A new free-form deformation technique is presented that generalizes previous methods by allowing 3-dimensional deformation lattices of arbitrary topology. The technique uses an extension of the Catmull-Clark subdivision methodology that successively refines a 3-dimensional lattice into a sequence of lattices that converge uniformly to a region of 3-dimensional space. Deformation of the lattice then implicitly defines a deformation of the space. An underlying model can be deformed by establishing positions of the points of the model within the converging sequence of lattices and then tracking the new positions of these points within the deformed sequence of lattices. This technique allows a greater variety of deformable regions to be defined, and thus a broader range of shape deformations can be generated.

A system for the creation of computer-generated sound patterns of two-dimensional line graphs is described. The objectives of the system are to provide the blind with a means of understanding line graphs in the holistic manner used by those with sight. A continuously varying pitch is used to represent motion in the x direction. To test the feasibility of using sound to represent graphs, a prototype system was developed and human factors experimenters were performed. Fourteen subjects were used to compare the tactile-graph methods normally used by the blind to these new sound graphs. It was discovered that mathematical concepts such as symmetry, monotonicity, and the slopes of lines could be determined quickly using sound. Even better performance may be expected with additional training. The flexibility, speed, cost-effectiveness, and greater measure of independence provided the blind or sight-impaired using these methods was demonstrated.

We present a new construction of lifted biorthogonal wavelets on surfaces of arbitrary two-manifold topology for compression and multiresolution representation. Our method combines three approaches: subdivision surfaces of arbitrary topology, B-spline wavelets, and the lifting scheme for biorthogonal wavelet construction. The simple building blocks of our wavelet transform are local lifting operations performed on polygonal meshes with subdivision hierarchy. Starting with a coarse, irregular polyhedral base mesh, our transform creates a subdivision hierarchy of meshes converging to a smooth limit surface. At every subdivision level, geometric detail can be expanded from wavelet coefficients and added to the surface. We present wavelet constructions for bilinear, bicubic, and biquintic B-Spline subdivision. While the bilinear and bicubic constructions perform well in numerical experiments, the biquintic construction turns out to be unstable. For lossless compression, our transform can be computed in integer arithmetic, mapping integer coordinates of control points to integer wavelet coefficients. Our approach provides a highly efficient and progressive representation for complex geometries of arbitrary topology.

Fig. 1. A path surface generated from a turbulent jet dataset, rendered in two different styles using the framework proposed in this paper. In the left image, the surface is opaque, and the front and back side are rendered with yellow and blue, respectively. An adaptive stripe pattern visualizes individual pathlines on the surface and provides the orientation of the flow. On the right, the surface is rendered transparently with a denser stripes to give a hatching-like appearance. Both figures emphasize surface silhouettes for better distinction of individual surface layers.Abstract-Integral surfaces are ideal tools to illustrate vector fields and fluid flow structures. However, these surfaces can be visually complex and exhibit difficult geometric properties, owing to strong stretching, shearing and folding of the flow from which they are derived. Many techniques for non-photorealistic rendering have been presented previously. It is, however, unclear how these techniques can be applied to integral surfaces. In this paper, we examine how transparency and texturing techniques can be used with integral surfaces to convey both shape and directional information. We present a rendering pipeline that combines these techniques aimed at faithfully and accurately representing integral surfaces while improving visualization insight. The presented pipeline is implemented directly on the GPU, providing real-time interaction for all rendering modes, and does not require expensive preprocessing of integral surfaces after computation.