quadric
Sign in to saveIn mathematics, a quadric or quadric surface is a generalization of conic sections (ellipses, parabolas, and hyperbolas). In three-dimensional space, quadrics include ellipsoids, paraboloids, and hyperboloids.
Article
29 sectionsContents
- Formulation
- Euclidean plane
- Euclidean space
- Intersection of a Ray with a Quadric Surface
- Quadric surface patches in graphical ray tracing
- Determining the quadric surface type and the displacement from standard position
- Quadric Surface Affine Transformation
- Latitude, longitude, and altitude as quadric surfaces
- Definition and basic properties
- Equation
- Normal form of projective quadrics
- Rational parametrization
- Example: circle and spheres
- Rational points
- Pythagorean triples
- Projective quadrics over fields
- Quadratic form
- ''n''-dimensional projective space over a field
- Projective quadric
- Polar space
- Intersection with a line
- ''f''-radical, ''q''-radical
- Symmetries
- ''q''-subspaces and index of a quadric
- Generalization of quadrics: quadratic sets
- See also
- References
- Bibliography
- External links
In mathematics, a quadric or quadric surface is a generalization of conic sections (ellipses, parabolas, and hyperbolas). In three-dimensional space, quadrics include ellipsoids, paraboloids, and hyperboloids.
More generally, a quadric hypersurface (of dimension D) embedded in a higher dimensional space (of dimension ) is defined as the zero set of an irreducible polynomial of degree two in variables; for example, D1 is the case of conic sections (plane curves). When the defining polynomial is not absolutely irreducible, the zero set is generally not considered a quadric, although it is often called a degenerate quadric or a reducible quadric.