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100
Lp Centroidal Voronoi Tessellation and its Applications
 ACM TRANSACTIONS ON GRAPHICS 29, 4 (2010)
, 2010
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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.
A wavebased anisotropic quadrangulation method
 ACM TRANS. GRAPH
, 2010
"... This paper proposes a new method for remeshing a surface into anisotropically sized quads. The basic idea is to construct a special standing wave on the surface to generate the global quadrilateral structure. This wave based quadrangulation method is capable of controlling the quad size in two dir ..."
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Cited by 16 (3 self)
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This paper proposes a new method for remeshing a surface into anisotropically sized quads. The basic idea is to construct a special standing wave on the surface to generate the global quadrilateral structure. This wave based quadrangulation method is capable of controlling the quad size in two directions and precisely aligning the quads with feature lines. Similar to the previous methods, we augment the input surface with a vector field to guide the quad orientation. The anisotropic size control is achieved by using two size fields on the surface. In order to reduce singularity points, the size fields are optimized by a new curl minimization method. The experimental results show that the proposed method can successfully handle various quadrangulation requirements and complex shapes, which is difficult for the existing stateoftheart methods.
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.
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 15 (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.
Designing unreinforced masonry models
 ACM Trans. Graph
, 2013
"... Figure 1: An input surface is automatically transformed into a masonry 3D model using our algorithm. The equilibrium of the surface is represented by two planar graphs that encode the directions and magnitudes of all forces. The generated blocks are 3Dprinted and assembled into a physical model of ..."
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Cited by 15 (4 self)
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Figure 1: An input surface is automatically transformed into a masonry 3D model using our algorithm. The equilibrium of the surface is represented by two planar graphs that encode the directions and magnitudes of all forces. The generated blocks are 3Dprinted and assembled into a physical model of the surface that stands in compression without using glue or reinforcements. We present a complete design pipeline that allows nonexpert users to design and analyze masonry structures without any structural knowledge. We optimize the force layouts both geometrically and topologically, finding a selfsupported structure that is as close as possible to a given target surface. The generated structures are tessellated into hexagonal blocks with a pattern that prevents sliding failure. The models can be used in physically plausible virtual environments or 3D printed and assembled without reinforcements.
General planar quadrilateral mesh design using conjugate direction field
 C○ 2013 THE AUTHOR(S) C○ 2013 THE EUROGRAPHICS ASSOCIATION AND BLACKWELL PUBLISHING LTD. ID: PAPER1067
"... We present a novel method to approximate a freeform shape with a planar quadrilateral (PQ) mesh for modeling architectural glass structures. Our method is based on the study of conjugate direction fields (CDF) which allow the presence of ±k/4(k ∈ Z) singularities. Starting with a triangle discreti ..."
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Cited by 14 (2 self)
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We present a novel method to approximate a freeform shape with a planar quadrilateral (PQ) mesh for modeling architectural glass structures. Our method is based on the study of conjugate direction fields (CDF) which allow the presence of ±k/4(k ∈ Z) singularities. Starting with a triangle discretization of a freeform shape, we first compute an as smooth as possible conjugate direction field satisfying the user’s directional and angular constraints, then apply mixedinteger quadrangulation and planarization techniques to generate a PQ mesh which approximates the input shape faithfully. We demonstrate that our method is effective and robust on various 3D models.