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### Outputting

 bool project (const Focus& f, const unsigned short proj, real factor) Function
 Calls Point::project(f, proj, factor) on the Points on the Path. If Point::project() fails (i.e., returns false), for any of the Points, this function returns false. Otherwise, it returns true.

 vector extract (const Focus& f, const unsigned short proj, real factor) Function
 Checks that the Points on points can be projected using the values for f, proj, and factor. If they can, a vector containing only this is returned. Called in Picture::output().

 bool set_extremes (void) Virtual function
 Sets the appropriate elements in projective_extremes to the minimum and maximum values of the x, y, and z-coordinates of the Points on the Path. Used in Picture::output() for determining whether a Path can be output using the arguments passed to Picture::output().

 const valarray get_extremes (void) Inline const virtual function
 Returns projective_extremes. Used in Picture::output().

 real get_minimum_z (void) const virtual function real get_mean_z (void) const virtual function real get_maximum_z (void) const virtual function
 These functions return the minimum, mean, or maximum value, respectively, of the z-coordinates of the Points on the Path. Used in the surface hiding algorithm in Picture::output().

 void suppress_output (void) Virtual function
 Called in Picture::output(). Sets do_output to false, if the Path cannot be output using the arguments passed to Picture::output().

 void unsuppress_output (void) Virtual function
 Called in Picture::output(). Resets do_output to true after output() is called on the Shapes on shapes in a Picture, so that the Path can be output if Picture::output() is called again, with arguments that allow the Path to be output.

 void output (void) Virtual function
 Called in Picture::output(). Writes the MetaPost code to out_stream for drawing, filling, filldrawing, undrawing, unfilling, or unfilldrawing the Path, if the latter was projectable using the arguments passed to Picture::output().