A wide variety of color schemes have been devised for mapping scalar data to color. Some use the data value to index a color scale. Others assign colors to different, usually blended disjoint materials, to handle areas where materials overlap. A number of methods can map low-dimensional data to color, however, these methods do not scale to higher dimensional data. Likewise, schemes that take a ...

We present two complementary approaches for the visualization and interaction of dimensionally reduced data sets using hybridization interfaces. Our implementations privilege syncretic systems allowing one to explore combinations (hybrids) of disparate elements of a data set through their placement in a 2-D space. The first approach allows for the placement of data points anywhere on the plane ...

We construct the first explicit example of a simplicial 3-ball B15,66 that is not collapsible. It has only 15 vertices. We exhibit a second 3-ball B12,38 with 12 vertices that is collapsible and not shellable, but evasive. Finally, we present the first explicit triangulation of a 3-sphere S18,125 (with only 18 vertices) that is not locally constructible. All these examples are based on knotted ...

This work introduces a novel tool for interactive, real-time transformations of two dimensional IFS fractals. We assign barycentric coordinates (relative to an arbitrary affine basis of R) to the points that constitute the image of a fractal. The tool uses some of the nice properties of the barycentric coordinates, enabling any affine transformation of the basis, done by click-and-drag, to be i...

In this paper, two basic approaches for kinematics modelling of multiple manipulator Space Free-Flying Robots (SFFRs) are developed. In the barycentric vector approach, the center of mass of the whole system is taken as a representative point for the system’s translational motion, and a set of body-fixed vectors which reflect both geometric configuration and mass distribution of the system are ...

Rips complexes are important structures for analyzing topological features of metric spaces. Unfortunately, generating these complexes constitutes an expensive task because of a combinatorial explosion in the complex size. For n points in R, we present a scheme to construct a 3 √ 2approximation of the multi-scale filtration of the L∞-Rips complex, which extends to a O(d0.25)approximation of the...

In 1988 the second author presented experimentally well-conditioned linear rational functions for global interpolation. We give here arrays of nodes for which one of these interpolants converges exponentially for analytic functions Introduction Let f be a complex function defined on an interval I of the real axis and let x0, x1, . . . , xn be n + 1 distinct points of I, which we do not assume e...

We give an easy description of the barycentric extension of a map of the unit circle to the closed unit disk using some ideas from dynamical systems. We then prove that every circle endomorphism of the unit circle of degree db 2 (with a topological expansion condition) has a conformally natural extension to the closed unit disk which is real analytic on the open unit disk. If the endomorphism i...

It is known that every hyperbolic Iterated Function System containing affine mappings can be represented in barycentric form by which it becomes affine invariant. Some properties were surveyed and some new ones were established. Examples of fractal sets supplement the theory.

An efficient algorithm is described for computing the barycentric coordinates of the projection of a point into the plane of a triangle. The method requires no square roots or conditionals, and only one floating point division, making it suitable for both CPU and GPU implementations.