| OCR Text |
Show 8 since any function can, in principle, be approximated arbitrarily closely by a polynomial of high enough degree. The order of the surface is then identified as the order of the polynomial function which describes it. As an example, the simplest type of surface is a plane. This surface is described in both cases by the sim?lest type of function, a linear (or first order) function. The algebraic form of a plane is: F(x,y,z) ax + by + cz + d o The parametric form is: x = eu + fv + g Y hu + iv + j z = ku + Iv + m For this simple case, there is a tansforming the algebraic form straightforward means of of the surface to the parametric form. In the case of higher oroer surfaces a simple solution, or even a closed form solution, may not exist. homogeneous Coordinates. coordinates sometimes represented by their rather than their physical Points in space are In this case the algebraic form becomes: (x,y,z,w) 0 and the parametric form becomes |
