Vector field design on surfaces is necessary for many graphics applications: example-based texture synthesis, nonphotorealistic rendering, and fluid simulation. For these applications, singularities contained in the input vector field often cause visual artifacts. In this article, we present a vector field design system that allows the user to create a wide variety of vector fields with control over vector field topology, such as the number and location of singularities. Our system combines basis vector fields to make an initial vector field that meets user specifications.The initial vector field often contains unwanted singularities. Such singularities cannot always be eliminated due to the Poincaré-Hopf index theorem. To reduce the visual artifacts caused by these singularities, our system allows the user to move a singularity to a more favorable location or to cancel a pair of singularities. These operations offer topological guarantees for the vector field in that they only affect user-specified singularities. We develop efficient implementations of these operations based on Conley index theory. Our system also provides other editing operations so that the user may change the topological and geometric characteristics of the vector field.To create continuous vector fields on curved surfaces represented as meshes, we make use of the ideas of geodesic polar maps and parallel transport to interpolate vector values defined at the vertices of the mesh. We also use geodesic polar maps and parallel transport to create basis vector fields on surfaces that meet the user specifications. These techniques enable our vector field design system to work for both planar domains and curved surfaces.We demonstrate our vector field design system for several applications: example-based texture synthesis, painterly rendering of images, and pencil sketch illustrations of smooth surfaces. 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 profit or direct commercial advantage and that copies show this notice on the first 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 specific permission and/or a fee. Permissions may be requested from Publications Dept., ACM, Inc., 2 Penn Plaza, Suite 701, New York, NY 10121-0701 USA, fax +1 ( . In nonphotorealistic rendering, vector fields are used to guide the orientation of brush strokes [Hertzmann 1998] and hatches [Hertzmann and Zorin 2000]. In fluid simulation, the external force is a vector field which need not correspond to any physical phenomenon and can exist on synthetic 3D surfaces [Stam 2003]. A vector field design system enables these applications to achieve many different visual effe...

Figure 1: High quality all-hex meshes of complex shapes automatically generated by our method and the PolyCubes we compute to create them. For the kiss both fine and coarse meshes are shown. AbstractWhile hexahedral mesh elements are preferred by a variety of simulation techniques, constructing quality all-hex meshes of general shapes remains a challenge. An attractive hex-meshing approach, often referred to as submapping, uses a low distortion mapping between the input model and a PolyCube (a solid formed from a union of cubes), to transfer a regular hex grid from the PolyCube to the input model. Unfortunately, the construction of suitable PolyCubes and corresponding volumetric maps for arbitrary shapes remains an open problem. Our work introduces a new method for computing low-distortion volumetric PolyCube deformations of general shapes and for subsequent all-hex remeshing. For a given input model, our method simultaneously generates an appropriate PolyCube structure and mapping between the input model and the PolyCube. From these we automatically generate good quality all-hex meshes of complex natural and man-made shapes.

Surface parameterization is necessary for many graphics tasks: texture-preserving simplification, remeshing, surface painting, and precomputation of solid textures. The stretch caused by a given parameterization determines the sampling rate on the surface. In this article, we present an automatic parameterization method for segmenting a surface into patches that are then flattened with little stretch.Many objects consist of regions of relatively simple shapes, each of which has a natural parameterization. Based on this observation, we describe a three-stage feature-based patch creation method for manifold surfaces. The first two stages, genus reduction and feature identification, are performed with the help of distance-based surface functions. In the last stage, we create one or two patches for each feature region based on a covariance matrix of the feature's surface points.To reduce stretch during patch unfolding, we notice that stretch is a 2 × 2 tensor, which in ideal situations is the identity. Therefore, we use the Green-Lagrange tensor to measure and to guide the optimization process. Furthermore, we allow the boundary vertices of a patch to be optimized by adding scaffold triangles. We demonstrate our feature-based patch creation and patch unfolding methods for several textured models.Finally, to evaluate the quality of a given parameterization, we describe an image-based error measure that takes into account stretch, seams, smoothness, packing efficiency, and surface visibility.

The Planteome project (http://www.planteome.org) provides a suite of reference and species-specific ontologies for plants and annotations to genes and phenotypes. Ontologies serve as common standards for semantic integration of a large and growing corpus of plant genomics, phenomics and genetics data. The reference ontologies include the Plant Ontology, Plant Trait Ontology and the Plant Experimental Conditions Ontology developed by the Planteome project, along with the Gene Ontology, Chemical Entities of Biological Interest, Phenotype and Attribute Ontology, and others. The project also provides access to species-specific Crop Ontologies developed by various plant breeding and research communities from around the world. We provide integrated data on plant traits, phenotypes, and gene function and expression from 95 plant taxa, annotated with reference ontology terms. The Planteome project is developing a plant gene annotation platform; Planteome Noctua, to facilitate community engagement. All the Planteome ontologies are publicly available and are maintained at the Planteome GitHub site (https://github.com/Planteome) for sharing, tracking revisions and new requests. The annotated data are freely accessible from the ontology browser (http://browser.planteome.org/amigo) and our data repository.

At the core of our analysis and design implementations is the observation that N-way rotational symmetries can be described by symmetric N-th order tensors, which allows an efficient vector-based representation that not only supports coherent definitions of arithmetic operations on rotational symmetries but also enables many analysis and design operations for vector fields to be adapted to rotational symmetry fields.To demonstrate the effectiveness of our approach, we apply our design system to pen-and-ink sketching and geometry remeshing.

No abstract

Figure 1: This figure shows the three steps of our pipeline. The input water map is based on a stretch of the Benue River in Nigeria. Left: Starting from topographical water and park maps, the user designs a tensor field. Middle: The tensor field and further editing operations are used to generate a road network. Right: Three-dimensional geometry is created. AbstractThis paper addresses the problem of interactively modeling large street networks. We introduce an intuitive and flexible modeling framework in which a user can create a street network from scratch or modify an existing street network. This is achieved through designing an underlying tensor field and editing the graph representing the street network. The framework is intuitive because it uses tensor fields to guide the generation of a street network. The framework is flexible because it allows the user to combine various global and local modeling operations such as brush strokes, smoothing, constraints, noise and rotation fields. Our results will show street networks and three-dimensional urban geometry of high visual quality.

We introduce a novel, automatic streamline seeding algorithm for vector fields defined on surfaces in 3D space.