On Some Remarkable Points and Line Segments in Triangles

Finding Segments and Triangles Spanned by Points in R3

Proximity Problems on Line Segments Spanned by Points

Finding the closest or farthest line segment (line) from a point are fundamental proximity problems. Given a set S of n points in the plane and another point q, we present optimal O(n logn) time, O(n) space algorithms for finding the closest and farthest line segments (lines) from q among those spanned by the points in S. We further show how to apply our techniques to find the minimum (maximum)...

Some notes on digital triangles

On Indexing Line Segments

In several image applications, it is necessary to retrieve specific line segments born a potentially very large set. In this paper, we consider the problem of indexing straight line segments to enable efficient retrieval of all line segments that (i) go through a specified point, or (ii) intersect a specified line segment. We propose a data organization, based on the Hough transform, that can b...

Grouping Edge Points into Line Segments by Sequential Hough Transformation

An algorithm to group edge points into digital line segments with Hough transformation is described in this paper. The edge points are mapped onto the parameter domain discretized at specific intervals, on which peaks appear to represent different line segments. By modeling each peak as a Gaussian function in the parameter domain, a region, to which the edge points are supposed to be mapped, is...