Mesh Editing Research Articles

Gradient domain editing of deforming mesh sequences

Many graphics applications, including computer games and 3D animated films, make heavy use of deforming mesh sequences. In this paper, we generalize gradient domain editing to deforming mesh sequences. Our framework is keyframe based. Given sparse and irregularly distributed constraints at unevenly spaced keyframes, our solution first adjusts the meshes at the keyframes to satisfy these constraints, and then smoothly propagate the constraints and deformations at keyframes to the whole sequence to generate new deforming mesh sequence. To achieve convenient keyframe editing, we have developed an efficient alternating least-squares method. It harnesses the power of subspace deformation and two-pass linear methods to achieve high-quality deformations. We have also developed an effective algorithm to define boundary conditions for all frames using handle trajectory editing. Our deforming mesh editing framework has been successfully applied to a number of editing scenarios with increasing complexity, including footprint editing, path editing, temporal filtering, handle-based deformation mixing, and spacetime morphing.

Gradient domain editing of deforming mesh sequences

Many graphics applications, including computer games and 3D animated films, make heavy use of deforming mesh sequences. In this paper, we generalize gradient domain editing to deforming mesh sequences. Our framework is keyframe based. Given sparse and irregularly distributed constraints at unevenly spaced keyframes, our solution first adjusts the meshes at the keyframes to satisfy these constraints, and then smoothly propagate the constraints and deformations at keyframes to the whole sequence to generate new deforming mesh sequence. To achieve convenient keyframe editing, we have developed an efficient alternating least-squares method. It harnesses the power of subspace deformation and two-pass linear methods to achieve high-quality deformations. We have also developed an effective algorithm to define boundary conditions for all frames using handle trajectory editing. Our deforming mesh editing framework has been successfully applied to a number of editing scenarios with increasing complexity, including footprint editing, path editing, temporal filtering, handle-based deformation mixing, and spacetime morphing.

Effective Derivation of Similarity Transformations for Implicit Laplacian Mesh Editing

Laplacian coordinates as a local shape descriptor have been employed in mesh editing. As they are encoded in the global coordinate system, they need to be transformed locally to reflect the changed local features of the deformed surface. We present a novel implicit Laplacian editing framework which is linear and effectively captures local rotation information during editing. Directly representing rotation with respect to vertex positions in 3D space leads to a nonlinear system. Instead, we first compute the affine transformations implicitly defined for all the Laplacian coordinates by solving a large sparse linear system, and then extract the rotation and uniform scaling information from each solved affine transformation. Unlike existing differential-based mesh editing techniques, our method produces visually pleasing deformation results under large angle rotations or big-scale translations of handles. Additionally, to demonstrate the advantage of our editing framework, we introduce a new intuitive editing technique, called configuration-independent merging, which produces the same merging result independent of the relative position, orientation, scale of input meshes.

Volume and shape preservation via moving frame manipulation

This article introduces a method for mesh editing that is aimed at preserving shape and volume. We present two new developments: The first is a minimization of a functional expressing a geometric distance measure between two isometric surfaces. The second is a local volume analysis linking the volume of an object to its surface curvature. Our method is based upon the moving frames representation of meshes. Applying a rotation field to the moving frames defines an isometry. Given rotational constraints, the mesh is deformed by an optimal isometry defined by minimizing the distance measure between original and deformed meshes. The resulting isometry nicely preserves the surface details, but when large rotations are applied, the volumetric behavior of the model may be unsatisfactory. Using the local volume analysis, we define a scalar field by which we scale the moving frames. Scaled and rotated moving frames restore volumetric properties of the original mesh, while properly maintaining the surface details. Our results show that even extreme deformations can be applied to meshes, with only minimal distortion of surface details and object volume.

Differential Representations for Mesh Processing

Abstract Surface representation and processing is one of the key topics in computer graphics and geometric modeling, since it greatly affects the range of possible applications. In this paper we will present recent advances in geometry processing that are related to the Laplacian processing framework and differential representations. This framework is based on linear operators defined on polygonal meshes, and furnishes a variety of processing applications, such as shape approximation and compact representation, mesh editing, watermarking and morphing. The core of the framework is the definition of differential coordinates and new bases for efficient mesh geometry representation, based on the mesh Laplacian operator.

