the region application_number US 45994699 A description prior to discussing the present invention and its embodiments it is appropriate to review current techniques for rendering texture mapped regions i a region of space r over which a two dimensional 2 d parameterization x u v x u v y u v is defined for example a ruled surface as in fig1 a or a coons patch as in fig1 b and ii some image texture map blend procedural texture or the like t u v that yields colour and or opacity value for given u v in suitable range it is possible to create an image distortion or curved colour blend or the like by taking the colour t u v at each u v value and drawing it at position x u v as illustrated in fig2 a and 2b conversely it is possible to determine the u v value for each point x in the region r look up the colour t u v at u v and draw it at x this presupposes that the mapping x u v is invertible and can be inverted with sufficient ease an alternative approach that has been used is to provide t u v an inverse distortion u v u x y and to derive the colour at each x y by first deriving u v then looking up t u v then drawing the colour at x x y in this scheme the region defined by u acts like a u201c cookie u201d section cutter on t then distorts the cut cookie section into a rectangle this approach has the advantage that an easily invertible mapping is not required however it is not easy with this method to.