Trivial Connections on Discrete Surfaces

Crane, Keenan; Desbrun, Mathieu; Schröder, Peter

doi:10.1111/j.1467-8659.2010.01761.x

Cited by 129 publications

(169 citation statements)

References 29 publications

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“…It turned out that such an interaction could be provided easily due to the available robust handling of linear constraints. In the extreme case of specifying all singularities within the orientation field our method is equivalent to [11] and [14]. However in contrast to them our approach is flexible enough to compute solutions for an arbitrary number of known singularities perfectly supporting an interactive design approach.…”

Section: Methodsmentioning

confidence: 99%

Practical Mixed-Integer Optimization for Geometry Processing

Bommes

Zimmer

Kobbelt

2012

Curves and Surfaces

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Abstract. Solving mixed-integer problems, i.e., optimization problems where some of the unknowns are continuous while others are discrete, is NP-hard. Unfortunately, real-world problems like e.g., quadrangular remeshing usually have a large number of unknowns such that exact methods become unfeasible. In this article we present a greedy strategy to rapidly approximate the solution of large quadratic mixed-integer problems within a practically sufficient accuracy. The algorithm, which is freely available as an open source library implemented in C++, determines the values of the discrete variables by successively solving relaxed problems. Additionally the specification of arbitrary linear equality constraints which typically arise as side conditions of the optimization problem is possible. The performance of the base algorithm is strongly improved by two novel extensions which are (1) simultaneously estimating sets of discrete variables which do not interfere and (2) a fill-in reducing reordering of the constraints. Exemplarily the solver is applied to the problem of quadrilateral surface remeshing, enabling a great flexibility by supporting different types of user guidance within a real-time modeling framework for input surfaces of moderate complexity.

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Section: Methodsmentioning

confidence: 99%

Practical Mixed-Integer Optimization for Geometry Processing

Bommes

Zimmer

Kobbelt

2012

Curves and Surfaces

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“…In the present work we give several possibilities for creating deformation directions. A vector field following principal curvature directions [17] is used for the snake example in Fig. 8.…”

Section: Deformation Directionsmentioning

confidence: 99%

Anisotropic deformation for local shape control

et al. 2017

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We present a novel approach to mesh deformation that enables simple context sensitive manipulation of 3D geometry. The method is based on locally anisotropic transformations and is extended to global control directions. This allows intuitive directional modeling within an easy to implement framework.The proposed method complements current sculpting paradigms by providing further possibilities for intuitive surface-based editing without the need for additional host geometries. We show the anisotropic deformation to be seamlessly transferable to free boundary parameterization methods, which allows us to solve the hard problem of flattening compression garments in the domain of apparel design.

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“…The sizing field is either user specified or automatically computed as a Lipschitz function from the local feature size estimate of the domain boundary [2]. The cross field is either specified by the user or automatically computed as the smoothest field that is tangential to the domain boundary [13]. Note that the mixed-integer approach [7] could also be used.…”

Section: Algorithmmentioning

confidence: 99%

“…Another key challenge comes from the fact that some of the requirements or quality criteria, although locally defined, have global constraints-e.g., the number of edges on the domain boundary must be even, and the total index of irregular vertices must obey Gauss-Bonnet theorem [13].…”

Section: Introductionmentioning

confidence: 99%

Isotropic 2D Quadrangle Meshing with Size and Orientation Control

Pellenard

Alliez

Morvan

2011

Proceedings of the 20th International Meshing Roundtable

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Summary. We propose an approach for automatically generating isotropic 2D quadrangle meshes from arbitrary domains with a fine control over sizing and orientation of the elements. At the heart of our algorithm is an optimization procedure that, from a coarse initial tiling of the 2D domain, enforces each of the desirable mesh quality criteria (size, shape, orientation, degree, regularity) one at a time, in an order designed not to undo previous enhancements. Our experiments demonstrate how well our resulting quadrangle meshes conform to a wide range of input sizing and orientation fields.

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Trivial Connections on Discrete Surfaces

Cited by 129 publications

References 29 publications

Practical Mixed-Integer Optimization for Geometry Processing

Practical Mixed-Integer Optimization for Geometry Processing

Anisotropic deformation for local shape control

Isotropic 2D Quadrangle Meshing with Size and Orientation Control

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