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Distance covered is the area under the line. Each time interval is coloured differently. The distance covered in the second and subsequent intervals is the area of its trapezium, which can be subdivided into triangles as shown. As each triangle has the same base and height, they have the same area as the triangle in the first interval.
One of the sensors is typically a digital camera device, and the other one can also be a camera or a light projector. The projection centers of the sensors and the considered point on the object's surface define a (spatial) triangle. Within this triangle, the distance between the sensors is the base b and must be known. By determining the ...
The modern systematic use of triangulation networks stems from the work of the Dutch mathematician Willebrord Snell, who in 1615 surveyed the distance from Alkmaar to Breda, approximately 72 miles (116 kilometres), using a chain of quadrangles containing 33 triangles in all. Snell underestimated the distance by 3.5%.
The Möller–Trumbore ray-triangle intersection algorithm, named after its inventors Tomas Möller and Ben Trumbore, is a fast method for calculating the intersection of a ray and a triangle in three dimensions without needing precomputation of the plane equation of the plane containing the triangle. [1]
The most well-established method for the inhomogeneous (source-related) descriptive equations of wave motion is one based on the Green's function technique. [4] For the circumstances described in Section 6.4 and Chapter 14 of Jackson's Classical Electrodynamics , [ 4 ] it can be reduced to calculation of the wave field via retarded potentials ...
Done naïvely, this will take O(n) time: we search through all the triangles to find the one that contains v, then we potentially flip away every triangle. Then the overall runtime is O( n 2 ) . If we insert vertices in random order, it turns out (by a somewhat intricate proof) that each insertion will flip, on average, only O(1) triangles ...
There is no accepted or widely-used general term for what is termed true-range multilateration here . That name is selected because it: (a) is an accurate description and partially familiar terminology (multilateration is often used in this context); (b) avoids specifying the number of ranges involved (as does, e.g., range-range; (c) avoids implying an application (as do, e.g., DME/DME ...
One way to determine the set of locations of D for which the ∠ADB angle is equal to 120° is to draw an equilateral ABE triangle (because each angle of an equilateral triangle is equal to 60°), where E is located outside the ABC triangle, and draw a circle round that triangle; then all the D' points of the circumference of that circle that ...