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21
On linear variational surface deformation methods
 IEEE Transaction on Visualization on Computer Graphics
, 2007
"... Abstract — This survey reviews the recent advances in linear variational mesh deformation techniques. These methods were developed for editing detailed highresolution meshes, like those produced by scanning realworld objects. The challenge of manipulating such complex surfaces is threefold: the d ..."
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Cited by 98 (7 self)
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Abstract — This survey reviews the recent advances in linear variational mesh deformation techniques. These methods were developed for editing detailed highresolution meshes, like those produced by scanning realworld objects. The challenge of manipulating such complex surfaces is threefold: the deformation technique has to be sufficiently fast, robust, and intuitive and easy to control to be useful for interactive applications. An intuitive, and thus predictable, deformation tool should provide physically plausible and aesthetically pleasing surface deformations, which in particular requires its geometric details to be preserved. The methods we survey generally formulate surface deformation as a global variational optimization problem that addresses the differential properties of the edited surface. Efficiency and robustness are achieved by linearizing the underlying objective functional, such that the global optimization amounts to solving a sparse linear system of equations. We review the different deformation energies and detail preservation techniques that were proposed in the recent years, together with the various techniques to rectify the linearization artifacts. Our goal is to provide the reader with a systematic classification and comparative description of the different techniques, revealing the strengths and weaknesses of each approach in common editing scenarios. Index Terms — mesh editing, linear optimization, discrete differential operators I.
Mixedinteger quadrangulation
 ACM Trans. Graph
, 2009
"... the input mesh by some simple heuristic or by the user. (b) In a global optimization procedure a cross field is generated on the mesh which interpolates the given constraints and is as smooth as possible elsewhere. The optimization includes the automatic generation and placement of singularities. (c ..."
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Cited by 50 (9 self)
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the input mesh by some simple heuristic or by the user. (b) In a global optimization procedure a cross field is generated on the mesh which interpolates the given constraints and is as smooth as possible elsewhere. The optimization includes the automatic generation and placement of singularities. (c) A globally smooth parametrization is computed on the surface whose isoparameter lines follow the cross field directions and singularities lie at integer locations. (d) Finally, a consistent, feature aligned quadmesh can be extracted. We present a novel method for quadrangulating a given triangle mesh. After constructing an as smooth as possible symmetric cross field satisfying a sparse set of directional constraints (to capture the geometric structure of the surface), the mesh is cut open in order to enable a low distortion unfolding. Then a seamless globally smooth parametrization is computed whose isoparameter lines follow the cross field directions. In contrast to previous methods, sparsely distributed directional constraints are sufficient to automatically determine the appropriate number, type and position of singularities in the quadrangulation. Both steps of the algorithm (cross field and parametrization) can be formulated as a mixedinteger problem which we solve very efficiently by an adaptive greedy solver. We show several complex examples where high quality quad meshes are generated in a fully automatic manner.
Realtime shape editing using radial basis functions
 Computer Graphics Forum
, 2005
"... Current surfacebased methods for interactive freeform editing of high resolution 3D models are very powerful, but at the same time require a certain minimum tessellation or sampling quality in order to guarantee sufficient robustness. In contrast to this, space deformation techniques do not depend ..."
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Cited by 45 (8 self)
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Current surfacebased methods for interactive freeform editing of high resolution 3D models are very powerful, but at the same time require a certain minimum tessellation or sampling quality in order to guarantee sufficient robustness. In contrast to this, space deformation techniques do not depend on the underlying surface representation and hence are affected neither by its complexity nor by its quality aspects. However, while analogously to surfacebased methods high quality deformations can be derived from variational optimization, the major drawback lies in the computation and evaluation, which is considerably more expensive for volumetric space deformations. In this paper we present techniques which allow us to use triharmonic radial basis functions for realtime freeform shape editing. An incremental leastsquares method enables us to approximately solve the involved linear systems in a robust and efficient manner and by precomputing a special set of deformation basis functions we are able to significantly reduce the perframe costs. Moreover, evaluating these linear basis functions on the GPU finally allows us to deform highly complex polygon meshes or pointbased models at a rate of 30M vertices or 13M splats per second, respectively. 1.
A fast multigrid algorithm for mesh deformation
 ACM Trans. Graph
, 2006
"... Figure 1: The idle CAMEL becomes a boxer with the help of MOCAP data and our mesh deformation system. In this paper, we present a multigrid technique for efficiently deforming large surface and volume meshes. We show that a previous leastsquares formulation for distortion minimization reduces to a ..."
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Cited by 44 (2 self)
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Figure 1: The idle CAMEL becomes a boxer with the help of MOCAP data and our mesh deformation system. In this paper, we present a multigrid technique for efficiently deforming large surface and volume meshes. We show that a previous leastsquares 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.
Design of tangent vector fields
 ACM Trans. Graph
, 2007
"... Tangent vector fields are an essential ingredient in controlling surface appearance for applications ranging from anisotropic shading to texture synthesis and nonphotorealistic rendering. To achieve a desired effect one is typically interested in smoothly varying fields that satisfy a sparse set of ..."
