Robust field-aligned global parametrization

Myles, Ashish; Pietroni, Nico; Zorin, Denis

doi:10.1145/2601097.2601154

Cited by 124 publications

(168 citation statements)

References 30 publications

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“…12. The improvement in energy and singularities of our exact (IOQ) and approximate (IOQe) methods relative to MIQ, computed by (E M I Q /E our s )(( |S | M I Q + 1)/( |S | our s + 1)) on the meshes from [Myles et al 2014], where |S | is the number of singularities. Note that for all meshes our result is bigger than 1, and thus improves on MIQ.…”

Section: Limitationsmentioning

confidence: 99%

Integer-only cross field computation

Farchi

Ben‐Chen

2018

ACM Trans. Graph.

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We propose a new iterative algorithm for computing smooth cross fields on triangle meshes that is simple, easily parallelizable on the GPU, and finds solutions with lower energy and fewer cone singularities than state-of-theart methods. Our approach is based on a formal equivalence, which we prove, between two formulations of the optimization problem. This equivalence allows us to eliminate the real variables and design an efficient grid search algorithm for the cone singularities. We leverage a recent graph-theoretical approximation of the resistance distance matrix of the triangle mesh to speed up the computation and enable a trade-off between the computation time and the smoothness of the output.

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Section: Limitationsmentioning

confidence: 99%

Integer-only cross field computation

Farchi

Ben‐Chen

2018

ACM Trans. Graph.

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“…Cignoni et al [2014] extended this concept and placed the elements driven by a feature-aligned input cross-field [Ray et al 2009;Bommes et al 2009], a mathematical entity that catches the overall structure and curvature of the object. Inspired by this concept, we compute potential candidates for cuts along smooth polylines that emerge from a field-aligned patch layout decomposition of the initial mesh [Tarini et al 2011;Campen et al 2012;Myles et al 2014;Razafindrazaka et al 2015].…”

Section: Shape Decomposition and Approximation For Fabricationmentioning

confidence: 99%

FlexMolds

et al. 2016

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We present FlexMolds, a novel computational approach to automatically design flexible, reusable molds that, once 3D printed, allow us to physically fabricate, by means of liquid casting, multiple copies of complex shapes with rich surface details and complex topology. The approach to design such flexible molds is based on a greedy bottom-up search of possible cuts over an object, evaluating for each possible cut the feasibility of the resulting mold. We use a dynamic simulation approach to evaluate candidate molds, providing a heuristic to generate forces that are able to open, detach, and remove a complex mold from the object it surrounds. We have tested the approach with a number of objects with nontrivial shapes and topologies.

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“…If a vector field is continuous and piecewise smooth in the atlas, it is possible to define first weak derivatives. Further, recent work by Ray and Sokolov [2013] and Myles et al [2014] showed how a combinatorial data structure can be used to represent vector fields while ensuring that field flow lines do not merge.…”

Section: Vector Field Representationmentioning

confidence: 99%

“…Such vector fields occur often in applications. For example, scalar functions are often discretized as piecewise linear on the vertices of the mesh, and their gradients [Kälberer et al 2007;Bommes et al 2009Bommes et al , 2013Campen et al 2012;Myles and Zorin 2013;Myles et al 2014;Panozzo et al 2014] piecewise constant vector fields are often given as constraints for controlling the alignment of the result. Hence, as we work directly with piecewise constant vector fields without requiring additional conversions to 1-forms or atlas-based representations, our approach is simpler, more intuitive, and easier to implement.…”

Section: Vector Field Representationmentioning

confidence: 99%

Discrete Derivatives of Vector Fields on Surfaces -- An Operator Approach

et al. 2015

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Vector fields on surfaces are fundamental in various applications in computer graphics and geometry processing. In many cases, in addition to representing vector fields, the need arises to compute their derivatives, for example, for solving partial differential equations on surfaces or for designing vector fields with prescribed smoothness properties. In this work, we consider the problem of computing the Levi-Civita covariant derivative, that is, the tangential component of the standard directional derivative, on triangle meshes. This problem is challenging since, formally, tangent vector fields on polygonal meshes are often viewed as being discontinuous, hence it is not obvious what a good derivative formulation would be. We leverage the relationship between the Levi-Civita covariant derivative of a vector field and the directional derivative of its component functions to provide a simple, easy-to-implement discretization for which we demonstrate experimental convergence. In addition, we introduce two linear operators which provide access to additional constructs in Riemannian geometry that are not easy to discretize otherwise, including the parallel transport operator which can be seen simply as a certain matrix exponential. Finally, we show the applicability of our operator to various tasks, such as fluid simulation on curved surfaces and vector field design, by posing algebraic constraints on the covariant derivative operator.

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Robust field-aligned global parametrization

Cited by 124 publications

References 30 publications

Integer-only cross field computation

Integer-only cross field computation

FlexMolds

Discrete Derivatives of Vector Fields on Surfaces -- An Operator Approach

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