| OCR Text |
Show 9 x = x(u,v) y y(u,v) z = z(u,v) w w(u,v) Use of homogeneous coordinates in the algebraic form does not lead to a richer set of surfaces for a given degree of polynomial. However, for polynomial functions, it does force the polynomi21 to be homogeneous (sum of the exponents of x,y,z,w in each term the same for all terms). polynomials are sometimes easier to deal with. Such Using homogeneous coordinates for parametric surfaces generates rational polynomials for the physical coordinate functions and does allow a broader class of surfaces. Geometrical Qations eces For Drawing There are several operations which must be performed on a surface in order to be able to draw a picture of it. This section will review these and the form they take with the two surfac types. Transformations The first operation, useful both for modellinq 2nd for drawing, is that of transform2tion. In particular we restrict ourselves to linear transformations of scaling and rotation and, if homogeneous representations are used, to translation s and perspective distortion. Such a transformation applied to an arbitrary homogeneous point may be expressed as a 4x4 matrix so that the transformed point |
