Quadrangular Parameterization for Reverse Engineering

Bommes, David; Vossemer, Tobias; Kobbelt, Leif

doi:10.1007/978-3-642-11620-9_5

Cited by 19 publications

(17 citation statements)

References 10 publications

(14 reference statements)

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“…Approaches within this class are sometimes driven by a cross field [Ray et al 2006;Kälberer et al 2007;Bommes et al 2009] or based on quad layouts [Dong et al 2006;Tong et al 2006;Bommes et al 2010;Huang et al 2008]. In any case, the problem of guaranteeing success of such a method is two fold, (1) determining integer positions of the singular vertices that admit a degeneracy free bijective parametrization and (2) finding such a map, which in addition optimizes the resulting mesh quality.…”

Section: Related Workmentioning

confidence: 98%

Integer-grid maps for reliable quad meshing

et al. 2013

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Greedy Rounding + StiffeningOur Reliable Approach Figure 1: (left) State-of-the-art parametrization based quad mesh generators, working with greedy rounding and stiffening, perform well if the target element sizing is chosen conservatively w.r.t. the distance of singularities but fail otherwise. Degeneracies in the map that prevent the iso-lines from stitching to a valid quad mesh -which mostly cannot be repaired locally -are highlighted in red. (right) Our novel reliable algorithm produces a valid output for any target sizing and thus in addition to ordinary quad-remeshing can be applied to coarse quad layout generation as well. The target edge length, indicated by bars, is identical for the left and the right triple. AbstractQuadrilateral remeshing approaches based on global parametrization enable many desirable mesh properties. Two of the most important ones are (1) high regularity due to explicit control over irregular vertices and (2) smooth distribution of distortion achieved by convex variational formulations. Apart from these strengths, state-of-the-art techniques suffer from limited reliability on realworld input data, i.e. the determined map might have degeneracies like (local) non-injectivities and consequently often cannot be used directly to generate a quadrilateral mesh. In this paper we propose a novel convex Mixed-Integer Quadratic Programming (MIQP) formulation which ensures by construction that the resulting map is within the class of so called Integer-Grid Maps that are guaranteed to imply a quad mesh. In order to overcome the NP-hardness of MIQP and to be able to remesh typical input geometries in acceptable time we propose two additional problem specific optimizations: a complexity reduction algorithm and singularity separating conditions. While the former decouples the dimension of the MIQP search space from the input complexity of the triangle mesh and thus is able to dramatically speed up the computation without inducing inaccuracies, the latter improves the continuous relaxation, which is crucial for the success of modern MIQP optimizers. Our experiments show that the reliability of the resulting algorithm does not only annihilate the main drawback of parametrization based quad-remeshing but moreover enables the global search for high-quality coarse quad layouts -a difficult task solely tackled by greedy methodologies before.

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Section: Related Workmentioning

confidence: 98%

Integer-grid maps for reliable quad meshing

et al. 2013

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“…In some works a completely manual creation of the layout, i.e. drawing of the individual layout vertices and edges on a surface is described or assumed [Krishnamurthy and Levoy 1996;Bommes et al 2008]. In other works some support is provided, e.g.…”

Section: Related Workmentioning

confidence: 99%

Dual strip weaving

Campen

Kobbelt

2014

ACM Trans. Graph.

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Figure 1: Overview of our Dual Strip Weaving approach for the design of quadrilateral patch layouts. a) When hovering over the object, the user is immediately presented with the best elastica strip (visualized using a stripe pattern) at the current pointer position. It can be selected and fixed with a single click. b) Fixed strips (blue) constrain the design space; only compatible strips are offered next (green). c) Indicators based on color-coding and stripe patterns guide the user to regions where modifications are recommended for the benefit of layout quality. d) Finally, the implied quad layout structure is derived from a collection of strips. The accompanying video shows the entire process. AbstractWe introduce Dual Strip Weaving, a novel concept for the interactive design of quad layouts, i.e. partitionings of freeform surfaces into quadrilateral patch networks. In contrast to established tools for the design of quad layouts or subdivision base meshes, which are often based on creating individual vertices, edges, and quads, our method takes a more global perspective, operating on a higher level of abstraction: the atomic operation of our method is the creation of an entire cyclic strip, delineating a large number of quad patches at once. The global consistency-preserving nature of this approach reduces demands on the user's expertise by requiring less advance planning. Efficiency is achieved using a novel method at the heart of our system, which automatically proposes geometrically and topologically suitable strips to the user. Based on this we provide interaction tools to influence the design process to any desired degree and visual guides to support the user in this task.

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“…Once a suitable singularity graph is provided by the user, these harmonic parametrizations produce nice quadrangulations. By allowing affine transition functions and optimizing the charts, [Bommes et al 2009] improved the distortion of the parametrization.…”

Section: Related Workmentioning

confidence: 99%

Mixed-integer quadrangulation

Bommes¹,

Zimmer²,

Kobbelt³

2009

ACM SIGGRAPH 2009 Papers

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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 iso-parameter 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 mixed-integer 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.

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Quadrangular Parameterization for Reverse Engineering

Cited by 19 publications

References 10 publications

Integer-grid maps for reliable quad meshing

Integer-grid maps for reliable quad meshing

Dual strip weaving

Mixed-integer quadrangulation

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