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A parametric equation for the sphere with radius > and center (,,) can be ... where ρ is the density (the ratio of mass to volume). Other geometric properties
In all cases, the equations are collectively called a parametric representation, [2] or parametric system, [3] or parameterization (alternatively spelled as parametrisation) of the object. [ 1 ] [ 4 ] [ 5 ]
For example, the unit sphere is an algebraic surface, as it may be defined by the implicit equation x 2 + y 2 + z 2 − 1 = 0. {\displaystyle x^{2}+y^{2}+z^{2}-1=0.} A surface may also be defined as the image , in some space of dimension at least 3, of a continuous function of two variables (some further conditions are required to ensure that ...
A parametric surface is a surface in the Euclidean space which is defined by a parametric equation with two parameters :. Parametric representation is a very general way to specify a surface, as well as implicit representation .
ellipsoid as an affine image of the unit sphere. The key to a parametric representation of an ellipsoid in general position is the alternative definition: An ellipsoid is an affine image of the unit sphere. An affine transformation can be represented by a translation with a vector f 0 and a regular 3 × 3 matrix A:
For example, one sphere that is described in Cartesian coordinates with the equation x 2 + y 2 + z 2 = c 2 can be described in spherical coordinates by the simple equation r = c. (In this system—shown here in the mathematics convention—the sphere is adapted as a unit sphere, where the radius is set to unity and then can generally be ignored ...
"Around the Horn" began in 2002 with Max Kellerman as its original host. Reali took over hosting duties in 2004 and has remained in the role ever since.
The equation of a spheroid with z as the symmetry axis is given by setting a = b: x 2 + y 2 a 2 + z 2 c 2 = 1. {\displaystyle {\frac {x^{2}+y^{2}}{a^{2}}}+{\frac {z^{2}}{c^{2}}}=1.} The semi-axis a is the equatorial radius of the spheroid, and c is the distance from centre to pole along the symmetry axis.