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1.
We introduce a unified optimization framework for geometry processing based on shape constraints. These constraints preserve or prescribe the shape of subsets of the points of a geometric data set, such as polygons, one‐ring cells, volume elements, or feature curves. Our method is based on two key concepts: a shape proximity function and shape projection operators. The proximity function encodes the distance of a desired least‐squares fitted elementary target shape to the corresponding vertices of the 3D model. Projection operators are employed to minimize the proximity function by relocating vertices in a minimal way to match the imposed shape constraints. We demonstrate that this approach leads to a simple, robust, and efficient algorithm that allows implementing a variety of geometry processing applications, simply by combining suitable projection operators. We show examples for computing planar and circular meshes, shape space exploration, mesh quality improvement, shape‐preserving deformation, and conformal parametrization. Our optimization framework provides a systematic way of building new solvers for geometry processing and produces similar or better results than state‐of‐the‐art methods.  相似文献   

2.
Interactive mesh deformation that preserves differential properties is a promising technique for the design of mechanical parts such as automobile sheet-metal panels. However, existing methods lack the ability to manipulate the form features and hard constraints that are commonly used in engineering applications. In this paper, we propose a new deformation framework that precisely preserves the shapes of form features during deformation. Geometrical shapes are interactively deformed so that mean curvature normals are approximately preserved in a least-squares sense and positional constraints and form-feature constraints are precisely satisfied. In our system, the combination of soft and hard constraints is solved using the Lagrange multiplier method. We also show how to constrain the motion of a form feature on a plane or a straight line using linear constraints. The implemented system achieves a real-time response for constrained deformation.  相似文献   

3.
We present a new algorithm for finding a most "developable" smooth mesh surface to interpolate a given set of arbitrary points or space curves. Inspired by the recent progress in mesh editing that employs the concepts of preserving the Laplacian coordinates and handle-based shape editing, we formulate the interpolation problem as a mesh deformation process that transforms an initial developable mesh surface, such as a planar figure, to a final mesh surface that interpolates the given points and/or curves. During the deformation, the developability of the intermediate mesh is maintained by means of preserving the zero-valued Gaussian curvature on the mesh. To treat the high nonlinearity of the geometric constrains owing to the preservation of Gaussian curvature, we linearize those nonlinear constraints using Taylor expansion and eventually construct a sparse and over-determined linear system which is subsequently solved by a robust least-squares solution. By iteratively performing this procedure, the initial mesh is gradually and smoothly "dragged" to the given points and/or curves. The initial experimental data has shown some promising aspects of the proposed algorithm as a general quasi-developable surface interpolation tool.  相似文献   

4.
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.  相似文献   

5.
We introduce a new simultaneously diagonalizable real algebra of symmetrical centrosymmetrical matrices having a Toeplitz-plus-Hankel structure. We give the corresponding orthonormal basis of eigenvectors which are alternately symmetrical and skewsymmetrical vectors. An application is the construction of a symmetrical Toeplitz-plus-centrosymmetrical Hankel matrix of equal row sums having a prescribed real spectrum. This matrix can be used as the starting matrix for symmetrical centrosymmetrical isospectral flows. In particular, for the isospectral flow corresponding to the construction of a regular Toeplitz matrix having prescribed eigenvalues. Moreover, if A is a noise representation of an unknown matrix in of rank k then we give a procedure to approximate A by a matrix in of rank k.  相似文献   

6.
Integral quadratic constraints (IQCs) are used in system theory to model nonlinear phenomena within the framework of linear feedback control. IQC theory addresses parametric robustness, saturation effects, sector nonlinearities, passivity, and much else. In IQC analysis specially structured linear matrix inequalities (LMIs) arise and are currently addressed by structure exploiting LMI solvers. Controller synthesis under IQC constraints is nonconvex and much harder and has been attempted sporadically by global optimization techniques such as branch and bound, cutting plane or D-K-type coordinate descent ideas. Here, we revisit IQC theory and propose a completely different algorithmic solution based on local and nonsmooth optimization methods. This is less ambitious than global methods, but is very promising in practice. Our approach, while aiming high at IQC synthesis, offers new answers even for IQC analysis, because we optimize without Lyapunov variables. For high-order systems this leads to a significant reduction of the number of unknowns.  相似文献   

