Multiresolution free-form deformation with subdivision surface of arbitrary topology

A new free-from deformation method is presented in this paper. Object deformation is controlled by a mesh of arbitrary topology, namely a control mesh. The subdivision surface determined by the control mesh spans an intermediate deformation space. The object is embedded into the space by the nearest point rule. When the shape of the control mesh is changed, the object embedded in the intermediate deformation space will be deformed accordingly. Since the subdivision surface has a multiresolution property, the proposed deformation method naturally has a multiresolution property. A technique for generating control meshes is also introduced in the paper. Compared with previous deformation methods with arbitrary topology control tools, the proposed method has the advantages of flexible control and computational efficiency.     

A unified subdivision approach for multi-dimensional non-manifold modeling

This paper presents a new unified subdivision scheme that is defined over a k-simplicial complex in n-D space with k≤3. We first present a series of definitions to facilitate topological inquiries during the subdivision process. The scheme is derived from the double (k+1)-directional box splines over k-simplicial domains. Thus, it guarantees a certain level of smoothness in the limit on a regular mesh. The subdivision rules are modified by spatial averaging to guarantee C¹ smoothness near extraordinary cases. Within a single framework, we combine the subdivision rules that can produce 1-, 2-, and 3-manifolds in arbitrary n-D space. Possible solutions for non-manifold regions between the manifolds with different dimensions are suggested as a form of selective subdivision rules according to user preference. We briefly describe the subdivision matrix analysis to ensure a reasonable smoothness across extraordinary topologies, and empirical results support our assumption. In addition, through modifications, we show that the scheme can easily represent objects with singularities, such as cusps, creases, or corners. We further develop local adaptive refinement rules that can achieve level-of-detail control for hierarchical modeling. Our implementation is based on the topological properties of a simplicial domain. Therefore, it is flexible and extendable. We also develop a solid modeling system founded on our subdivision schemes to show potential benefits of our work in industrial design, geometric processing, and other applications.     

A direct approach for subdivision surface fitting from a dense triangle mesh

This article presents a new and direct approach for fitting a subdivision surface from an irregular and dense triangle mesh of arbitrary topological type. All feature edges and feature vertices of the original mesh model are first identified. A topology- and feature-preserving mesh simplification algorithm is developed to further simplify the dense triangle mesh into a coarse mesh. A subdivision surface with exactly the same topological structure and sharp features as that of the simplified mesh is finally fitted from a subset of vertices of the original dense mesh. During the fitting process, both the position masks and subdivision rules are used for setting up the fitting equation. Some examples are provided to demonstrate the proposed approach.     

Smooth blending of subdivision surfaces

A technique for merging freeform objects modeled with subdivision surfaces is proposed. The method takes into consideration the possible distortion of the surfaces while the smoothness of the blending surface connecting the objects is maintained. A blend region between the given object surfaces is located. The topology of the surfaces in the vicinity of the blend region is refined and the boundary curves of the blend region are smoothed to reduce possible distortion in the blending surface. A blend curve between the two surfaces is used for connecting the given surfaces. Vertices on the blend curve are regular whereas extraordinary vertices are restricted to locate along the boundary of the blend region. Locations of the blend vertices are adjusted such that the curvature of the surfaces along the boundaries of the blend region is minimized. This ensures extraordinary vertices on the boundaries to lie on a relatively flat region, and hence, minimizes the distortion of the surfaces in the merging process.     

Integration of CAD and boundary element analysis through subdivision methods

Subdivision methods have been mainly used in computer graphics. This paper extends their applications to mechanical design and boundary element analysis (BEA), and fulfills the seamless integration of CAD and BEA in the model and representation.Traditionally, geometric design and BEA are treated as separate modules requiring different representations and models, which include continuous parametric models and discrete models. Due to the incompatibility of the involved representations and models, the post-processing in geometric design or the pre-processing in BEA is essential. The transition from geometric design to BEA requires substantial effort and errors are inevitably introduced during the transition. In this paper, a framework of realizing the integration of CAD and BEA was first presented based on subdivision methods. A common model or a unified representation for geometric design and BEA was created with subdivision surfaces. For general 3D structures, automatic mesh generation for geometric design and BEA was fulfilled through subdivision methods. The seamless integration improves the accuracy of numerical analysis and shortens the cycle of geometric design and BEA.     

