| OCR Text |
Show 7 F(x,y,z)=O or Parametrically oS being those points generated by three bivariate functions as the parameters vary: X=X(u,v) Y=Y(u,v) Z=Z (u,v) Algebraic surfaces are generally treated in the mathematical discipline known as Algebraic Geometry. The algebraic form is good for solving gometrical problems of the nature of "Is this point on the surface?". Parametric surfaces are generally treated in the mathematical discipline known as Differential Geometry. The parametric form is good for solving geometrical problems of the nature of "Generate all points on the surface.". Each representation is good for its particular type of problem. For simpler surfaces (e.g. planes) it is trivial to switch back and forth between forms. For higher order surfaces it may not be. Many of the basic problems come when we have a surface in one form and we wish to ask the question pertinent to the other form. The problem then becomes one of conversion (at least locally) between forms. The degree of complexity of the surface is, of course, dependent on the complexity of the functions which describe it. It is, however, customary to restrict discussion to functions which are polynomials or rational polynomials, |