Easy Mesh Cutting

Abstract We present Easy Mesh Cutting, an intuitive and easy‐to‐use mesh cutout tool. Users can cut meaningful components from meshes by simply drawing freehand sketches on the mesh. Our system provides instant visual feedback to obtain the cutting results based on an improved region growing algorithm using a feature sensitive metric. The cutting boundary can be automatically optimized or easily edited by users. Extensive experimentation shows that our approach produces good cutting results while requiring little skill or effort from the user and provides a good user experience. Based on the easy mesh cutting framework, we introduce two applications including sketch‐based mesh editing and mesh merging for geometry processing. Categories and Subject Descriptors (according to ACM CCS): I.3.5 [Computer Graphics]: Geometric algorithms, languages, and systems

Digital Differential Geometry Processing

The theory and methods of digital geometry processing has been a hot research area in computer graphics, as geometric models serves as the core data for 3D graphics applications. The purpose of this paper is to introduce some recent advances in digital geometry processing, particularly mesh fairing, surface parameterization and mesh editing, that heavily use differential geometry quantities. Some related concepts from differential geometry, such as normal, curvature, gradient, Laplacian and their counterparts on digital geometry are also reviewed for understanding the strength and weakness of various digital geometry processing methods.

A fast multigrid algorithm for mesh deformation

In this paper, we present a multigrid technique for efficiently deforming large surface and volume meshes. We show that a previous least-squares formulation for distortion minimization reduces to a Laplacian system on a general graph structure for which we derive an analytic expression. We then describe an efficient multigrid algorithm for solving the relevant equations. Here we develop novel prolongation and restriction operators used in the multigrid cycles. Combined with a simple but effective graph coarsening strategy, our algorithm can outperform other multigrid solvers and the factorization stage of direct solvers in both time and memory costs for large meshes. It is demonstrated that our solver can trade off accuracy for speed to achieve greater interactivity, which is attractive for manipulating large meshes. Our multigrid solver is particularly well suited for a mesh editing environment which does not permit extensive precomputation. Experimental evidence of these advantages is provided on a number of meshes with a wide range of size. With our mesh deformation solver, we also successfully demonstrate that visually appealing mesh animations can be generated from both motion capture data and a single base mesh even when they are inconsistent.

Adaptive sampling for mesh spectrum editing

A mesh editing framework is presented in this paper, which integrates Free-Form Deformation (FFD) and geometry signal processing. By using simplified model from original mesh, the editing task can be accomplished with a few operations. We take the deformation of the proxy and the position coordinates of the mesh models as geometry signal. Wavelet analysis is employed to separate local detail information gracefully. The crucial innovation of this paper is a new adaptive regular sampling approach for our signal analysis based editing framework. In our approach, an original mesh is resampled and then refined iteratively which reflects optimization of our proposed spectrum preserving energy. As an extension of our spectrum editing scheme, the editing principle is applied to geometry details transferring, which brings satisfying results.

Mean-Value Geometry Encoding

Geometry editing operations commonly use mesh encodings which capture the shape properties of the models. Given modified positions for a set of anchor vertices, the encoding is used to compute the positions for the rest of the mesh vertices, preserving the model shape as much as possible. In this paper, we introduce a new shape preserving and rotation invariant mesh encoding. We use this encoding for a variety of mesh editing applications: deformation, morphing, blending and motion reconstruction from Mocap data. The editing algorithms based on our encoding and decoding mechanism generate natural looking models that preserve the shape properties of the input.

Dual Laplacian editing for meshes

Recently, differential information as local intrinsic feature descriptors has been used for mesh editing. Given certain user input as constraints, a deformed mesh is reconstructed by minimizing the changes in the differential information. Since the differential information is encoded in a global coordinate system, it must somehow be transformed to fit the orientations of details in the deformed surface, otherwise distortion will appear. We observe that visually pleasing deformed meshes should preserve both local parameterization and geometry details. We propose to encode these two types of information in the dual mesh domain due to the simplicity of the neighborhood structure of dual mesh vertices. Both sets of information are nondirectional and nonlinearly dependent on the vertex positions. Thus, we present a novel editing framework that iteratively updates both the primal vertex positions and the dual Laplacian coordinates to progressively reduce distortion in parametrization and geometry. Unlike previous related work, our method can produce visually pleasing deformations with simple user interaction, requiring only the handle positions, not local frames at the handles.

