Abstract not found

original motion exemplar synthesized detail motion combined motion field original density field final density field Figure 1: Motion field texture synthesis. Given a low-resolution motion field and an input exemplar, we synthesize a high-resolution detailed motion field that resembles the exemplar while follows the local orientation of the low-resolution field. This synthesized detail motion field is then combined with the original low-res motion field to produce the final motion. Our method can produce non-physics-based artistic effects such as fluids with heart-shaped 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 example-based texture synthesis for motion fields. Our

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 user-specified singularities and directional constraints.

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 evenly-spaced 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.

Vector fields are a common concept for the representation of many different kinds of flow phenomena in science and engineering. Topology-based 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 topology-based 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, Space-Time Domain Approaches, Local Methods, and Stochastic and Multi-Field Approaches. Furthermore, we illustrated our review with practical examples for the different approaches.

Abstract—Designing rotational symmetry fields on surfaces is an important task for a wide range of graphics applications. This work introduces a rigorous and practical approach for automatic N-RoSy field design on arbitrary surfaces with user defined field topologies. The user has full control of the number, positions and indices of the singularities (as long as they are compatible with necessary global constraints), the turning numbers of the loops, and is able to edit the field interactively. We formulate N-RoSy field construction as designing a Riemannian metric, such that the holonomy along any loop is compatible with the local symmetry of N-RoSy fields. We prove the compatibility condition using discrete parallel transport. The complexity of N-RoSy field design is caused by curvatures. In our work, we propose to simplify the Riemannian metric to make it flat almost everywhere. This approach greatly simplifies the process and improves the flexibility, such that, it can design N-RoSy fields with single singularity, and mixed-RoSy fields. This approach can also be generalized to construct regular remeshing on surfaces. To demonstrate the effectiveness of our approach, we apply our design system to pen-and-ink sketching and geometry remeshing. Furthermore, based on our remeshing results with high global symmetry, we generate Celtic knots on surfaces directly.

Abstract. We present a novel algorithm for automatic parameterization of tube-like surfaces of arbitrary genus such as the surfaces of knots, trees, blood vessels, neurons, or any tubular graph with a globally consistent stripe texture. Mathematically these surfaces can be described as thickened graphs, and the calculated parameterization stripe will follow either around the tube, along the underlying graph, a spiraling combination of both, or obey an arbitrary texture map whose charts have a 180 degree symmetry. We use the principal curvature frame field of the underlying tube-like surface to guide the creation of a global, topologically consistent stripe parameterization of the surface. Our algorithm extends the QuadCover algorithm and is based, first, on the use of so-called projective vector fields instead of frame fields, and second, on different types of branch points. That does not only simplify the mathematical theory, but also reduces computation time by the decomposition of the underlying stiffness matrices. 1

© ACM, (2012). This is the author's version of the work. It is posted here by permission of ACM for your personal use. Not for redistribution. The definitive version is published in ACM Transactions on Graphics 31{1}, 2012. This article presents an algorithm for learning hatching styles from line drawings. An artist draws a single hatching illustration of a 3D object. Her strokes are analyzed to extract the following per-pixel properties: hatching level (hatching, cross-hatching, or no strokes), stroke orientation, spacing, intensity, length, and thickness. A mapping is learned from input geometric, contextual, and shading features of the 3D object to these hatching properties, using classification, regression, and clustering techniques. Then, a new illustration can be generated in the artist’s style, as follows. First, given a new view of a 3D object, the learned mapping is applied to synthesize target stroke properties for each pixel. A new illustration is then generated by synthesizing hatching strokes according to the target properties.

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 user-specified singularities and directional constraints. Categories and Subject Descriptors (according to ACM CCS): I.3.3 [Computer Graphics]: Picture/Image Generation— Line and curve generation

Many algorithms in texture synthesis, non-photorealistic rendering (hatching), or re-meshing 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 (N-RoSy and N-symmetry 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 paper 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).