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Circle grid analysis (CGA), also known as circle grid strain analysis, is a method of measuring the strain levels of sheet metal after a part is formed by stamping or drawing. The name itself is a fairly accurate description of the process. Literally, a grid of circles of known diameter is etched to the surface of the sheet metal to be formed ...
Gauss's circle problem asks how many points there are inside this circle of the form (,) where and are both integers. Since the equation of this circle is given in Cartesian coordinates by x 2 + y 2 = r 2 {\displaystyle x^{2}+y^{2}=r^{2}} , the question is equivalently asking how many pairs of integers m and n there are such that
The most efficient way to pack different-sized circles together is not obvious. In geometry, circle packing is the study of the arrangement of circles (of equal or varying sizes) on a given surface such that no overlapping occurs and so that no circle can be enlarged without creating an overlap.
For example, one might want to find the nearest hospital or the most similar object in a database. A large application is vector quantization , commonly used in data compression . In geometry , Voronoi diagrams can be used to find the largest empty circle amid a set of points, and in an enclosing polygon; e.g. to build a new supermarket as far ...
An illustration of Monte Carlo integration. In this example, the domain D is the inner circle and the domain E is the square. Because the square's area (4) can be easily calculated, the area of the circle (π*1.0 2) can be estimated by the ratio (0.8) of the points inside the circle (40) to the total number of points (50), yielding an approximation for the circle's area of 4*0.8 = 3.2 ≈ π.
The related circle packing problem deals with packing circles, possibly of different sizes, on a surface, for instance the plane or a sphere. The counterparts of a circle in other dimensions can never be packed with complete efficiency in dimensions larger than one (in a one-dimensional universe, the circle analogue is just two points). That is ...
The TIN model was developed in the early 1970s as a simple way to build a surface from a set of irregularly spaced points. The first triangulated irregular network program for GIS was written by W. Randolph Franklin, under the direction of David Douglas and Thomas Peucker (Poiker), at Canada's Simon Fraser University, in 1973. [2]
For example, a single-threaded serial version would only need to cache interpolated results for one row of the input grid. It is also possible to reduce the size of the output by using indexed geometric primitives, i.e. create an array of 2D vertices and specify lines or polygons with short integer offsets into the array.