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23
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 21 (5 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
Integergrid maps for reliable quad meshing
"... Quadrilateral 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. Apa ..."
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Cited by 20 (6 self)
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Quadrilateral 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, stateoftheart techniques suffer from limited reliability on realworld input data, i.e. the determined map might have degeneracies like (local) noninjectivities and consequently often cannot be used directly to generate a quadrilateral mesh. In this paper we propose a
Practical quad mesh simplification
 CG Forum (Eurographics
, 2010
"... In this paper we present an innovative approach to incremental quad mesh simplification, i.e. the task of producing a low complexity quad mesh starting from a high complexity one. The process is based on a novel set of strictly local operations which preserve quad structure. We show how good tessell ..."
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Cited by 19 (6 self)
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In this paper we present an innovative approach to incremental quad mesh simplification, i.e. the task of producing a low complexity quad mesh starting from a high complexity one. The process is based on a novel set of strictly local operations which preserve quad structure. We show how good tessellation quality (e.g. in terms of vertex valencies) can be achieved by pursuing uniform length and canonical proportions of edges and diagonals. The decimation process is interleaved with smoothing in tangent space. The latter strongly contributes to identify a suitable sequence of local modification operations. The method is naturally extended to manage preservation of feature lines (e.g. creases) and varying (e.g. adaptive) tessellation densities. We also present an original TriangletoQuad conversion algorithm that behaves well in terms of geometrical complexity and tessellation quality, which we use to obtain the initial quad mesh from a given triangle mesh.
Simple Quad Domains for Field Aligned Mesh Parametrization
"... Figure 1: (Left) An input mesh of quads induces a cross field with an entangled graph of separatrices defining almost eight thousand domains; (center) the graph is disentangled with small distortion from the input field to obtain just twenty parametrization domains; (right) parametrization is smooth ..."
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Cited by 16 (6 self)
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Figure 1: (Left) An input mesh of quads induces a cross field with an entangled graph of separatrices defining almost eight thousand domains; (center) the graph is disentangled with small distortion from the input field to obtain just twenty parametrization domains; (right) parametrization is smoothed to make it conformal; an example of remeshing from the parametrization. We present a method for the global parametrization of meshes that preserves alignment to a cross field in input while obtaining a parametric domain made of few coarse axisaligned rectangular patches, which form an abstract base complex without Tjunctions. The method is based on the topological simplification of the cross field in input, followed by global smoothing.
Dual Loops Meshing: Quality Quad Layouts on Manifolds
 TO APPEAR IN ACM TOG 31(4)
, 2012
"... We present a theoretical framework and practical method for the automatic construction of simple, allquadrilateral patch layouts on manifold surfaces. The resulting layouts are coarse, surfaceembedded cell complexes well adapted to the geometric structure, hence they are ideally suited as domains ..."
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Cited by 15 (8 self)
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We present a theoretical framework and practical method for the automatic construction of simple, allquadrilateral patch layouts on manifold surfaces. The resulting layouts are coarse, surfaceembedded cell complexes well adapted to the geometric structure, hence they are ideally suited as domains and base complexes for surface parameterization, spline fitting, or subdivision surfaces and can be used to generate quad meshes with a highlevel patch structure that are advantageous in many application scenarios. Our approach is based on the careful construction of the layout graph’s combinatorial dual. In contrast to the primal this dual perspective provides direct control over the globally interdependent structural constraints inherent to quad layouts. The dual layout is built from curvatureguided, crossing loops on the surface. A novel method to construct these efficiently in a geometry and structureaware manner constitutes the core of our approach.
Connectivity Editing for Quadrilateral Meshes
, 2011
"... We propose new connectivity editing operations for quadrilateral meshes with the unique ability to explicitly control the location, orientation, type, and number of the irregular vertices (valence not equal to four) in the mesh while preserving sharp edges. We provide theoretical analysis on what e ..."
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Cited by 12 (2 self)
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We propose new connectivity editing operations for quadrilateral meshes with the unique ability to explicitly control the location, orientation, type, and number of the irregular vertices (valence not equal to four) in the mesh while preserving sharp edges. We provide theoretical analysis on what editing operations are possible and impossible and introduce three fundamental operations to move and reorient a pair of irregular vertices. We argue that our editing operations are fundamental, because they only change the quad mesh in the smallest possible region and involve the fewest irregular vertices (i.e., two). The irregular vertex movement operations are supplemented by operations for the splitting, merging, canceling, and aligning of irregular vertices. We explain how the proposed highlevel operations are realized through graphlevel editing operations such as quad collapses, edge flips, and edge splits. The utility of these mesh editing operations are demonstrated by improving the connectivity of quad meshes generated from stateofart quadrangulation techniques.