Accurate detection of symmetries in 3D shapes

We propose an automatic method for finding symmetries of 3D shapes, that is, isometric transforms which leave a shape globally unchanged. These symmetries are deterministically found through the use of an intermediate quantity: the generalized moments. By examining the extrema and spherical harmonic coefficients of these moments, we recover the parameters of the symmetries of the shape. The computation for large composite models is made efficient by using this information in an incremental algorithm capable of recovering the symmetries of a whole shape using the symmetries of its subparts. Applications of this work range from coherent remeshing of geometry with respect to the symmetries of a shape to geometric compression, intelligent mesh editing, and automatic instantiation.

Interactive Mesh Deformation with Hard Constraints

Interactive mesh editing techniques typically encode geometric shapes using discrete differential equations and approximately solve them using the least squares method. However, these techniques fail to precisely preserve user-defined constraints. In our method, user-defined constraints, such as positional constraints, are treated as hard constraints, and then the combination of hard and soft constraints is converted into a typical least-squares system using QR decomposition. Our method stably and efficiently calculates vertex positions that preserve differential properties. A well-known problem with hard constraints is over-constraints. If over-constraints are involved, they may cause the solver to halt the computation. We show how our framework resolves over-constrained situations, which include redundant and conflicting constraints.

BatTri: A two-dimensional bathymetry-based unstructured triangular grid generator for finite element circulation modeling

A brief summary of Delaunay unstructured triangular grid refinement algorithms, including the recent “off-centers” method, is provided and mesh generation requirements that are imperative to meet the criteria of the circulation modeling community are defined. A Matlab public-domain two-dimensional (2-D) mesh generation package (BatTri) based on these requirements is then presented and its efficiency shown through examples. BatTri consists of a graphical mesh editing interface and several bathymetry-based refinement algorithms, complemented by a set of diagnostic utilities to check and improve grid quality. The final output mesh node locations, node depths and element incidence list are obtained starting from only a basic set of bathymetric data. This simple but efficient setup allows fast interactive mesh customization and provides circulation modelers with problem-specific flexibility while satisfying the usual requirements on mesh size and element quality. A test of the “off-centers” method performed on 100 domains with randomly generated coastline and bathymetry shows an overall 25% reduction in the number of elements with only slight decrease in element quality. More importantly, this shows that BatTri is easily upgradeable to meet the future demands by the addition of new grid generation algorithms and Delaunay refinement schemes as they are made available.

Mesh blending

A new method for smoothly connecting different patches on triangle meshes with arbitrary connectivity, called mesh blending, is presented. A major feature of mesh blending is to move vertices of the blending region to a virtual blending surface by choosing an appropriate parameterization of those vertices. Once blending is completed, the parameterization optimization is performed to perfect the final meshes. Combining mesh blending with multiresolution techniques, an effective blending technique for meshes is obtained. Our method has several advantages: (1) the user can intuitively control the blending result using different blending radii, (2) the shape of cross-section curves can be adjusted to flexibly design complex models, and (3) the resulting mesh has the same connectivity as the original mesh. In this paper, some examples about smoothing, sharpening, and mesh editing show the efficiency of the method.

Geometry completion and detail generation by texture synthesis

We present a novel method for patching holes in polygonal meshes and synthesizing surfaces with details based on existing geometry. The most novel feature of our proposed method is that we transform the 3D geometry synthesis problem into a 2D domain by parameterizing surfaces and solve this problem in that domain. We then derive local geometry gradient images that encode intrinsic local geometry properties, which are invariant to object translation and rotation. The 3D geometry of holes is then reconstructed from synthesized local gradient images. This method can be extended to execute other mesh editing operations such as geometry detail transfer or synthesis. The resulting major benefits of performing geometry synthesis in 2D are more flexible and robust control, better leveraging of the wealth of current 2D image completion methods, and greater efficiency.

Mesh-based inverse kinematics

The ability to position a small subset of mesh vertices and produce a meaningful overall deformation of the entire mesh is a fundamental task in mesh editing and animation. However, the class of meaningful deformations varies from mesh to mesh and depends on mesh kinematics, which prescribes valid mesh configurations, and a selection mechanism for choosing among them. Drawing an analogy to the traditional use of skeleton-based inverse kinematics for posing skeletons. we define mesh-based inverse kinematics as the problem of finding meaningful mesh deformations that meet specified vertex constraints.Our solution relies on example meshes to indicate the class of meaningful deformations. Each example is represented with a feature vector of deformation gradients that capture the affine transformations which individual triangles undergo relative to a reference pose. To pose a mesh, our algorithm efficiently searches among all meshes with specified vertex positions to find the one that is closest to some pose in a nonlinear span of the example feature vectors. Since the search is not restricted to the span of example shapes, this produces compelling deformations even when the constraints require poses that are different from those observed in the examples. Furthermore, because the span is formed by a nonlinear blend of the example feature vectors, the blending component of our system may also be used independently to pose meshes by specifying blending weights or to compute multi-way morph sequences.

