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In mathematics, a quadric or quadric surface (quadric hypersurface in higher dimensions), is a generalization of conic sections (ellipses, parabolas, and hyperbolas).It is a hypersurface (of dimension D) in a (D + 1)-dimensional space, and it is defined as the zero set of an irreducible polynomial of degree two in D + 1 variables; for example, D = 1 in the case of conic sections.
The two families of lines on a smooth (split) quadric surface. In mathematics, a quadric or quadric hypersurface is the subspace of N-dimensional space defined by a polynomial equation of degree 2 over a field. Quadrics are fundamental examples in algebraic geometry. The theory is simplified by working in projective space rather than affine ...
Hidden-surface algorithms can be used for hidden-line removal, but not the other way around. Reif and Sen [17] proposed an O(log 4 n)-time algorithm for the hidden-surface problem, using O((n + v)/log n) CREW PRAM processors for a restricted model of polyhedral terrains, where v is the output size.
Plücker coordinates allow concise solutions to problems of line geometry in 3-dimensional space, ... a hyperboloid of one sheet is a quadric surface in ...
More generally, a smooth quadric (degree 2) hypersurface X of any dimension n is rational, by stereographic projection. (For X a quadric over a field k, X must be assumed to have a k-rational point; this is automatic if k is algebraically closed.) To define stereographic projection, let p be a point in X.
It is an easy task to determine the intersection points of a line with a quadric (i.e. line-sphere); one only has to solve a quadratic equation. So, any intersection curve of a cone or a cylinder (they are generated by lines) with a quadric consists of intersection points of lines and the quadric (see pictures).
In geometry, a paraboloid is a quadric surface that has exactly one axis of symmetry and no center of symmetry. The term "paraboloid" is derived from parabola, which refers to a conic section that has a similar property of symmetry. Every plane section of a paraboloid made by a plane parallel to the axis of symmetry is a parabola.
This problem asks for the number and construction of circles that are tangent to three given circles, points or lines. In general, the problem for three given circles has eight solutions, which can be seen as 2 3, each tangency condition imposing a quadratic condition on the space of circles. However, for special arrangements of the given ...