منابع مشابه
Measure of Straight Lines and its Applications in Digital Geometry
In digital geometry, objects such as digital straight lines can be considered as equivalent classes of Euclidean straight lines with respect to a digitization process. This paper investigates the analysis of the set of straight lines whose digitization is a given digital straight segment with the help of tools from integral geometry. After a definition of a measure on such sets, we illustrate s...
متن کاملGeometry and construction of straight lines in log-polar images
This paper investigates, how straight lines are mapped to the non-Euclidean log-polar image plane and how their properties in logpolar coordinates can be used to perform two fundamental measurement operations: the construction of straight lines of given orientation angle and the measurement of distances along these lines. It is shown, how the two operations can be efficiently implemented for di...
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lines, pseudolines, polar coordinates, trilinear coordinates, non-linear programming, geometry We present a graph-drawing algorithm which respects extended co-linearity constraints. These are expressed as a set of ‘straight’ paths in a planar graph. Constraints of this sort are translated into a set of inequalities over polar coordinates of lines. These inequalities provide necessary and suffic...
متن کاملCubic pencils of lines and bivariate interpolation
Abstract: Cubic pencils of lines are classified up to projectivities. Explicit formulae for the addition of lines on the set of nonsingular lines of the pencils are given. These formulae can be used for constructing planar generalized principal lattices, which are sets of points giving rise to simple Lagrange formulae in bivariate interpolation. Special attention is paid to the irreducible nons...
متن کاملEuclid’s straight lines
We raise two questions on Euclid’s Elements: How to explain that Propositions 16 and 27 in his first book do not follow, strictly speaking, from his postulates (or are perhaps meaningless)? and: What are the mathematical consequences of the meanings of the term eutheia which we today often prefer to consider as different? The answer to the first question is that orientability is a tacit assumpt...
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ژورنال
عنوان ژورنال: Facta universitatis - series: Architecture and Civil Engineering
سال: 2002
ISSN: 0354-4605,2406-0860
DOI: 10.2298/fuace0204291j