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61
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.
Conformal Flattening by Curvature Prescription and Metric Scaling
, 2008
"... We present an efficient method to conformally parameterize 3D mesh data sets to the plane. The idea behind our method is to concentrate all the 3D curvature at a small number of select mesh vertices, called cone singularities, and then cut the mesh through those singular vertices to obtain disk topo ..."
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Cited by 35 (2 self)
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We present an efficient method to conformally parameterize 3D mesh data sets to the plane. The idea behind our method is to concentrate all the 3D curvature at a small number of select mesh vertices, called cone singularities, and then cut the mesh through those singular vertices to obtain disk topology. The singular vertices are chosen automatically. As opposed to most previous methods, our flattening process involves only the solution of linear systems of Poisson equations, thus is very efficient. Our method is shown to be faster than existing methods, yet generates parameterizations having comparable quasiconformal distortion.
Spectral quadrangulation with orientation and alignment control
 IN ACM SIGGRAPH ASIA
, 2008
"... This paper presents a new quadrangulation algorithm, extending the spectral surface quadrangulation approach where the coarse quadrangular structure is derived from the MorseSmale complex of an eigenfunction of the Laplacian operator on the input mesh. In contrast to the original scheme, we provi ..."
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Cited by 26 (5 self)
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This paper presents a new quadrangulation algorithm, extending the spectral surface quadrangulation approach where the coarse quadrangular structure is derived from the MorseSmale complex of an eigenfunction of the Laplacian operator on the input mesh. In contrast to the original scheme, we provide flexible explicit controls of the shape, size, orientation and feature alignment of the quadrangular faces. We achieve this by proper selection of the optimal eigenvalue (shape), by adaption of the area term in the Laplacian operator (size), and by adding special constraints to the Laplace eigenproblem (orientation and alignment). By solving a generalized eigenproblem we can generate a scalar field on the mesh whose MorseSmale complex is of high quality and satisfies all the user requirements. The final quadrilateral mesh is generated from the MorseSmale complex by computing a globally smooth parametrization. Here we additionally introduce edge constraints to preserve user specified feature lines accurately.
Quadrilateral mesh simplification
 In ACM SIGGRAPH Asia 2008 papers
, 2008
"... Figure 1: Our simplification algorithm can be used to generate a pure quad levelofdetail hierarchy. The algorithm preserves topology during simplification, and attempts to optimize geometric fidelity and quad structure (vertex valences near 4) throughout the process. We introduce a simplification ..."
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Cited by 17 (5 self)
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Figure 1: Our simplification algorithm can be used to generate a pure quad levelofdetail hierarchy. The algorithm preserves topology during simplification, and attempts to optimize geometric fidelity and quad structure (vertex valences near 4) throughout the process. We introduce a simplification algorithm for meshes composed of quadrilateral elements. It is reminiscent of edgecollapse based methods for triangle meshes, but takes a novel approach to the challenging problem of maintaining the quadrilateral connectivity during levelofdetail creation. The method consists of a set of unit operations applied to the dual of the mesh, each designed to improve mesh structure and maintain topological genus. Geometric shape is maintained by an extension of a quadric error metric to quad meshes. The technique is straightforward to implement and efficient enough to be applied to realworld models. Our technique can handle models with sharp features, and can be used to remesh general polygonal, i.e. tri and quaddominant, meshes into quadonly meshes. 1
Lp Centroidal Voronoi Tessellation and its Applications
 ACM TRANSACTIONS ON GRAPHICS 29, 4 (2010)
, 2010
"... ..."
An Incremental Approach to Feature Aligned Quad Dominant Remeshing
, 2008
"... In this paper we present a new algorithm which turns an unstructured triangle mesh into a quaddominant mesh with edges aligned to the principal directions of the underlying geometry. Instead of computing a globally smooth parameterization or integrating curvature lines along a tangent vector field, ..."
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Cited by 16 (3 self)
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In this paper we present a new algorithm which turns an unstructured triangle mesh into a quaddominant mesh with edges aligned to the principal directions of the underlying geometry. 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. The quaddominant mesh is eventually obtained by dropping the notaligned diagonals from the triangle mesh. A postprocessing 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 very wellsuited, e.g., as CatmullClark Subdivision control meshes.
Global Structure Optimization of Quadrilateral Meshes
"... We introduce a fully automatic algorithm which optimizes the highlevel structure of a given quadrilateral mesh to achieve a coarser quadrangular base complex. Such a topological optimization is highly desirable, since stateoftheart quadrangulation techniques lead to meshes which have an appropria ..."
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Cited by 13 (4 self)
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We introduce a fully automatic algorithm which optimizes the highlevel structure of a given quadrilateral mesh to achieve a coarser quadrangular base complex. Such a topological optimization is highly desirable, since stateoftheart quadrangulation techniques lead to meshes which have an appropriate singularity distribution and an anisotropic element alignment, but usually they are still far away from the highlevel structure which is typical for carefully designed meshes manually created by specialists and used e.g. in animation or simulation. In this paper we show that the quality of the highlevel structure is negatively affected by helical configurations within the quadrilateral mesh. Consequently we present an algorithm which detects helices and is able to remove most of them by applying a novel grid preserving simplification operator (GPoperator) which is guaranteed to maintain an allquadrilateral mesh. Additionally it preserves the given singularity distribution and in particular does not introduce new singularities. For each helix we construct a directed graph in which cycles through the start vertex encode operations to remove the corresponding helix. Therefore a simple graph search algorithm can be performed iteratively to remove as many helices as possible and thus improve the highlevel structure in a greedy fashion. We demonstrate the usefulness of our automatic structure optimization technique by showing several examples with varying complexity. Categories and Subject Descriptors (according to ACM CCS): I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling—Hierarchy and geometric transformations, Curve, surface, solid, and object representations
Almost isometric mesh parameterization through abstract domains
 621–635, July/August 2010. [Online]. Available: http://vcg.isti.cnr.it/Publications/ 2010/PTC10
"... domains ..."
Trivial Connections on Discrete Surfaces
 SGP 2010 / COMPUTER GRAPHICS FORUM
, 2010
"... This paper presents a straightforward algorithm for constructing connections on discrete surfaces that are as smooth as possible everywhere but on a set of isolated singularities with given index. We compute these connections by solving a single linear system built from standard operators. The solut ..."
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Cited by 7 (1 self)
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This paper presents a straightforward algorithm for constructing connections on discrete surfaces that are as smooth as possible everywhere but on a set of isolated singularities with given index. We compute these connections by solving a single linear system built from standard operators. The solution can be used to design rotationally symmetric direction fields with userspecified singularities and directional constraints.
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