Tapering (mathematics)
Introduction In mathematics, physics, and theoretical computer graphics, '''tapering''' is a kind of shape deformation. Just as an affine transformation, such as scaling or shearing, is a first-order model of shape deformation, tapering is a higher order deformation just as twisting and bending. Tapering can be thought of as non-constant scaling by a given tapering function. The resultant deformations can be linear or nonlinear.To create a nonlinear taper, instead of scaling in ''x'' and ''y'' for all ''z'' with constants as in:: let ''a'' and ''b'' be functions of ''z'' so that:: An example of a linear taper is , and a quadratic taper .As another example, if the parametric equation of a cube were given by ''ƒ''(''t'') = (''x''(''t''), ''y''(''t''), ''z''(''t'')), a nonlinear taper could be applied so that the cube's volume slowly decreases (or tapers) as the function moves in the positive ''z'' direction. For the given cube, an example of a nonlinear taper along ''z'' would be if, for instance, the function ''T''(''z'') = 1/(''a'' + ''bt'') were applied to the cube's equation such that ''ƒ''(''t'') = (''T''(''z'')''x''(''t''), ''T''(''z'')''y''(''t''), ''T''(''z'')''z''(''t'')), for some real constants ''a'' and ''b''.
See also *3D projection
References
External links * , Computer Graphics Notes. University of Toronto. (See: Tapering). * , 3D Transformations. Brown University. (See: Nonlinear deformations). * , ScienceWorld article on Tapering in Image Synthesis.