A sketch-based interface for detail-preserving mesh editing

In this paper we present a method for the intuitive editing of surface meshes by means of view-dependent sketching. In most existing shape deformation work, editing is carried out by selecting and moving a handle , usually a set of vertices. Our system lets the user easily determine the handle, either by silhouette selection and cropping, or by sketching directly onto the surface. Subsequently, an edit is carried out by sketching a new, view-dependent handle position or by indirectly influencing differential properties along the sketch. Combined, these editing and handle metaphors greatly simplify otherwise complex shape modeling tasks.

LAPLACIAN FRAMEWORK FOR INTERACTIVE MESH EDITING

Recent works in geometric modeling show the advantage of local differential coordinates in various surface processing applications. In this paper we review recent methods that advocate surface representation via differential coordinates as a basis to interactive mesh editing. One of the main challenges in editing a mesh is to retain the visual appearance of the surface after applying various modifications. The differential coordinates capture the local geometric details and therefore are a natural surface representation for editing applications. The coordinates are obtained by applying a linear operator to the mesh geometry. Given suitable deformation constraints, the mesh geometry is reconstructed from the differential representation by solving a sparse linear system. The differential coordinates are not rotation-invariant and thus their rotation must be explicitly handled in order to retain the correct orientation of the surface details. We review two methods for computing the local rotations: the first estimates them heuristically using a deformation which only preserves the underlying smooth surface, and the second estimates the rotations implicitly through a variational representation of the problem. We show that the linear reconstruction system can be solved fast enough to guarantee interactive response time thanks to a precomputed factorization of the coefficient matrix. We demonstrate that this approach enables to edit complex meshes while retaining the shape of the details in their natural orientation.

삼차원 메쉬에 대한 기하학 라이브와이어와 기하학 라이브레인

이차원 영상에서 정의된 에지와 유사하게 삼차원 메쉬에서도 주요 부위의 경계를 표현하는 기하학 특징을 정의할 수 있다. 삼차원 메쉬에서 기하학 특징은 메쉬 단순화, 메쉬 변형과 메쉬 편집 등과 같은 여러 응용에 기본적인 항목으로 사용되고 있다. 본 논문에서는 삼차원 메쉬의 기학적 특징을 효과적으로 찾기 위하여 이차원 영상의 라이브와이어와 라이브레인 기법을 삼차원 메쉬로 확장한 기하학 라이브와이어와 기하학하 라이브레인 기법을 제안한다. 제안된 기법에서는 메쉬의 기하학 특징을 나타내기 위하여 근사곡률을 사용하였고 메쉬 그 자체를 정의된 비용함수를 에지의 가중치고 가지는 가중치 방향그래프로 나타내었다. 그리고 만들어진 가중치 방향그래프에 대해 잘 알려진 최단경로 탐색 알고리즘을 이용하여 사용자에 의해 지정된 점들 사이에 존재하는 삼차원 메쉬에서의 기하학 특징을 추출하였다. 본 논문에서는 사람 얼굴, 소, 신발과 치어 메쉬 모델에 나타나는 기하학 특징을 추출하기 위하여 제안한 기법을 적용하여 얻어진 결과를 가시화한다. Similarly to the edges defined in a 2D image, we can define the geometric features representing the boundary of the distinctive parts appearing on 3D meshes. The geometric features have been used as basic primitives in several applications such as mesh simplification, mesh deformation, and mesh editing. In this paper, we propose geometric livewire and geometric livelane for extracting geometric features in a 3D mesh, which are the extentions of livewire and livelane methods in images. In these methods, approximate curvatures are adopted to represent the geometric features in a 3D mesh and the 3D mesh itself is represented as a weighted directed graph in which cost functions are defined for the weights of edges. Using a well-known shortest path finding algorithm in the weighted directed graph, we extracted geometric features in the 3D mesh among points selected by a user. In this paper, we also visualize the results obtained from applying the techniques to extracting geometric features in the general meshes modeled after human faces, cows, shoes, and single teeth.