‐based Proximity Queries using Distance Fields

Proximity queries such as closest point computation and collision detection have many applications in computer graphics, including computer animation, physics‐based modelling, augmented and virtual reality. We present efficient algorithms for proximity queries between a closed rigid object and an arbitrary, possibly deformable, polygonal mesh. Using graphics hardware to densely sample the distance field of the rigid object over the arbitrary mesh, we compute minimal proximity and collision response information on the graphics processing unit (GPU) using blending and depth buffering, as well as parallel reduction techniques, thus minimizing the readback bottleneck. Although limited to image‐space resolution, our algorithm provides high and steady performance when compared with other similar algorithms. Proximity queries between arbitrary meshes with hundreds of thousands of triangles and detailed distance fields of rigid objects are computed in a few milliseconds at high‐sampling resolution, even in situations with large overlap.     

A Colour Interpolation Scheme for Topologically Unrestricted Gradient Meshes

Gradient meshes are a 2D vector graphics primitive where colour is interpolated between mesh vertices. The current implementations of gradient meshes are restricted to rectangular mesh topology. Our new interpolation method relaxes this restriction by supporting arbitrary manifold topology of the input gradient mesh. Our method is based on the Catmull‐Clark subdivision scheme, which is well‐known to support arbitrary mesh topology in 3D. We adapt this scheme to support gradient mesh colour interpolation, adding extensions to handle interpolation of colours of the control points, interpolation only inside the given colour space and emulation of gradient constraints seen in related closed‐form solutions. These extensions make subdivision a viable option for interpolating arbitrary‐topology gradient meshes for 2D vector graphics.     

Embedded Implicit Stand-Ins for Animated Meshes: A Case of Hybrid Modelling

In this paper, we address shape modelling problems, encountered in computer animation and computer games development that are difficult to solve just using polygonal meshes. Our approach is based on a hybrid-modelling concept that combines polygonal meshes with implicit surfaces. A hybrid model consists of an animated polygonal mesh and an approximation of this mesh by a convolution surface stand-in that is embedded within it or is attached to it. The motions of both objects are synchronised using a rigging skeleton. We model the interaction between an animated mesh object and a viscoelastic substance, which is normally represented in an implicit form. Our approach is aimed at achieving verisimilitude rather than physically based simulation. The adhesive behaviour of the viscous object is modelled using geometric blending operations on the corresponding implicit surfaces. Another application of this approach is the creation of metamorphosing implicit surface parts that are attached to an animated mesh. A prototype implementation of the proposed approach and several examples of modelling and animation with near real-time preview times are presented.     

Animation‐Aware Quadrangulation

Geometric meshes that model animated characters must be designed while taking into account the deformations that the shape will undergo during animation. We analyze an input sequence of meshes with point‐to‐point correspondence, and we automatically produce a quadrangular mesh that fits well the input animation. We first analyze the local deformation that the surface undergoes at each point, and we initialize a cross field that remains as aligned as possible to the principal directions of deformation throughout the sequence. We then smooth this cross field based on an energy that uses a weighted combination of the initial field and the local amount of stretch. Finally, we compute a field‐aligned quadrangulation with an off‐the‐shelf method. Our technique is fast and very simple to implement, and it significantly improves the quality of the output quad mesh and its suitability for character animation, compared to creating the quad mesh based on a single pose. We present experimental results and comparisons with a state‐of‐the‐art quadrangulation method, on both sequences from 3D scanning and synthetic sequences obtained by a rough animation of a triangulated model.     

3D点云形状特征的二维主流形描述

首先,对空间分布不均匀且无序的三维点云构造其二维主流形,并以与球面同胚的封闭曲面网格形式给出其二维主流形的二次优化逼近,以主流形网格有序均匀的结点分布表示三维点云空间分布无序且不均匀的形状特征,降低了三维形状描述的难度;然后,以基本几何变换作为快速粗对齐、以迭代最近法向点(ICNP)方法作为精准对齐,确定两个主曲面网格之间最佳刚性变换,ICNP方法在寻找最近点时考虑法向夹角,利用了更多的几何信息,实现快速精准的刚性对齐,兼顾计算精度和速度;最后,以对齐误差作为两个3D点云之间形状差异测度.实验结果表明:所提出的基于主流形二次曲面网格优化逼近的三维点云模型形状描述方法对三维点云的分辨率和噪声等干扰因素具有较高的健壮性,可以用于三维检索的形状描述.     