DesignDriven Quadrangulation of Closed 3D Curves
"... (a) input curve network (c) pairing and iterative refinement (f) design rendering (b) initial segmentation (d) final quadrangulation and quadmesh (e) designdriven quadrangulation Figure 1: Steps to quadrangulating a design network of closed 3D curves (a) : Closed curves are independently segmented ..."
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Cited by 11 (4 self)
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(a) input curve network (c) pairing and iterative refinement (f) design rendering (b) initial segmentation (d) final quadrangulation and quadmesh (e) designdriven quadrangulation Figure 1: Steps to quadrangulating a design network of closed 3D curves (a) : Closed curves are independently segmented (b) and iteratively paired and refined to capture dominant flowlines as well as overall flowline quality (c); final quadrangulation in green and dense quadmesh (d); quadrangulations are aligned across adjacent cycles to generate a single densely sampled mesh (e), suitable for design rendering and downstream applications (f). We propose a novel, designdriven, approach to quadrangulation of closed 3D curves created by sketchbased or other curve modeling systems. Unlike the multitude of approaches for quadremeshing of existing surfaces, we rely solely on the input curves to both conceive and construct the quadmesh of an artist imagined surface bounded by them. We observe that viewers complete the intended shape by envisioning a dense network of smooth, gradually changing, flowlines that interpolates the input curves. Components of the network bridge pairs of input curve segments with similar orientation and shape. Our algorithm mimics this behavior. It first segments the input closed curves into pairs of matching segments, defining dominant flow line sequences across the surface. It then interpolates the input curves by a network of quadrilateral cycles whose isolines define the desired flow line network. We proceed to interpolate these networks with allquad meshes that convey designer intent. We evaluate our results by showing convincing quadrangulations of complex and diverse curve networks with concave, nonplanar cycles, and validate our approach by comparing our results to artist generated interpolating meshes. 1
Easy Integral Surfaces: A Fast, Quadbased Stream and Path Surface Algorithm
 COMPUTER GRAPHICS FORUM
, 1981
"... Despite the clear benefits that stream and path surfaces bring when visualizing 3D vector fields, their use in both industry and for research has not proliferated. This is due, in part, to the complexity of previous construction algorithms. We introduce a novel algorithm for the construction of stre ..."
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Cited by 11 (7 self)
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Despite the clear benefits that stream and path surfaces bring when visualizing 3D vector fields, their use in both industry and for research has not proliferated. This is due, in part, to the complexity of previous construction algorithms. We introduce a novel algorithm for the construction of stream and path surfaces that is fast, simple and does not rely on any complicated data structures or surface parameterization, thus making it suitable for inclusion into any visualization application. We demonstrate the technique on a series of simulation data sets and show that a number of benefits stem naturally from this approach including: easy timelines and timeribbons, easy stream arrows and easy evenlyspaced flow lines. We also introduce a novel interaction tool called a surface painter in order to address the perceptual challenges associated with visualizing 3D flow. The key to our integral surface generation algorithm’s simplicity is performing local computations on quad primitives.
QuadMesh Generation and Processing: a survey
"... Triangle meshes have been nearly ubiquitous in computer graphics, and a large body of data structures and geometry processing algorithms based on them has been developed in the literature. At the same time, quadrilateral meshes, especially semiregular ones, have advantages for many applications, an ..."
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Cited by 8 (2 self)
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Triangle meshes have been nearly ubiquitous in computer graphics, and a large body of data structures and geometry processing algorithms based on them has been developed in the literature. At the same time, quadrilateral meshes, especially semiregular ones, have advantages for many applications, and significant progress was made in quadrilateral mesh generation and processing during the last several years. In this survey we discuss the advantages and problems of techniques operating on quadrilateral meshes, including surface analysis and mesh quality, simplification, adaptive refinement, alignment with features, parametrization, and remeshing.
State of the Art in Quad Meshing
"... Triangle meshes have been nearly ubiquitous in computer graphics, and a large body of data structures and geometry processing algorithms based on them has been developed in the literature. At the same time, quadrilateral meshes, especially semiregular ones, have advantages for many applications, an ..."
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Cited by 4 (2 self)
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Triangle meshes have been nearly ubiquitous in computer graphics, and a large body of data structures and geometry processing algorithms based on them has been developed in the literature. At the same time, quadrilateral meshes, especially semiregular ones, have advantages for many applications, and significant progress was made in quadrilateral mesh generation and processing during the last several years. In this State of the Art Report, we discuss the advantages and problems of techniques operating on quadrilateral meshes, including surface analysis and mesh quality, simplification, adaptive refinement, alignment with features, parametrization, and remeshing.