Ellipsoid and Hyperboloid

Shortcuts: Differences, Similarities, Jaccard Similarity Coefficient, References.

Difference between Ellipsoid and Hyperboloid

Ellipsoid vs. Hyperboloid

An ellipsoid is a surface that may be obtained from a sphere by deforming it by means of directional scalings, or more generally, of an affine transformation. In geometry, a hyperboloid of revolution, sometimes called circular hyperboloid, is a surface that may be generated by rotating a hyperbola around one of its principal axes.

Affine transformation

In geometry, an affine transformation, affine mapBerger, Marcel (1987), p. 38.

Affine transformation and Ellipsoid · Affine transformation and Hyperboloid · See more »

Cartesian coordinate system

A Cartesian coordinate system is a coordinate system that specifies each point uniquely in a plane by a pair of numerical coordinates, which are the signed distances to the point from two fixed perpendicular directed lines, measured in the same unit of length.

Cartesian coordinate system and Ellipsoid · Cartesian coordinate system and Hyperboloid · See more »

Circular section

In geometry a circular section is a circle on a quadric surface (such as an ellipsoid or hyperboloid).

Circular section and Ellipsoid · Circular section and Hyperboloid · See more »

Cylinder

A cylinder (from Greek κύλινδρος – kulindros, "roller, tumbler"), has traditionally been a three-dimensional solid, one of the most basic of curvilinear geometric shapes.

Cylinder and Ellipsoid · Cylinder and Hyperboloid · See more »

Eigenvalues and eigenvectors

In linear algebra, an eigenvector or characteristic vector of a linear transformation is a non-zero vector that changes by only a scalar factor when that linear transformation is applied to it.

Eigenvalues and eigenvectors and Ellipsoid · Eigenvalues and eigenvectors and Hyperboloid · See more »

Euclidean vector

In mathematics, physics, and engineering, a Euclidean vector (sometimes called a geometric or spatial vector, or—as here—simply a vector) is a geometric object that has magnitude (or length) and direction.

Ellipsoid and Euclidean vector · Euclidean vector and Hyperboloid · See more »

Paraboloid

In geometry, a paraboloid is a quadric surface that has (exactly) one axis of symmetry and no center of symmetry.

Ellipsoid and Paraboloid · Hyperboloid and Paraboloid · See more »

Perpendicular

In elementary geometry, the property of being perpendicular (perpendicularity) is the relationship between two lines which meet at a right angle (90 degrees).

Ellipsoid and Perpendicular · Hyperboloid and Perpendicular · See more »

Point reflection

In geometry, a point reflection or inversion in a point (or inversion through a point, or central inversion) is a type of isometry of Euclidean space.

Ellipsoid and Point reflection · Hyperboloid and Point reflection · See more »

Polynomial

In mathematics, a polynomial is an expression consisting of variables (also called indeterminates) and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables.

Ellipsoid and Polynomial · Hyperboloid and Polynomial · See more »

Quadric

In mathematics, a quadric or quadric surface (quadric hypersurface in higher dimensions), is a generalization of conic sections (ellipses, parabolas, and hyperbolas).

Ellipsoid and Quadric · Hyperboloid and Quadric · See more »

Rotational symmetry

Rotational symmetry, also known as radial symmetry in biology, is the property a shape has when it looks the same after some rotation by a partial turn.

Ellipsoid and Rotational symmetry · Hyperboloid and Rotational symmetry · See more »

Scaling (geometry)

In Euclidean geometry, uniform scaling (or isotropic scaling) is a linear transformation that enlarges (increases) or shrinks (diminishes) objects by a scale factor that is the same in all directions.

Ellipsoid and Scaling (geometry) · Hyperboloid and Scaling (geometry) · See more »

Semi-major and semi-minor axes

In geometry, the major axis of an ellipse is its longest diameter: a line segment that runs through the center and both foci, with ends at the widest points of the perimeter.

Ellipsoid and Semi-major and semi-minor axes · Hyperboloid and Semi-major and semi-minor axes · See more »

Sphere

A sphere (from Greek σφαῖρα — sphaira, "globe, ball") is a perfectly round geometrical object in three-dimensional space that is the surface of a completely round ball (viz., analogous to the circular objects in two dimensions, where a "circle" circumscribes its "disk").

Ellipsoid and Sphere · Hyperboloid and Sphere · See more »

Spherical coordinate system

In mathematics, a spherical coordinate system is a coordinate system for three-dimensional space where the position of a point is specified by three numbers: the radial distance of that point from a fixed origin, its polar angle measured from a fixed zenith direction, and the azimuth angle of its orthogonal projection on a reference plane that passes through the origin and is orthogonal to the zenith, measured from a fixed reference direction on that plane.

Ellipsoid and Spherical coordinate system · Hyperboloid and Spherical coordinate system · See more »

Surface (mathematics)

In mathematics, a surface is a generalization of a plane which needs not be flat, that is, the curvature is not necessarily zero.

Ellipsoid and Surface (mathematics) · Hyperboloid and Surface (mathematics) · See more »

Zero of a function

In mathematics, a zero, also sometimes called a root, of a real-, complex- or generally vector-valued function f is a member x of the domain of f such that f(x) vanishes at x; that is, x is a solution of the equation f(x).

Ellipsoid and Zero of a function · Hyperboloid and Zero of a function · See more »