Example‐Based Retargeting of Human Motion to Arbitrary Mesh Models

We present a novel method for retargeting human motion to arbitrary 3D mesh models with as little user interaction as possible. Traditional motion‐retargeting systems try to preserve the original motion, while satisfying several motion constraints. Our method uses a few pose‐to‐pose examples provided by the user to extract the desired semantics behind the retargeting process while not limiting the transfer to being only literal. Thus, mesh models with different structures and/or motion semantics from humanoid skeletons become possible targets. Also considering the fact that most publicly available mesh models lack additional structure (e.g. skeleton), our method dispenses with the need for such a structure by means of a built‐in surface‐based deformation system. As deformation for animation purposes may require non‐rigid behaviour, we augment existing rigid deformation approaches to provide volume‐preserving and squash‐and‐stretch deformations. We demonstrate our approach on well‐known mesh models along with several publicly available motion‐capture sequences.     

任意三角形网格的基于二元四次箱样条分片C1曲面

提出一种以任意三角剖分为控制网格的二元箱样条曲面算法.二元三方向剖分是方向最少的三角剖分,建立在其上的二元三向四次箱样条在CAGD等领域有着广泛的应用.其规范的箱样条曲面计算仅适用于控制点的价数均为6的网格.从规范的算法出发,提出了一种任意价数控制网格的曲面计算算法,并对算法的连续性等进行了详细的分析.生成的曲面具有保凸性,且是分片C¹连续的.该算法可进行3D离散点全局或局部插值,并可应用于3D曲面重构等领域.     

Fracturing rigid materials

We propose a novel approach to fracturing (and denting) brittle materials. To avoid the computational burden imposed by the stringent time step restrictions of explicit methods or with solving nonlinear systems of equations for implicit methods, we treat the material as a fully rigid body in the limit of infinite stiffness. In addition to a triangulated surface mesh and level set volume for collisions, each rigid body is outfitted with a tetrahedral mesh upon which finite element analysis can be carried out to provide a stress map for fracture criteria. We demonstrate that the commonly used stress criteria can lead to arbitrary fracture (especially for stiff materials) and instead propose the notion of a time averaged stress directly into the FEM analysis. When objects fracture, the virtual node algorithm provides new triangle and tetrahedral meshes in a straightforward and robust fashion. Although each new rigid body can be rasterized to obtain a new level set, small shards can be difficult to accurately resolve. Therefore, we propose a novel collision handling technique for treating both rigid bodies and rigid body thin shells represented by only a triangle mesh     

Principal Geodesic Analysis in the Space of Discrete Shells

Important sources of shape variability, such as articulated motion of body models or soft tissue dynamics, are highly nonlinear and are usually superposed on top of rigid body motion which must be factored out. We propose a novel, nonlinear, rigid body motion invariant Principal Geodesic Analysis (PGA) that allows us to analyse this variability, compress large variations based on statistical shape analysis and fit a model to measurements. For given input shape data sets we show how to compute a low dimensional approximating submanifold on the space of discrete shells, making our approach a hybrid between a physical and statistical model. General discrete shells can be projected onto the submanifold and sparsely represented by a small set of coefficients. We demonstrate two specific applications: model‐constrained mesh editing and reconstruction of a dense animated mesh from sparse motion capture markers using the statistical knowledge as a prior.     

Evolution of T-spline level sets for meshing non-uniformly sampled and incomplete data

Given a large set of unorganized point sample data, we propose a new framework for computing a triangular mesh representing an approximating piecewise smooth surface. The data may be non-uniformly distributed, noisy, and may contain holes. This framework is based on the combination of two types of surface representations, triangular meshes and T-spline level sets, which are implicit surfaces defined by refinable spline functions allowing T-junctions. Our method contains three main steps. Firstly, we construct an implicit representation of a smooth (C ² in our case) surface, by using an evolution process of T-spline level sets, such that the implicit surface captures the topology and outline of the object to be reconstructed. The initial mesh with high quality is obtained through the marching triangulation of the implicit surface. Secondly, we project each data point to the initial mesh, and get a scalar displacement field. Detailed features will be captured by the displaced mesh. Finally, we present an additional evolution process, which combines data-driven velocities and feature-preserving bilateral filters, in order to reproduce sharp features. We also show that various shape constraints, such as distance field constraints, range constraints and volume constraints can be naturally added to our framework, which is helpful to obtain a desired reconstruction result, especially when the given data contains noise and inaccuracies.     

