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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 ...
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 ...
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.
The graph of this function is shown to the right. Since the graph of an affine(*) function is a line, the graph of a piecewise linear function consists of line segments and rays. The x values (in the above example −3, 0, and 3) where the slope changes are typically called breakpoints, changepoints, threshold values or knots. As in many ...
Signum function = . In mathematics, the sign function or signum function (from signum, Latin for "sign") is a function that has the value −1, +1 or 0 according to whether the sign of a given real number is positive or negative, or the given number is itself zero.
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 ...
Related to approximation of functions is the asymptotic value of a function, i.e. the value as one or more of a function's parameters becomes arbitrarily large. For example, the sum k / 2 + k / 4 + k / 8 + ⋯ + k / 2 n {\displaystyle k/2+k/4+k/8+\cdots +k/2^{n}} is asymptotically equal to k .
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