7.
Robust control of flexible structures with stable bandpass controllers   总被引:1,自引:0,他引:1  
Alberto  Giuseppe  Ciro  Salvatore   《Automatica》2008,44(5):1251-1260
In this paper, a control law for the active vibration control of mechanical flexible systems is considered. The proposed strategy minimizes an index and results in a stable stabilizing controller with bandpass frequency shape, due to the presence of zeros at the origin. The control authority is thus effective in a chosen band of frequency, resulting in a selective broadband control action, as opposed to narrow-band (tonal) vibration reduction. Moreover, the explicit closed-form solution of the controller is also obtained, thus avoiding numerical calculation of the solution of the Riccati equations, which can be ill-conditioned in the case of very high-order, poorly damped flexible systems. The parametrization of all the controllers is also given and a family of controllers with the above properties is deduced. The case is also obtained as a byproduct. The controller is based on a colocated actuators/sensors pair strategy and numerical simulations are presented, showing the robustness of the proposed approach even for systems with zero damping. Finally, experimental results on a skin panel of a Boeing 717 aircraft also prove the effectiveness of the proposed approach in practical complex applications, with global vibration reduction performances.  相似文献   

8.
Image-based modelling allows the reconstruction of highly realistic digital models from real-world objects. This paper presents a model-based approach to recover animated models of people from multiple view video images. Two contributions are made, a multiple resolution model-based framework is introduced that combines multiple visual cues in reconstruction. Second, a novel mesh parameterisation is presented to preserve the vertex parameterisation in the model for animation. A prior humanoid surface model is first decomposed into multiple levels of detail and represented as a hierarchical deformable model for image fitting. A novel mesh parameterisation is presented that allows propagation of deformation in the model hierarchy and regularisation of surface deformation to preserve vertex parameterisation and animation structure. The hierarchical model is then used to fuse multiple shape cues from silhouette, stereo and sparse feature data in a coarse-to-fine strategy to recover a model that reproduces the appearance in the images. The framework is compared to physics-based deformable surface fitting at a single resolution, demonstrating an improved reconstruction accuracy against ground-truth data with a reduced model distortion. Results demonstrate realistic modelling of real people with accurate shape and appearance while preserving model structure for use in animation.  相似文献   

9.
We give a framework for developing the least model semantics, fixpoint semantics, and SLD-resolution calculi for logic programs in multimodal logics whose frame restrictions consist of the conditions of seriality (i.e. ) and some classical first-order Horn clauses. Our approach is direct and no special restriction on occurrences of i and i is required. We apply our framework for a large class of basic serial multimodal logics, which are parameterized by an arbitrary combination of generalized versions of axioms T, B, 4, 5 (in the form, e.g. 4:□i→□jk) and I:□i→□j. Another part of the work is devoted to programming in multimodal logics intended for reasoning about multidegree belief, for use in distributed systems of belief, or for reasoning about epistemic states of agents in multiagent systems. For that we also use the framework, and although these latter logics belong to the mentioned class of basic serial multimodal logics, the special SLD-resolution calculi proposed for them are more efficient.  相似文献   

10.
Lizheng  Guozhao 《Computer aided design》2006,38(12):1215-1223
Given a triangular Bézier surface of degree n, the problem of multi-degree reduction by a triangular Bézier surface of degree m with boundary constraints is investigated. This paper considers the continuity of triangular Bézier surfaces at the three corners, so that the boundary curves preserve endpoints continuity of any order . The l2- and L2-norm combined with the constrained least-squares method are used to get the matrix representations for the control points of the degree reduced surfaces. Both methods can be applied to piecewise continuous triangular patches or to only a triangular patch with the combination of surface subdivision. And the resulting piecewise approximating patches are globally C0 continuous. Finally, error estimation is given and numerical examples demonstrate the effectiveness of our methods.  相似文献   

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