Tapering (mathematics)


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 = , y, z), a nonlinear taper could be applied so that the cube's volume slowly decreases 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 = 1/ were applied to the cube's equation such that ƒ = x, T'y, T'z), for some real constants a and b.