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Since computing the mean line segment length involves calculating multidimensional integrals, various methods for numerical integration can be used to approximate this value for any shape. One such method is the Monte Carlo method. To approximate the mean line segment length of a given shape, two points are randomly chosen in its interior and ...
The line with equation ax + by + c = 0 has slope -a/b, so any line perpendicular to it will have slope b/a (the negative reciprocal). Let (m, n) be the point of intersection of the line ax + by + c = 0 and the line perpendicular to it which passes through the point (x 0, y 0). The line through these two points is perpendicular to the original ...
One of the important properties of this norm, relative to other norms, is that it remains unchanged under arbitrary rotations of space around the origin. [23] By Dvoretzky's theorem , every finite-dimensional normed vector space has a high-dimensional subspace on which the norm is approximately Euclidean; the Euclidean norm is the only norm ...
Above: monochrome screening; below: Gupta-Sproull anti-aliasing; the ideal line is considered here as a surface. In computer graphics, a line drawing algorithm is an algorithm for approximating a line segment on discrete graphical media, such as pixel-based displays and printers. On such media, line drawing requires an approximation (in ...
A closed line segment includes both endpoints, while an open line segment excludes both endpoints; a half-open line segment includes exactly one of the endpoints. In geometry , a line segment is often denoted using an overline ( vinculum ) above the symbols for the two endpoints, such as in AB .
Bresenham's line algorithm is a line drawing algorithm that determines the points of an n-dimensional raster that should be selected in order to form a close approximation to a straight line between two points.
Linear interpolation has been used since antiquity for filling the gaps in tables. Suppose that one has a table listing the population of some country in 1970, 1980, 1990 and 2000, and that one wanted to estimate the population in 1994. Linear interpolation is an easy way to do this.
The boundary of a cell is the system of edges that touch it, and the boundary of an edge is the set of vertices that touch it (one vertex for a ray and two for a line segment). The system of objects of all three types, linked by this boundary operator, form a cell complex covering the plane.