• Corpus ID: 117982550

Problems in computational geometry

  title={Problems in computational geometry},
  author={Michael Ian Shamos},

- 1-Solving Geometric Problems with the Rotating Calipers *

This paper shows that the diameter of a convex n-sided polygon could be computed in O(n) time using a very elegant and simple procedure which resembles rotating a set of calipers around the polygon once, and that this simple idea can be generalized in two ways.

Convexity preserving deformations of digital sets: Characterization of removable and insertable pixels

In this paper, we are interested in digital convexity. This notion is applied in several domains like image processing and discrete tomography. We choose to study the inflation and deflation of

Peeling Sequences

Given an n-element point set in the plane, in how many ways can it be peeled off until no point remains? Only one extreme point can be removed at a time. The answer obviously depends on the point

Largest and smallest area triangles on imprecise points

Maximum-Area Triangle in a Convex Polygon, Revisited

Medial axis: an application to selectivelaser manufacturing

Selective laser melting, which is based on the principle of material incremental manufacturing, has been recognised as a promising additive manufacturing technology. The technology is suited for

The Largest Contained Quadrilateral and the Smallest Enclosing Parallelogram of a Convex Polygon

We present a linear-time algorithm for finding the quadrilateral of largest area contained in a convex polygon, and we show that it is closely related to an old algorithm for the smallest enclosing

Multi-GPU parallelization of a dynamic heat transfer model on the Moon

Thermal models in aerospace engineering are constantly growing in complexity to achieve increasingly accurate results and improve safety and equipment design efficiency. One such model is the Thermal

Caging Polygonal Objects Using Formationally Similar Three-Finger Hands

The problem of computing the critical cage formation that allows the object to escape the hand is reduced to a search along a caging graph constructed in the hand's contact space, which determines the caging regions surrounding the immobilizing grasp.



Spatial Analysis in Archaeology

Preface 1. Introduction 2. Archaeological distribution maps: a quantified approach and associated problems 3. Point pattern analysis 4. Some models for settlement patterns 5. The distribution of

Layout, Interconnection, and Placement

  • M. Hanan
  • Computer Science, Mathematics
  • 1975

Helly's theorems on convex domains and Tchebycheff's approximation problem

Professor Dresden called to our attention the following theorem : If S1, S2, … , Sm are m line segments parallel to the y-axis, all of equal lengths, whose projections on the x-axis are equally

Computer implementation of the finite element method

A detailed study of the implementation of finite element methods for solving two-dimensional elliptic partial differential equations shows that much of the manipulation of the basis functions necessary in the derivation of the approximation equations can be done semi-symbolically rather than numerically as is usually done.

The Minimum Covering Sphere Problem

A finite decomposition algorithm, based on the Simplex method of quadratic programming, is developed for which computer storage requirements are independent of the number of points and computing time is approximately linear in the numberof points.

The convex hull of a random set of points

SUMMARY Various expectations concerning the convex hull of N independently and identically distributed random points in the plane or in space are evaluated. Integral expressions are given for the