Saeed Jafaripour; Zahra Nilforoushan; Keivan Borna
Abstract
Deciding whether a musical rhythm is good or not, depends on many factors like geographical conditions of a region, culture, the mood of society, the view of rhythm over years, and so on. In this paper, we want to make a decision from the scientific point of view, using geometric features of rhythms, ...
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Deciding whether a musical rhythm is good or not, depends on many factors like geographical conditions of a region, culture, the mood of society, the view of rhythm over years, and so on. In this paper, we want to make a decision from the scientific point of view, using geometric features of rhythms, about bad ones. The researchers who are investigating the relationship between geometry and music, certainly realize that there is a big vacuum in this regard, not using computers to detect a good or bad rhythm. Here, using computer programming and applying geometric features to more than four thousand rhythms, we decide on the bad musical rhythms. Then we present algorithms for deciding about bad rhythms using geometrical features.
Keivan Borna
Abstract
Convex hull of some given points is the intersection of all convex sets containing them. It is used as primary structure in many other problems in computational geometry and other areas like image processing, model identification, geographical data systems, and triangular computation of a set of points ...
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Convex hull of some given points is the intersection of all convex sets containing them. It is used as primary structure in many other problems in computational geometry and other areas like image processing, model identification, geographical data systems, and triangular computation of a set of points and so on. Computing the convex hull of a set of point is one of the most fundamental and important problems of computational geometry. In this paper a new algorithm is presented for computing the convex hull of a set of random points in the plane by using a sweep-line strategy. The sweep-line is a horizontal line that is moved from top to bottom on a map of points. Our algorithm is optimal and has time complexity $O(nlogn)$ where $n$ is the size of input.