Showing papers on "Computational geometry published in 1975"
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05 May 1975
TL;DR: An effort is made to recast classical theorems into a useful computational form and analogies are developed between constructibility questions in Euclidean geometry and computability questions in modern computational complexity.
Abstract: The complexity of a number of fundamental problems in computational geometry is examined and a number of new fast algorithms are presented and analyzed. General methods for obtaining results in geometric complexity are given and upper and lower bounds are obtained for problems involving sets of points, lines, and polygons in the plane. An effort is made to recast classical theorems into a useful computational form and analogies are developed between constructibility questions in Euclidean geometry and computability questions in modern computational complexity.
287 citations
TL;DR: In this paper, a new design procedure for coupled parallel microstrip lines is presented, which enables the geometry of the coupled lines to be obtained directly from the required even and odd-mode impedances and uses single microstrip-line geometry as an intermediate step.
Abstract: Although graphical results and formulas are available for the design of microstrip couplers, the design procedure is hampered because even- and odd-mode impedances are always expressed in terms of the physical geometry. In practice the designer obtains these impedances and then requires to know the geometry given by them. A new design procedure for coupled parallel microstrip lines is therefore presented. The technique enables the geometry of the coupled lines to be obtained directly from the required even- and odd-mode impedances and uses single microstrip-line geometry as an intermediate step. The results are presented in graphical form using only two universal families of curves. Results are also presented in the form of simple formulas for design programs and also comparisons with practical results are made.
119 citations
19 May 1975
TL;DR: This paper identifies some problems of modelling free-form geometry in a computer, and discusses attributes of a good model and good parameters for a model, interested in representing arbitrary shape information.
Abstract: This paper identifies some problems of modelling free-form geometry in a computer, and discusses attributes of a good model and good parameters for a model. In particular, we are interested in representing arbitrary shape information, shapes that may not have special names and may not be well defined except at particular points (or curves) of interest occasionally referred to as "hard points" or "hard constraints." There may remain considerable freedom in modelling the "soft points" or "soft constraints." Paradigms of this problem include modelling an automobile fender, a shoe last, or a boat hull. This is an aspect of an area that Forrest calls computational geometry.
14 citations