Extension of half-edges for the representation of multiresolution subdivision surfaces

We address in this paper the problem of the data structures used for the representation and the manipulation of multiresolution subdivision surfaces. The classically used data structures are based on quadtrees, straightforwardly derived from the nested hierarchy of faces generated by the subdivision schemes. Nevertheless, these structures have some drawbacks: specificity to the kind of mesh (triangle or quad); the time complexity of neighborhood queries is not optimal; topological cracks are created in the mesh in the adaptive subdivision case. We present in this paper a new topological model for encoding multiresolution subdivision surfaces. This model is an extension to the well-known half-edge data structure. It allows instant and efficient navigation at any resolution level of the mesh. Its generality allows the support of many subdivision schemes including primal and dual schemes. Moreover, subdividing the mesh adaptively does not create topological cracks in the mesh. The extension proposed here is formalized in the combinatorial maps framework. This allows us to give a very general formulation of our extension.     

A deformable model for fingerprint matching

The process of automatic fingerprint matching is affected by the nonlinear deformation introduced in the image during fingerprint sensing. Given several template impressions of a finger, we estimate the “average” deformation of each template impression by comparing it with the rest of the impressions of that finger. The average deformation is developed using the thin plate spline (TPS) model and is based on minutia point correspondences between pairs of fingerprint impressions. The estimated average deformation is utilized to pre-distort the minutiae points in the template image before matching it with the minutiae points in the query image. We show that the use of an average deformation model leads to a better alignment between the template and query minutiae points. An index of deformation is proposed for choosing the deformation model with the least variability arising from a set of template impressions corresponding to a finger. Our experimental data consists of 1600 fingerprints corresponding to 50 different fingers collected over a period of 2 weeks. It is shown that the average deformation model leads to an improvement in the alignment between impressions originating from the same finger.     

Interpolatory,solid subdivision of unstructured hexahedral meshes

This paper presents a new, volumetric subdivision scheme for interpolation of arbitrary hexahedral meshes. To date, nearly every existing volumetric subdivision scheme is approximating, i.e., with each application of the subdivision algorithm, the geometry shrinks away from its control mesh. Often, an approximating algorithm is undesirable and inappropriate, producing unsatisfactory results for certain applications in solid modeling and engineering design (e.g., finite element meshing). We address this lack of smooth, interpolatory subdivision algorithms by devising a new scheme founded upon the concept of tri-cubic Lagrange interpolating polynomials. We show that our algorithm is a natural generalization of the butterfly subdivision surface scheme to a tri-variate, volumetric setting.     

A subdivision method for computing nearest gcd with certification

A new subdivision method for computing the nearest univariate gcd is described and analyzed. It is based on an exclusion test and an inclusion test. The exclusion test in a cell exploits Taylor expansion of the polynomial at the center of the cell. The inclusion test uses Smale’s α-theorems to certify the existence and unicity of a solution in a cell.Under the condition of simple roots for the distance minimization problem, we analyze the complexity of the algorithm in terms of a condition number, which is the inverse of the distance to the set of degenerate systems.We report on some experimentation on representative examples to illustrate the behavior of the algorithm.     

Subdivision for Generating Quadrics

Quadrics are of basic importance in Computer Graphics and Computer Aided Design. In this paper,we design a subdivision scheme based on the method suggested by G. Morin and J. Warren to generate conics and quadrics conveniently. Given the control polygon(p     

A new space subdivision method for ray tracing CSG modelled scenes

A new algorithm for space tracing with CSG modelled scenes is presented. Space is divided in an irregular fashion to fit the objects as closely as possible. For this reason, primitive minimal bounding boxes are computed. Space subdivision is achieved in two steps: partitioning in projection plane and depth partitioning. A set of 3D regions named cells are then created. A Boolean CSG tree is distributed into the cell structure to form in each cell the minimal boolean CSG tree using the relevant primitives. The searching process for the next cell along the ray path is performed by using a local data structure associated with each cell. The goal of this structure is to link the cells together. An improvement, named mailbox, for all space tracing algorithms is detailed. Results are presented for two scenes to compare this new algorithm with Roth's algorithm.     

