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GeometryAware Direction Field Processing
, 2009
"... Many algorithms in texture synthesis, nonphotorealistic rendering (hatching), or remeshing require to define the orientation of some features (texture, hatches, or edges) at each point of a surface. In early works, tangent vector (or tensor) fields were used to define the orientation of these featur ..."
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Cited by 20 (1 self)
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Many algorithms in texture synthesis, nonphotorealistic rendering (hatching), or remeshing require to define the orientation of some features (texture, hatches, or edges) at each point of a surface. In early works, tangent vector (or tensor) fields were used to define the orientation of these features. Extrapolating and smoothing such fields is usually performed by minimizing an energy composed of a smoothness term and of a data fitting term. More recently, dedicated structures (NRoSy and Nsymmetry direction fields) were introduced in order to unify the manipulation of these fields, and provide control over the field’s topology (singularities). On the one hand, controlling the topology makes it possible to have few singularities, even in the presence of high frequencies (fine details) in the surface geometry. On the other hand, the user has to explicitly specify all singularities, which can be a tedious task. It would be better to let them emerge naturally from the direction extrapolation and smoothing. This article introduces an intermediate representation that still allows the intuitive design operations such as smoothing and directional constraints, but restates the objective function in a way that avoids the singularities yielded by smaller geometric details. The resulting design tool is intuitive, simple, and allows to create fields with simple topology, even in the presence of high geometric frequencies. The generated field can be used to steer global parameterization methods (e.g., QuadCover).
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.
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.
G.: 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
"... Figure 1: Left: An airport terminal model with planar quad faces generated by our conjugate direction field method. The maximum value of the planarity measure (the angular difference in degrees between the sum of four internal angles of a quad face and 360◦) is 0.05◦. Right: A comparison of the plan ..."
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Cited by 14 (1 self)
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Figure 1: Left: An airport terminal model with planar quad faces generated by our conjugate direction field method. The maximum value of the planarity measure (the angular difference in degrees between the sum of four internal angles of a quad face and 360◦) is 0.05◦. Right: A comparison of the planar quad mesh on the roof of this model from the principal curvature network (top) and our method (bottom). Our method allows us to control the layout of the planar quad mesh and reduces the number of singularities (nonfourvalence vertices). 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.
Global parametrization by incremental flattening
 ACM Transactions on Graphics (TOG
, 2012
"... Copyright Notice Permission to make digital or hard copies of part or all of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profi t or direct commercial advantage and that copies show this notice on the fi rst page or initial scree ..."
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Cited by 12 (2 self)
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Copyright Notice Permission to make digital or hard copies of part or all of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profi t or direct commercial advantage and that copies show this notice on the fi rst page or initial screen of a display along with the full citation. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, to republish, to post on servers, to redistribute to lists, or to use any component of this work in other works requires prior specifi c permission and/or a fee. Permissions may be
Motion Field Texture Synthesis
"... original motion exemplar synthesized detail motion combined motion field original density field final density field Figure 1: Motion field texture synthesis. Given a lowresolution motion field and an input exemplar, we synthesize a highresolution detailed motion field that resembles the exemplar w ..."
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Cited by 10 (3 self)
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original motion exemplar synthesized detail motion combined motion field original density field final density field Figure 1: Motion field texture synthesis. Given a lowresolution motion field and an input exemplar, we synthesize a highresolution detailed motion field that resembles the exemplar while follows the local orientation of the lowresolution field. This synthesized detail motion field is then combined with the original lowres motion field to produce the final motion. Our method can produce nonphysicsbased artistic effects such as fluids with heartshaped motions. A variety of animation effects such as herds and fluids contain detailed motion fields characterized by repetitive structures. Such detailed motion fields are often visually important, but tedious to specify manually or expensive to simulate computationally. Due to the repetitive nature, some of these motion fields (e.g. turbulence in fluids) could be synthesized by procedural texturing, but procedural texturing is known for its limited generality. We apply examplebased texture synthesis for motion fields. Our
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 10 (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.
On the Way Towards TopologyBased Visualization of Unsteady Flow  the State of the Art
, 2010
"... Vector fields are a common concept for the representation of many different kinds of flow phenomena in science and engineering. Topologybased methods have shown their convenience for visualizing and analyzing steady flow but a counterpart for unsteady flow is still missing. However, a lot of good a ..."
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Cited by 10 (4 self)
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Vector fields are a common concept for the representation of many different kinds of flow phenomena in science and engineering. Topologybased methods have shown their convenience for visualizing and analyzing steady flow but a counterpart for unsteady flow is still missing. However, a lot of good and relevant work has been done aiming at such a solution. We give an overview of the research done on the way towards topologybased visualization of unsteady flow, pointing out the different approaches and methodologies involved as well as their relation to each other, taking classical (i.e. steady) vector field topology as our starting point. Particularly, we focus on Lagrangian Methods, SpaceTime Domain Approaches, Local Methods, and Stochastic and MultiField Approaches. Furthermore, we illustrated our review with practical examples for the different approaches.
Boundary Aligned Smooth 3D CrossFrame Field
"... Figure 1: Snapshots of the optimization procedure to construct a boundary aligned 3D crossframe field. The top row shows the internal streamlines. The next row contains another visualization with cubes spread by a parameterization along the current crossframe field and rotated by the current local ..."
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Cited by 10 (2 self)
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Figure 1: Snapshots of the optimization procedure to construct a boundary aligned 3D crossframe field. The top row shows the internal streamlines. The next row contains another visualization with cubes spread by a parameterization along the current crossframe field and rotated by the current local frame R(Φ). The corresponding number of iteration is shown at the bottom. In this paper, we present a method for constructing a 3D crossframe field, a 3D extension of the 2D crossframe field as applied to surfaces in applications such as quadrangulation and texture synthesis. In contrast to the surface crossframe field (equivalent to a 4Way RotationalSymmetry vector field), symmetry for 3D crossframe fields cannot be formulated by simple oneparameter 2D rotations in the tangent planes. To address this critical issue, we represent the 3D frames by spherical harmonics, in a manner invariant to combinations of rotations around any axis by multiples of π/2. With such a representation, we can formulate an efficient smoothness measure of the crossframe field. Through minimization of this measure under certain boundary conditions, we can construct a smooth 3D crossframe field that is aligned with the surface normal at the boundary. We visualize the resulting crossframe field through restrictions to the boundary surface, streamline tracing in the volume, and singularities. We also demonstrate the application of the 3D crossframe field to producing hexahedrondominant meshes for given volumes, and discuss its potential in highquality hexahedralization, much as its 2D counterpart has shown in quadrangulation.