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In the theory of three-dimensional rotation, Rodrigues' rotation formula, named after Olinde Rodrigues, is an efficient algorithm for rotating a vector in space, given an axis and angle of rotation. By extension, this can be used to transform all three basis vectors to compute a rotation matrix in SO(3) , the group of all rotation matrices ...
It is possible to enumerate boxes of this kind in linear time with the approach called rotating calipers by Godfried Toussaint in 1983. [2] The same approach is applicable for finding the minimum-perimeter enclosing rectangle. [2] A C++ implementation of the algorithm that is robust against floating point errors is available. [3]
The rotating calipers technique for designing geometric algorithms may also be interpreted as a form of the plane sweep, in the projective dual of the input plane: a form of projective duality transforms the slope of a line in one plane into the x-coordinate of a point in the dual plane, so the progression through lines in sorted order by their ...
In computational geometry, the method of rotating calipers is an algorithm design technique that can be used to solve optimization problems including finding the width or diameter of a set of points. The method is so named because the idea is analogous to rotating a spring-loaded vernier caliper around the outside of a convex polygon . [ 1 ]
The lower half of this figure is a magnification of the upper half, showing how the apparent sharpness of the left-hand line is created. Bicubic interpolation causes overshoot, which increases acutance. The bicubic algorithm is frequently used for scaling images and video for display (see bitmap resampling).
In the common case where source is defined by some simple function, such as the integers from 0 to n − 1, source may simply be replaced with the function. To initialize an array a[] of n elements to a randomly shuffled copy of source[], both 0-based: for i from 0 to n − 1 do j ← random integer such that 0 ≤ j ≤ i a[i] ← source[i] a ...
The following JavaScript implementation takes a data set and produces a monotone cubic spline interpolant function: /* * Monotone cubic spline interpolation * Usage example listed at bottom; this is a fully-functional package.
In computer graphics, the centripetal Catmull–Rom spline is a variant form of the Catmull–Rom spline, originally formulated by Edwin Catmull and Raphael Rom, [1] which can be evaluated using a recursive algorithm proposed by Barry and Goldman. [2]