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This formula generalizes Heron's formula for the area of a triangle. A triangle may be regarded as a quadrilateral with one side of length zero. From this perspective, as d approaches zero, a cyclic quadrilateral converges into a cyclic triangle (all triangles are cyclic), and Brahmagupta's formula simplifies to Heron's formula.
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 ...
A triangle with sides a, b, and c. In geometry, Heron's formula (or Hero's formula) gives the area of a triangle in terms of the three side lengths , , . Letting be the semiperimeter of the triangle, = (+ +), the area is [1]
Shoelace scheme for determining the area of a polygon with point coordinates (,),..., (,). The shoelace formula, also known as Gauss's area formula and the surveyor's formula, [1] is a mathematical algorithm to determine the area of a simple polygon whose vertices are described by their Cartesian coordinates in the plane. [2]
GPkit is a Python package for cleanly defining and manipulating geometric programming models. There are a number of example GP models written with this package here . GGPLAB is a MATLAB toolbox for specifying and solving geometric programs (GPs) and generalized geometric programs (GGPs).
A slerp path is, in fact, the spherical geometry equivalent of a path along a line segment in the plane; a great circle is a spherical geodesic. Oblique vector rectifies to slerp factor. More familiar than the general slerp formula is the case when the end vectors are perpendicular, in which case the formula is p 0 cos θ + p 1 sin θ.
The superformula is a generalization of the superellipse and was proposed by Johan Gielis in 2003. [1] Gielis suggested that the formula can be used to describe many complex shapes and curves that are found in nature.
Online calculators with JavaScript source code by Chris Veness (Creative Commons Attribution license): Vincenty Direct (destination point) Vincenty Inverse (distance between points) GeographicLib provides a utility GeodSolve (with MIT/X11 licensed source code) for solving direct and inverse geodesic problems. Compared to Vincenty, this is about ...