Direct anisotropic quad-dominant remeshing

Marinov, Martin; Kobbelt, Leif

doi:10.1109/pccga.2004.1348351

Cited by 70 publications

(71 citation statements)

References 25 publications

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“…Marinov and Kobbelt [23] extend this work by directly integrating curves on the input model. Streamline integration methods add integration curves in a greedy fashion, thus they cannot guarantee a globally uniform distribution.…”

Section: Quad Remeshingmentioning

confidence: 88%

Feature aligned quad dominant remeshing using iterative local updates

Lai

Kobbelt

2010

Computer-Aided Design

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In this paper we present a new algorithm which turns an unstructured triangle mesh into a quad-dominant mesh with edges well aligned to the principal directions of the underlying surface. Instead of computing a globally smooth parameterization or integrating curvature lines along a tangent vector field, we simply apply an iterative relaxation scheme which incrementally aligns the mesh edges to the principal directions. We further obtain the quad-dominant mesh by dropping the not-aligned diagonal edges from the triangle mesh. A post-processing stage is introduced to further improve the results. The major advantage of our algorithm is its conceptual simplicity since it is merely based on elementary mesh operations such as edge collapse, flip, and split. The resulting meshes exhibit a very good alignment to surface features and rather uniform distribution of mesh vertices. This makes them well-suited, e.g., as Catmull-Clark Subdivision control meshes.

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Section: Quad Remeshingmentioning

confidence: 88%

Feature aligned quad dominant remeshing using iterative local updates

Lai

Kobbelt

2010

Computer-Aided Design

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“…Generally, there are two classes of approaches, namely explicit quadrangulations and parametrization based techniques. Examples of explicit approaches are [Alliez et al 2003;Marinov and Kobbelt 2004] which trace curves along the principal curvature directions or [Lai et al 2008] which iteratively transforms a triangular mesh into a quad-dominant mesh. For all such methods it is difficult to obtain coarse meshes consisting of quads only.…”

Section: Related Workmentioning

confidence: 99%

Mixed-integer quadrangulation

Bommes¹,

Zimmer²,

Kobbelt³

2009

ACM SIGGRAPH 2009 Papers

157

369

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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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“…Including methods devised to generate quadrangle surface tilings, the rich literature on this topic contains approaches which proceed by quadrangulation [9,3], square packing [28], advancing front [22], conversion [8], decimation [18], Morse-Smale complexes [14,33,17], clustering [4,20], local and global operators [23,19], whisker weaving [32], medial axis [24], streamlining [1,21] and parameterization [25,29,7].…”

Section: Previous Workmentioning

confidence: 99%

“…Among these approaches, some favor the conformance of the final mesh to an input cross field either by construction [21], or by solving for the smoothest cross field given a set of orientation constraints [7]. Conformance to an input sizing field is either derived from the triangle mesh before conversion [8], or encoded in a density function before clustering [20].…”

Section: Previous Workmentioning

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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Direct anisotropic quad-dominant remeshing

Cited by 70 publications

References 25 publications

Feature aligned quad dominant remeshing using iterative local updates

Feature aligned quad dominant remeshing using iterative local updates

Mixed-integer quadrangulation

Isotropic 2D Quadrangle Meshing with Size and Orientation Control

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