Clustering is a classical data analysis technique that is applied to a wide range of applications in the sciences and engineering. For very large data sets, the performance of a clustering alorithm becomes critical. Although clustering has been thoroughly studied over the last decades, little has been done on utilizing modern multi-processor machines to accelerate the analysis process. We propose a scalable clustering technique that benefits from existing parallel computers and networks of workstations. It supports the creation of multiresolution representation for very large geometric data sets. The output of the clustering process can be used for interactive data exploration, useful for view-dependent rendering, user-guided refinement, and progressive transmission.

In order to obtain insight into a complex vector field, it is often necessary to construct a hierarchical representation of the field. One way to construct such a hierarchy is based on grouping vectors together using certain similarity criteria. In this paper, we present a study of a 2D vector field clustering technique that is based on piecewise linear vector field approximations and an extension of a data clustering method called Normalized Cut (NC). Specifically, two steps are taken to implement the extended NC method. First, a similarity measurement for vector data is defined. Second, an eigenproblem solver is used to find the eigenvector used for partitioning. After the construction of first-level clusters, we can obtain a finer-level clustering by recursively applying the same procedure to intermediate clusters. The resulting clusters capture the features around the critical points.

We introduce a novel wavelet decomposition algorithm that makes a number of powerful new surface design operations practical. Wavelets, and hierarchical representations generally, have held promise to facilitate a variety of design tasks in a unified way by approximating results very precisely, thus avoiding a proliferation of undergirding mathematical representations. However, traditional wavelet decomposition is defined from fine to coarse resolution, thus limiting its efficiency for highly precise surface manipulation when attempting to create new non-local editing methods. Our key contribution is the progressive wavelet decomposition algorithm, a generalpurpose coarse-to-fine method for hierarchical fitting, based in this paper on an underlying multiresolution representation called dyadic splines. The algorithm requests input via a generic interval query mechanism, allowing a wide variety of non-local operations to be quickly implemented. The algorithm performs work proportionate to the tiny compressed output size, rather than to some arbitrarily high resolution that would otherwise be required, thus increasing performance by several orders of magnitude. We describe several design operations that are made tractable because of the progressive decomposition. Free-form pasting is a generalization of the traditional control-mesh edit, but for which the shape of the change is completely general and where the shape can be placed using a free-form deformation within the surface domain. Smoothing and roughening operations are enhanced so that an arbitrary loop in the domain specifies the area of effect. Finally, the sculpting effect of moving a tool shape along a path is simulated.

Direct Volume Rendering (DVR) is commonly used to visualize scalar fiends. Quality and significance of rendered images depend on the choice of appropriate transfer functions that assigns optical properties (e.g., color and opacity) to scalar values. We present a method that automatically generates a transfer function based on the topology of a isosurface i.e., a surface representing all locations where the scalar fiend assumes a certain value v, changes. We then generate a transfer fucntion that emphasizes on scalar values around those critical isovalues. Images rendered using the resulting transfer function reveal the fundamental topogical structure of a scalar data set.

Clustering is a classical data analysis technique that is applied to a wide range of applications in the sciences and engineering. For very large data sets, the performance of a clustering algorithm becomes critical. Although clustering has been thoroughly studied over the last decades, little has been done on utilizing modern multi-processor machines to accelerate the analysis process. We propose a scalable clustering technique that benefits from existing parallel computers and networks of workstations. It supports the creation of multiresolution representation for very large geometric data sets. The output of the clustering process can be used for interactive data exploration, useful for view-dependent rendering, user-guided refinement, and progressive transmission.

Multiresolution methods provide a means for representing data at multiple levels of detail. They are typically based on a hierarchical data organization scheme and update rules needed for data value computation. We use a data organization that is based on what we call 'nth-root-of-2' subdivision, where n is the dimension of the data set. The main advantage of 'nth-root-of-2' subdivision, compared to quadtree (n=2) or octree (n=3) organizations, is that the number of vertices is only doubled in each subdivision step instead of multiplied by a factor of 2^n, i.\,e., four or eight, respectively. To update data values we use n-variate B-spline wavelets, which yield better approximations for each level of detail. We develop a lifting scheme for n=2 and n=3 based on the 'nth-root-of-2'-subdivision scheme. We obtain narrow masks that provide a basis for out-of-core techniques as well as view-dependent visualization and adaptive, localized refinement.