Design of time-varying vector fields, i.e., vector fields that can change over time, has a wide variety of important applications
in computer graphics. Existing vector field design techniques do not address time-varying vector fields. In this paper, we present a
framework for the design of time-varying vector fields, both for...
Vector field design has a wide variety of applications in computer
graphics, including texture synthesis, non-photorealistic rendering, fluid and crowd simulation, and shape deformation. This paper addresses the problem of the design of time-varying vector fields on surfaces. The additional time dimension poses a number of unique challenges to the...
Design and control of vector fields is critical for many visualization and graphics tasks such as vector field visualization, fluid simulation, and texture synthesis. The fundamental qualitative structures associated with vector fields are fixed points, periodic orbits, and separatrices. In this paper we provide a new technique that allows for...
In this paper, we introduce a new approach to computing a Morse decomposition of a vector field on a triangulated manifold surface. The basic idea is to convert the input vector field to a piecewise constant (PC) vector field, whose trajectories can be computed using simple geometric rules. To overcome...
Vector field analysis plays a crucial role in many engineering applications, such as weather prediction, tsunami and hurricane study, and airplane and automotive design. Existing vector field analysis techniques focus on individual trajectories such as fixed points, periodic orbits and separatrices which are sensitive to noise and errors introduced by...
Reliable analysis of vector elds is crucial for the rigorous interpretation of the ow data stemming from a wide range of
engineering applications. Morse decomposition of a vector field has proven a useful topological representation that is more numerically stable than previous vector field skeletons. In this paper, we enhance...
The divergence theorem in its usual form applies only to suitably smooth vector fields. For vector fields which are merely piecewise smooth, as is natural at a boundary between regions with different physical properties, one must patch together the divergence theorem applied separately in each region. We give an elegant...
A parametric manifold is a manifold on which all tensor fields depend on an additional parameter, such as time, together with a parametric structure, namely a given (parametric) one‐form field. Such a manifold admits natural generalizations of Lie differentiation, exterior differentiation, and covariant differentiation, all based on a nonstandard action...
A parametric manifold can be viewed as the manifold of orbits of a (regular) foliation of a manifold by means of a family of curves. If the foliation is hypersurface orthogonal, the parametric manifold is equivalent to the one‐parameter family of hypersurfaces orthogonal to the curves, each of which inherits...
Existing topology-based vector field analysis techniques rely on the ability to extract the individual trajectories such as fixed points, periodic orbits and separatrices which are sensitive to noise and errors introduced by simulation and interpolation. This can make such vector field analysis unsuitable for rigorous interpretations. We advocate the use...