Ruler, Compass and Computer

The term “computational geometry” was originally coined by Robin Forrest[21] to denote the study of computational techniques in the realm of computer-aided design. More recently, this term has been used to name a somewhat different field, in a way broader and in a way narrower than Forrest’s conception, which is considered part of theoretical computer science. This new use of the name “computational geometry,” whose origin can be traced to Shamos,[62] refers to the design and analysis of algorithms for all kinds of geometric problems; it is the sense in which the term will be used in this paper.

[1]  Nimrod Megiddo,et al.  Linear Programming in Linear Time When the Dimension Is Fixed , 1984, JACM.

[2]  L. A. Santaló Introduction to integral geometry , 1953 .

[3]  Leonidas J. Guibas,et al.  Visibility and intersectin problems in plane geometry , 1985, SCG '85.

[4]  Narendra Karmarkar,et al.  A new polynomial-time algorithm for linear programming , 1984, Comb..

[5]  S. Chern Review: Luis A. Santaló, Integral geometry and geometric probability , 1977 .

[6]  L. Santaló Integral geometry and geometric probability , 1976 .

[7]  A. R. Forrest II. Current developments in the design and production of three- dimensional curved objects - Computational geometry , 1971, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[8]  Micha Sharir,et al.  Almost linear upper bounds on the length of general davenport—schinzel sequences , 1987, Comb..

[9]  Kurt Mehlhorn,et al.  Sorting Jordan Sequences in Linear Time Using Level-Linked Search Trees , 1986, Inf. Control..

[10]  Michael Ian Shamos,et al.  Geometric intersection problems , 1976, 17th Annual Symposium on Foundations of Computer Science (sfcs 1976).

[11]  David G. Kirkpatrick,et al.  The Ultimate Planar Convex Hull Algorithm? , 1986, SIAM J. Comput..

[12]  Steven Fortune,et al.  A sweepline algorithm for Voronoi diagrams , 1986, SCG '86.

[13]  Robert E. Tarjan,et al.  Planar point location using persistent search trees , 1986, CACM.

[14]  David G. Kirkpatrick,et al.  Optimal Search in Planar Subdivisions , 1983, SIAM J. Comput..

[15]  R. E. Miles On the homogeneous planar Poisson point process , 1970 .

[16]  Kevin Q. Brown Geometric transforms for fast geometric algorithms , 1979 .

[17]  F. P. Preparata,et al.  Convex hulls of finite sets of points in two and three dimensions , 1977, CACM.

[18]  Micha Sharir,et al.  Planning, geometry, and complexity of robot motion , 1986 .

[19]  Leonidas J. Guibas,et al.  A kinetic framework for computational geometry , 1983, 24th Annual Symposium on Foundations of Computer Science (sfcs 1983).

[20]  Manuel Blum,et al.  Time Bounds for Selection , 1973, J. Comput. Syst. Sci..

[21]  Edward M. McCreight,et al.  Priority Search Trees , 1985, SIAM J. Comput..

[22]  Michael Ian Shamos,et al.  Computational geometry: an introduction , 1985 .

[23]  Ronald L. Graham,et al.  An Efficient Algorithm for Determining the Convex Hull of a Finite Planar Set , 1972, Inf. Process. Lett..

[24]  Leonidas J. Guibas,et al.  Primitives for the manipulation of general subdivisions and the computation of Voronoi diagrams , 1983, STOC.

[25]  Alfred V. Aho,et al.  The Design and Analysis of Computer Algorithms , 1974 .

[26]  Mark J. Post,et al.  A minimum spanning ellipse algorithm , 1981, 22nd Annual Symposium on Foundations of Computer Science (sfcs 1981).

[27]  David G. Kirkpatrick,et al.  Fast Detection of Polyhedral Intersections , 1982, ICALP.

[28]  R. E. Miles RANDOM POLYGONS DETERMINED BY RANDOM LINES IN A PLANE, II. , 1964, Proceedings of the National Academy of Sciences of the United States of America.

[29]  Raimund Seidel,et al.  Constructing arrangements of lines and hyperplanes with applications , 1983, 24th Annual Symposium on Foundations of Computer Science (sfcs 1983).

[30]  Micha Sharir,et al.  On minima of function, intersection patterns of curves, and davenport-schinzel sequences , 1985, 26th Annual Symposium on Foundations of Computer Science (sfcs 1985).

[31]  D. T. Lee,et al.  Computational Geometry—A Survey , 1984, IEEE Transactions on Computers.

[32]  Leonidas J. Guibas,et al.  Computing convolutions by reciprocal search , 1986, SCG '86.

[33]  Leonidas J. Guibas,et al.  A new representation for linear lists , 1977, STOC '77.

[34]  Robert E. Tarjan,et al.  Triangulating a Simple Polygon , 1978, Inf. Process. Lett..

[35]  Thomas Ottmann,et al.  Algorithms for Reporting and Counting Geometric Intersections , 1979, IEEE Transactions on Computers.

[36]  R. Tarjan Amortized Computational Complexity , 1985 .

[37]  Bernard Chazelle,et al.  A theorem on polygon cutting with applications , 1982, 23rd Annual Symposium on Foundations of Computer Science (sfcs 1982).

[38]  Leonidas J. Guibas,et al.  Topologically sweeping an arrangement , 1986, STOC '86.

[39]  Bernard Chazelle,et al.  The power of geometric duality , 1985, BIT Comput. Sci. Sect..

[40]  Micha Sharir,et al.  On the shortest paths between two convex polyhedra , 2018, JACM.

[41]  Leonidas J. Guibas,et al.  Visibility and intersection problems in plane geometry , 1989, Discret. Comput. Geom..

[42]  Robert E. Tarjan,et al.  Making data structures persistent , 1986, STOC '86.

[43]  David G. Kirkpatrick,et al.  A Linear Algorithm for Determining the Separation of Convex Polyhedra , 1985, J. Algorithms.

[44]  Micha Sharir,et al.  Improved lower bounds on the length of Davenport-Schinzel sequences , 1988, Comb..

[45]  Leonidas J. Guibas,et al.  Optimal Shortest Path Queries in a Simple Polygon , 1989, J. Comput. Syst. Sci..

[46]  A. Rényi,et al.  über die konvexe Hülle von n zufällig gewählten Punkten , 1963 .

[47]  Alfred V. Aho,et al.  Data Structures and Algorithms , 1983 .

[48]  Franco P. Preparata,et al.  Plane-sweep algorithms for intersecting geometric figures , 1982, CACM.

[49]  Der-Tsai Lee Proximity and reachability in the plane. , 1978 .

[50]  Andrew Chi-Chih Yao,et al.  A Lower Bound to Finding Convex Hulls , 1981, JACM.

[51]  Nimrod Megiddo,et al.  Linear-Time Algorithms for Linear Programming in R^3 and Related Problems , 1982, FOCS.

[52]  R. E. Miles Probability Distribution of a Network of Triangles (Mary Beth Stearns) , 1969 .

[53]  Raimund Seidel,et al.  Constructing Arrangements of Lines and Hyperplanes with Applications , 1986, SIAM J. Comput..

[54]  Robin Sibson,et al.  Computing Dirichlet Tessellations in the Plane , 1978, Comput. J..

[55]  Takao Asano,et al.  Minimum partition of polygonal regions into trapezoids , 1983, 24th Annual Symposium on Foundations of Computer Science (sfcs 1983).