5.4.2 Parametric

Another method to describe a surface is by a parametrization. The syntax of the corresponding parametric object is

PARAMETRIC:
  parametric { USER_FUNCTION_X, USER_FUNCTION_Y, USER_FUNCTION_Z 
    CORNER1, CORNER2 [PARAMETRIC_ITEMS] [OBJECT_MODIFIERS] }

PARAMETRIC_ITEMS:
  [contained_by { CONTAINER } ] & [max_gradient FLOAT] 
    & [accuracy FLOAT] & [precompute I_DEPTH, x, y, z]

CONTAINER:
  sphere { V_CENTER, F_RADIUS } | box { V_CORNER1, V_CORNER2 }

See also:

• [pov:6.5.5]Parametric Object

This describes the object given by the image of the function

$$(u,v)\mapsto \langle f_X(u,v),f_Y(u,v),f_Z(u,v)\rangle,$$

where $f_X$, $f_Y$ , $f_Z$ are the USER_FUNCTION's and $(u,v)$ varies in the 2-dimensional box given by two opposite corners CORNER1 and CORNER2.