Computational geometry is concerned with the design and analysis of algorithms for geometrical problems. In addition, other more practically oriented, areas of computer science— such as computer graphics, computer-aided design, robotics, pattern recognition, and operations research—give rise to problems that inherently are geometrical. This is one reason computational geometry has attracted enormous research interest in the past decade and is a well-established area today. (For standard sources, we refer to the survey article by Lee and Preparata [19841 and to the textbooks by Preparata and Shames [1985] and Edelsbrunner [1987bl.) Readers familiar with the literature of computational geometry will have noticed, especially in the last few years, an increasing interest in a geometrical construct called the Voronoi diagram. This trend can also be observed in combinatorial geometry and in a considerable number of articles in natural science journals that address the Voronoi diagram under different names specific to the respective area. Given some number of points in the plane, their Voronoi diagram divides the plane according to the nearest-neighbor

Voronoi diagrams—a survey of a fundamental geometric data structure

Data mining applications place special requirements on clustering algorithms including: the ability to find clusters embedded in subspaces of high dimensional data, scalability, end-user comprehensibility of the results, non-presumption of any canonical data distribution, and insensitivity to the order of input records. We present CLIQUE, a clustering algorithm that satisfies each of these requirements. CLIQUE identifies dense clusters in subspaces of maximum dimensionality. It generates cluster descriptions in the form of DNF expressions that are minimized for ease of comprehension. It produces identical results irrespective of the order in which input records are presented and does not presume any specific mathematical form for data distribution. Through experiments, we show that CLIQUE efficiently finds accurate cluster in large high dimensional datasets.

/pdf/automatic-subspace-clustering-of-high-dimensional-data-for-541pkakmb5.pdf

Automatic subspace clustering of high dimensional data for data mining applications

This book offers a modern approach to computational geo- metry, an area thatstudies the computational complexity of geometric problems. Combinatorial investigations play an important role in this study.

Algorithms in Combinatorial Geometry

Nature’s hierarchical materials

Solution and mesh generation algorithms for solving the Euler equations on unstructured meshes consisting of triangle and quadrilateral control volumes are presented. Cell-centered and mesh-vertex upwind finite-volume schemes are developed which utilize multi-dimensional monotone linear reconstruction procedures. These algorithms differ from existing algorithms (even on structured meshes). Numerical results in two dimensions are presented.

The design and application of upwind schemes on unstructured meshes

Computing Dirichlet tessellations

Biomimetics, a name coined by Otto Schmitt in the 1950s for the transfer of ideas and analogues from biology to technology, has produced some significant and successful devices and concepts in the past 50 years, but is still empirical. We show that TRIZ, the Russian system of problem solving, can be adapted to illuminate and manipulate this process of transfer. Analysis using TRIZ shows that there is only 12% similarity between biology and technology in the principles which solutions to problems illustrate, and while technology solves problems largely by manipulating usage of energy, biology uses information and structure, two factors largely ignored by technology.

/pdf/biomimetics-its-practice-and-theory-461qgvupu6.pdf

Biomimetics: its practice and theory.

This paper presents the results to date of the RepRap project ??? an ongoing project that has made and distributed freely a replicating rapid prototyper We give the background reasoning that led to the invention of the machine, the selection of the processes that we and others have used to implement it, the designs of key parts of the machine and how these have evolved from their initial concepts and experiments, and estimates of the machine's reproductive success out in the world up to the time of writing (about 4500 machines in two and a half years)

/pdf/reprap-the-replicating-rapid-prototyper-4qhadvdyj6.pdf

Reprap ??? the replicating rapid prototyper

A novel pH- and ionic-strength-sensitive carboxy methyl dextran hydrogel

This paper introduces jumping robots as a means to traverse rough terrain; such terrain can pose problems for traditional wheeled, tracked and legged designs. The diversity of jumping mechanisms found in nature is explored to support the theory that jumping is a desirable ability for a robot locomotion system to incorporate, and then the size-related constraints are determined from first principles. A series of existing jumping robots are presented and their performance summarized. The authors present two new biologically inspired jumping robots, Jollbot and Glumper, both of which incorporate additional locomotion techniques of rolling and gliding respectively. Jollbot consists of metal hoop springs forming a 300 mm diameter sphere, and when jumping it raises its centre of gravity by 0.22 m and clears a height of 0.18 m. Glumper is of octahedral shape, with four 'legs' that each comprise two 500 mm lengths of CFRP tube articulating around torsion spring 'knees'. It is able to raise its centre of gravity by 1.60 m and clears a height of 1.17 m. The jumping performance of the jumping robot designs presented is discussed and compared against some specialized jumping animals. Specific power output is thought to be the performance-limiting factor for a jumping robot, which requires the maximization of the amount of energy that can be stored together with a minimization of mass. It is demonstrated that this can be achieved through optimization and careful materials selection.

https://iopscience.iop.org/article/10.1088/1748-3182/2/3/S01/pdf

Adrian Bowyer

Papers

Computing Dirichlet tessellations

Biomimetics: its practice and theory.

Reprap ??? the replicating rapid prototyper

A novel pH- and ionic-strength-sensitive carboxy methyl dextran hydrogel

Jumping robots: a biomimetic solution to locomotion across rough terrain