Roland Kunkli

Skinning of circles and spheres

Skinning of an ordered set of discrete circles is discussed in this paper. By skinning we mean the geometric construction of two G^1 continuous curves touching each of the circles at a point, separately. After precisely defining the admissible configuration of initial circles and the desired geometric properties of the skin, we construct the touching points and tangents of the skin by applying classical geometric methods, like cyclography and the ancient problem of Apollonius, finding touching circles of three given circles. Comparing the proposed method to a recent technique (Slabaugh et al., 2008, 2010), larger class of admissible data set and fast computation are the main advantages. Spatial extension of the problem for skinning of spheres by a surface is also discussed in detail.

Isoptics of Bézier curves

Given a planar curve s(t), the locus of those points from which the curve can be seen under a fixed angle is called isoptic curve of s(t). Isoptics are well-known and widely studied, especially for some classical curves such as e.g. conics (Loria, 1911). They can theoretically be computed for a large class of parametric curves by the help of their support functions or by direct computation based on the definition, but unfortunately these computations are extremely complicated even for simple curves. Our purpose is to describe the isoptics of those curves which are still frequently used in geometric modeling - the Bezier curves. It turns out that for low degree Bezier curves the direct computation is possible, but already for degree 4 or 5 the formulas are getting too complicated even for computer algebra systems. Thus we provide a new way to solve the problem, proving some geometric relations of the curve and their isoptics, and computing the isoptics as the envelope of envelopes of families of isoptic circles over the chords of the curve.

KSpheres - an efficient algorithm for joining skinning surfaces

Besides classical point based surface design, sphere based creation of characters and other surfaces has been introduced by some of the recently developed modeling tools in computer graphics. ZSpheres? by Pixologic, or Spore? by Electronic Arts are just two prominent examples of these softwares. In this paper we introduce a new sphere based modeling tool, which allows us to create smooth, tubular-like surfaces by skinning a user-defined set of spheres. The main advantage of the new method is to provide a parametric surface with more natural and smoother shape, especially at the connection of branches than the surfaces provided by the existing softwares and methods.

TabularVis - a Circos-inspired interactive web client based tool for improving the clarity of tabular data visualization.

Table visualization is one of the earliest problems in the field of data visualization, and there are many applications which provide different solutions to this task. One of the most popular ones is Circos, a well-known genome visualization software package based on the so-called circular layout technique. In this work, we present an interactive web-based visualization tool inspired by Circos’ table viewer web application, in which we provide new extensions and techniques beyond its existing main ideas, for improving the clarity of the generated visualization. One of them is making the links easier to follow by giving an automatic solution to reduce the number of intersections between the links. We also present different tools which could be particularly useful in such situations, in which the table’s data induce extreme scatter, i.e., the difference between the data is significantly large or small. Our proposed visualization accepts tables with non-negative numbers, and the amount of efficiently displayable data depends on the number of zeros in the table. In the paper, besides describing our contributions in detail, we also compare the outputs of our method and Circos table viewer to confirm the legitimacy of our application and the implemented techniques it contains.

New algorithm to find isoptic surfaces of polyhedral meshes

Abstract The isoptic surface of a three-dimensional shape is recently defined by Csima and Szirmai (2016) as the generalization of the well-known notion of isoptics of curves. In that paper, an algorithm has also been presented to determine isoptic surfaces of convex polyhedra. However, the computation of isoptic surfaces by that algorithm requires extending computational time and CAS resources (in Csima and Szirmai, 2016 Wolfram Mathematica Inc, 2015 was used), even for simple regular polyhedra. Moreover, the method cannot be extended to concave shapes. In this paper, we present a new searching algorithm to find points of the isoptic surface of a triangulated model in E 3 , which works for convex and concave polyhedral meshes as well. Alternative definition of the isoptic surface of a shape is also presented, and isoptic surfaces are computed based on this new approach as well.