实时形状匹配变形体动画

给出了一个仿真变形体的方法。物体被几何方法推动变形,操纵基于点的物体并且不需要连接信息,这是一个不需要任何预处理,计算简单,并提供无条件稳定的动态仿真方法。主要思想是通过几何约束替换能量和通过当前位置到目标位置的距离替换力。这些目标位置通过一个通用的无变形的静止状态和点云的当前变形状态之间的形状匹配来决定,因为点总是在定义好的位置被绘制,显式积分方法的过度不稳定问题被消除。相关物体表现方法的灵活性能被控制,相关内存和计算是有效的,动态仿真上的无条件稳定性让这个方法特别适合游戏开发。     

A discrete mechanics model for deformable bodies

This paper describes the theory and implications of a discrete mechanics model for deformable bodies, incorporating behavior such as motion, collision, deformation, etc. The model is fundamentally based on inter-atomic interaction, and recursively reduces resolution by approximating collections of many high-resolution elements with fewer lower-resolution elements. The model can be viewed as an extended mass-spring model. We begin by examining the domain of conceptual design, and find there is a need for physics based simulation, both for interactive shape modeling and analysis. We then proceed with describing a theoretical base for our model, as well as pragmatic additions. Applications in both interactive physics based shape modeling and analysis are presented. The model is aimed at conceptual mechanical design, rapid prototyping, or similar areas where adherence to physical principles, generality and simplicity are more important than metric correctness.     

Feature based object decomposition for finite element meshing

Performing a finite element analysis requires overlaying an object with a mesh of varying density based on the expected stress levels within the part. Attempts have been made in the past to automat the finite element meshing procedure. The method presented here is intelligent in the sense that it examines the complete part for potential stress gradients and decomposes the part into hexahedral regions according to the geometry gradients in the part. High geometry gradients are regions of high curvature, especially edges. The algorithm segregates high gradient features into isolation volumes. It then continues to decompose each isolation volume dependent on the particular geometry contained in the feature. The result is a set of hexahedral bricks suitable for passing to an automatic meshing routine.     

A new interpolation subdivision scheme for triangle/quad mesh

In this paper, we present a new interpolation subdivision scheme for mixed triangle/quad meshes that is C¹ continuous. The new scheme is capable of reproducing the well-known four-point based interpolation subdivision in the quad region but does not reproduce Butterfly subdivision in the triangular part. The new scheme defines rules that produce surfaces both at the regular quad/triangle vertices and isolated, extraordinary points. We demonstrate the visually satisfying of our surfaces through several examples.     

A cascadic geometric filtering approach to subdivision

A new approach to subdivision based on the evolution of surfaces under curvature motion is presented. Such an evolution can be understood as a natural geometric filter process where time corresponds to the filter width. Thus, subdivision can be interpreted as the application of a geometric filter on an initial surface. The concrete scheme is a model of such a filtering based on a successively improved spatial approximation starting with some initial coarse mesh and leading to a smooth limit surface.

In every subdivision step the underlying grid is refined by some regular refinement rule and a linear finite element problem is either solved exactly or, especially on fine grid levels, one confines to a small number of smoothing steps within the corresponding iterative linear solver. The approach closely connects subdivision to surface fairing concerning the geometric smoothing and to cascadic multigrid methods with respect to the actual numerical procedure. The derived method does not distinguish between different valences of nodes nor between different mesh refinement types. Furthermore, the method comes along with a new approach for the theoretical treatment of subdivision.     

A 4-point interpolatory subdivision scheme for curve design

A 4-point interpolatory subdivision scheme with a tension parameter is analysed. It is shown that for a certain range of the tension parameter the resulting curve is C¹. The role of the tension parameter is demonstrated by a few examples. The application to surfaces and some further potential generalizations are discussed.     

A statistical atlas based approach to automated subject-specific FE modeling

Subject-specific modeling is increasingly important in biomechanics simulation. However, how to automatically create high-quality finite element (FE) mesh and how to automatically impose boundary condition are challenging.This paper presents a statistical atlas based approach for automatic meshing of subject-specific shapes. In our approach, shape variations among a shape population are explicitly modeled and the correspondence between a given subject-specific shape and the statistical atlas is sought within the “legal” shape variations. This approach involves three parts: (1) constructing a statistical atlas from a shape population, including the statistical shape model and the FE model of the mean shape; (2) establishing the correspondence between a given subject shape and the atlas; and (3) deforming the atlas to the subject shape based on the shape correspondence. Numerical results on 2D hands, 3D femur bones and 3D aorta demonstrate the effectiveness of the proposed approach.