Optimized triangle mesh reconstruction from unstructured points

A variety of approaches have been proposed for polygon mesh reconstruction from a set of unstructured sample points. Suffering from severe aliases at sharp features and having a large number of unnecessary faces, most resulting meshes need to be optimized using input sample points in a postprocess. In this paper, we propose a fast algorithm to reconstruct high-quality meshes from sample data. The core of our proposed algorithm is a new mesh evaluation criterion which takes full advantage of the relation between the sample points and the reconstructed mesh. Based on our proposed evaluation criterion, we develop necessary operations to efficiently incorporate the functions of data preprocessing, isosurface polygonization, mesh optimization and mesh simplification into one simple algorithm, which can generate high-quality meshes from unstructured point clouds with time and space efficiency. Published online: 28 January 2003 Correspondence to: Y.-J. Liu     

An adaptive learning approach for 3-D surface reconstruction from point clouds.

In this paper, we propose a multiresolution approach for surface reconstruction from clouds of unorganized points representing an object surface in 3-D space. The proposed method uses a set of mesh operators and simple rules for selective mesh refinement, with a strategy based on Kohonen's self-organizing map (SOM). Basically, a self-adaptive scheme is used for iteratively moving vertices of an initial simple mesh in the direction of the set of points, ideally the object boundary. Successive refinement and motion of vertices are applied leading to a more detailed surface, in a multiresolution, iterative scheme. Reconstruction was experimented on with several point sets, including different shapes and sizes. Results show generated meshes very close to object final shapes. We include measures of performance and discuss robustness.     

Diffusion equations over arbitrary triangulated surfaces for filtering and texture applications

In computer graphics, triangular mesh representations of surfaces have become very popular. Compared with parametric and implicit forms of surfaces, triangular mesh surfaces have many advantages, such as easy to render, convenient to store and the ability to model geometric objects with arbitrary topology. In this paper, we are interested in data processing over triangular mesh surfaces through PDEs (partial differential equations). We study several diffusion equations over triangular mesh surfaces, and present corresponding numerical schemes to solve them. Our methods work for triangular mesh surfaces with arbitrary geometry (the angles of each triangle are arbitrary) and topology (open meshes or closed meshes of arbitrary genus). Besides the flexibility, our methods are efficient due to the implicit/semi-implicit time discretization. We finally apply our methods to several filtering and texture applications such as image processing, texture generating and regularization of harmonic maps over triangular mesh surfaces. The results demonstrate the flexibility and effectiveness of our methods.     

Efficient tetrahedral mesh generation based on sampling optimization

We present a heuristic approach to tetrahedral mesh generation for implicit closed surfaces. It consists of a surface sampling step and a volume sampling step that both work in a unified optimization framework. First, high‐quality isotropic samplings as well as a triangular mesh on the surface are generated. Then uniform volume samplings are determined by optimizing the point distribution inside the closed surface domain. Finally, the tetrahedral mesh is easily obtained by constrained Delaunay triangulation. Experimental results show that the new method can generate ideal tetrahedral meshes for closed implicit surfaces efficiently that are Delaunay based. Our method has the advantage of high efficiency and nice performance at surface boundaries. Copyright © 2015 John Wiley & Sons, Ltd.     

Perceptual Metrics for Static and Dynamic Triangle Meshes

Almost all mesh processing procedures cause some more or less visible changes in the appearance of objects represented by polygonal meshes. In many cases, such as mesh watermarking, simplification or lossy compression, the objective is to make the change in appearance negligible, or as small as possible, given some other constraints. Measuring the amount of distortion requires taking into account the final purpose of the data. In many applications, the final consumer of the data is a human observer, and therefore the perceptibility of the introduced appearance change by a human observer should be the criterion that is taken into account when designing and configuring the processing algorithms. In this review, we discuss the existing comparison metrics for static and dynamic (animated) triangle meshes. We describe the concepts used in perception‐oriented metrics used for 2D image comparison, and we show how these concepts are employed in existing 3D mesh metrics. We describe the character of subjective data used for evaluation of mesh metrics and provide comparison results identifying the advantages and drawbacks of each method. Finally, we also discuss employing the perception‐correlated metrics in perception‐oriented mesh processing algorithms.