Search results
Results from the WOW.Com Content Network
A sphere of radius r has area element = . This can be found from the volume element in spherical coordinates with r held constant. [9] A sphere of any radius centered at zero is an integral surface of the following differential form: + + =
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 ]
The quarter of Viviani's curve that lies in the all-positive quadrant of 3D space cannot be represented exactly by a regular Bézier curve of any degree.. However, it can be represented exactly by a 3D rational Bézier segment of degree 4, and there is an infinite family of rational Bézier control points generating that segment.
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 ...
Such a parametric equation completely determines the curve, without the need of any interpretation of t as time, and is thus called a parametric equation of the curve (this is sometimes abbreviated by saying that one has a parametric curve). One similarly gets the parametric equation of a surface by considering functions of two parameters t and u.
In vector notation, the equations are as follows: . Equation for a sphere ‖ ‖ = : points on the sphere : center point : radius of the sphere; Equation for a line starting at
A sphere of radius r has surface area 4πr 2.. The surface area (symbol A) of a solid object is a measure of the total area that the surface of the object occupies. [1] The mathematical definition of surface area in the presence of curved surfaces is considerably more involved than the definition of arc length of one-dimensional curves, or of the surface area for polyhedra (i.e., objects with ...
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 .