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Cited by 41 (4 self)
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Tangent vector fields are an essential ingredient in controlling surface appearance for applications ranging from anisotropic shading to texture synthesis and nonphotorealistic rendering. To achieve a desired effect one is typically interested in smoothly varying fields that satisfy a sparse set of userprovided constraints. Using tools from Discrete Exterior Calculus, we present a simple and efficient algorithm for designing such fields over arbitrary triangle meshes. By representing the field as scalars over mesh edges (i.e., discrete 1forms), we obtain an intrinsic, coordinatefree formulation in which field smoothness is enforced through discrete Laplace operators. Unlike previous methods, such a formulation leads to a linear system whose sparsity permits efficient prefactorization. Constraints are incorporated through weighted least squares and can be updated rapidly enough to enable interactive design, as we demonstrate in the context of anisotropic texture synthesis.
Concurrent number cruncher: a gpu implementation of a general sparse linear solver
 Int. J. Parallel Emerg. Distrib. Syst
"... A wide class of numerical methods needs to solve a linear system, where the matrix pattern of nonzero coefficients can be arbitrary. These problems can greatly benefit from highly multithreaded computational power and large memory bandwidth available on GPUs, especially since dedicated general purp ..."
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Cited by 18 (0 self)
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A wide class of numerical methods needs to solve a linear system, where the matrix pattern of nonzero coefficients can be arbitrary. These problems can greatly benefit from highly multithreaded computational power and large memory bandwidth available on GPUs, especially since dedicated general purpose APIs such as CTM (AMDATI) and CUDA (NVIDIA) have appeared. CUDA even provides a BLAS implementation, but only for dense matrices (CuBLAS). Other existing linear solvers for the GPU are also limited by their internal matrix representation. This paper describes how to combine recent GPU programming techniques and new GPU dedicated APIs with high performance computing strategies (namely block compressed row storage, register blocking and vectorization), to implement a sparse generalpurpose linear solver. Our implementation of the Jacobipreconditioned Conjugate Gradient algorithm outperforms by up to a factor of 6.0x leadingedge CPU counterparts, making it attractive for applications which content with single precision.
Evolution of Tspline Level Sets with Distance Field Constraints for Geometry Reconstruction and Image Segmentation
, 2005
"... We study the evolution of Tspline level sets (i.e, implicitly defined Tspline curves and surfaces). The use of Tsplines leads to a sparse representation of the geometry and allows for an adaptation to the given data, which can be unorganized points or images. The evolution process is governed by ..."
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Cited by 15 (12 self)
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We study the evolution of Tspline level sets (i.e, implicitly defined Tspline curves and surfaces). The use of Tsplines leads to a sparse representation of the geometry and allows for an adaptation to the given data, which can be unorganized points or images. The evolution process is governed by a combination of prescribed, datadriven normal velocities, and additional distance field constraints. By incorporating the distance field constraints we are able to avoid additional branches and singularities of the Tspline level sets without having to use reinitialization steps. Experimental examples are presented to demonstrate the effectiveness of our approach.
Quadrangular parameterization for reverse engineering
 Lecture Notes in Computer Science
, 2009
"... Abstract. The aim of Reverse Engineering is to convert an unstructured representation of a geometric object, emerging e.g. from laser scanners, into a natural, structured representation in the spirit of CAD models, which is suitable for numerical computations. Therefore we present a usercontrolled, ..."
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Cited by 7 (5 self)
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Abstract. The aim of Reverse Engineering is to convert an unstructured representation of a geometric object, emerging e.g. from laser scanners, into a natural, structured representation in the spirit of CAD models, which is suitable for numerical computations. Therefore we present a usercontrolled, as isometric as possible parameterization technique which is able to prescribe geometric features of the input and produces highquality quadmeshes with low distortion. Starting with a coarse, userprescribed layout this is achieved by using affine functions for the transition between nonorthogonal quadrangular charts of a global parameterization. The shape of each chart is optimized nonlinearly for isometry of the underlying parameterization to produce meshes with low edgelength distortion. To provide full control over the meshing alignment the user can additionally tag an arbitrary subset of the layout edges which are guaranteed to be represented by enforcing them to lie on isolines of the parameterization but still allowing the global parameterization to relax in the direction of the isolines. Key words: reverse engineering, quadrangular remeshing, global parameterization 1
Biharmonic Distance
"... Measuring distances between pairs of points on a 3D surface is a fundamental problem in computer graphics and geometric processing. For most applications, the important properties of a distance are that it is a metric, smooth, locally isotropic, globally “shapeaware, ” isometry invariant, insensiti ..."
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Cited by 6 (0 self)
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Measuring distances between pairs of points on a 3D surface is a fundamental problem in computer graphics and geometric processing. For most applications, the important properties of a distance are that it is a metric, smooth, locally isotropic, globally “shapeaware, ” isometry invariant, insensitive to noise and small topology changes, parameterfree, and practical to compute on a discrete mesh. However, the basic methods currently popular in computer graphics (e.g., geodesic and diffusion distances) do not have these basic properties. In this paper, we propose a new distance measure based on the biharmonic differential operator that has all the desired properties. This new surface distance is related to the diffusion and commutetime distances, but applies different (inverse squared) weighting to the eigenvalues of the LaplaceBeltrami operator, which provides a nice tradeoff between nearly geodesic distances for small distances and global shapeawareness for large distances. The paper provides theoretical and empirical analysis for a large number of meshes. Categories and Subject Descriptors: