Abstract :
A hyperbolic paraboloid is a rather fancy name for a second-order surface more commonly called a saddle point. Three mutually skew lines in space K,L and M determine a unique hyperbolic paraboloid in which they are all embedded. We discuss about the construction of two-and three-line construction geometry. The implicit equation and the parametric equation for one of the two families of embedded lines sweeping out the surface is explained. for this is represented. We explain in detail about the lines in space and their geometric relationship.
Keywords :
computational geometry; hyperbolic equations; parabolic equations; embedded line; geometric relationship; hyperbolic paraboloid; implicit equation; parametric equation; saddle point; second-order surface; three-line geometry; two-line geometry; Clocks; Covariance matrix; Equations; Geometry; Plugs; Symmetric matrices; Testing; Transforms; Algorithms; Computer Graphics; Numerical Analysis, Computer-Assisted;
Journal_Title :
Computer Graphics and Applications, IEEE
DOI :
10.1109/MCG.2004.1297018
