


                                  - 1 -



       COMMAND

       rrrrccccoooosssspppprrrroooopppp,,,, rrrrssssiiiinnnnpppprrrroooopppp ---- nnnnoooonnnn----lllliiiinnnneeeeaaaarrrr rrrraaaaddddiiiiuuuussss pppprrrrooooppppoooorrrrttttiiiioooonnnniiiinnnngggg

       USAGE

       rrrrccccoooosssspppprrrroooopppp [----bbbb] _p_r_o_p _l_g_p_e_r_i_o_d _l_g_n_o_d_e

       rrrrssssiiiinnnnpppprrrroooopppp [----bbbb] _p_r_o_p _l_t_p_e_r_i_o_d _l_t_n_o_d_e

       DESCRIPTION

       ----bbbb          Blend the effect sinusoidally in the orthogonal
                   direction.

       _p_r_o_p        Proportion to _p_r_o_p percent at the point of
                   maximum effect.

       _l_g_p_e_r_i_o_d    Vary proportioning effect through one cycle in
                   _l_g_p_e_r_i_o_d longitudes.

       _l_t_p_e_r_i_o_d    Vary proportioning effect through one cycle in
                   _l_t_p_e_r_i_o_d latitudes.

       _l_g_n_o_d_e      Shift the phase of the effect to produce zero
                   change at _l_g_n_o_d_e.

       _l_t_n_o_d_e      Shift the phase of the effect to produce zero
                   change at _l_t_n_o_d_e.

       RRRRccccoooosssspppprrrroooopppp and rrrrssssiiiinnnnpppprrrroooopppp are companion commands which enable
       you to effect a wide variety of image tailoring tasks by
       systematically adjusting radii in a manner proportional to
       some interval of a sinusoidal waveform.  Such an interval
       may display shape characteristics which you would like the
       image to reflect either throughout or in some subregion of
       that image.  RRRRccccoooosssspppprrrroooopppp will effect such a shaping in a
       peripheral or azimuthal sense along lines of latitude.
       Alternatively, you can use rrrrssssiiiinnnnpppprrrroooopppp to effect such shaping
       in the axial or vertical sense along lines of longitude.

       You can apply either command in a manner which will achieve
       smooth and continuous transitions at the range boundaries of
       the coordinate orthogonal to the normal proportioning
       direction by employing the optional bbbblending feature.  This
       option automatically sets the node point at mid-range in the
       orthogonal direction and the period is set to coincide with
       their full range in that direction.  The amplitude of
       proportioning in the blending direction is set to coincide
       with the phase of the proportioning in the primary direction
       for the command you are employing.











                                  - 2 -



       As with most EEEEcccchhhhoooo commands, use of these two functions is
       facilitated by judicious choice of latitude and longitude
       limits.  The arguments of these commands are specified in
       terms of familiar image parameters and the region in which
       their effect is applied is confined strictly to the
       ltrange/lgrange window.

       The first of the three mandatory arguments for these
       commands specifies the percentage scale to which the image
       radii would be adjusted if such radii subjected to a linear
       proportioning such as would be the case if you were to
       employ the rrrrpppprrrroooopppp command.  Unlike the latter command, the
       percentage scale for rrrrccccoooosssspppprrrroooopppp and rrrrssssiiiinnnnpppprrrroooopppp may be expressed
       in floating point form, however, its value must be not be
       less than 0.0 nor greater than 400.0 percent.  The second
       argument specifies the number of longitudes (rrrrccccoooosssspppprrrroooopppp) or
       latitudes (rrrrssssiiiinnnnpppprrrroooopppp) spanned by one complete cycle of the
       sinusoidal waveform.

       The third argument specifies a latitude or longitude, i.e.,
       a nodal point, at which radii coincide with the minimum
       (zero) change along the waveform.  Together these arguments
       uniquely define the amplitude, period and phase of the
       underlying sinusoidal radius proportioning regime while the
       current ltrange/lgrange window controls the region of the
       image within which that regime is to be applied.

       A simple example of an application of rrrrssssiiiinnnnpppprrrroooopppp is that of
       modifying the lower latitudes of a portrait sculpture image
       to achieve the effect of a sculpted base design with
       somewhat undercut shoulders rather than the usual
       cylindrical projection from the shoulder to the bottom
       plane.  The sequence of commands:

       llllttttrrrraaaannnnggggeeee 0000 66663333

       and

       rrrrssssiiiinnnnpppprrrroooopppp 88882222 111122228888 66663333

       result in just such an effect.

       The effect is restricted to the lower quarter of the image
       by llllttttrrrraaaannnnggggeeee while rrrrssssiiiinnnnpppprrrroooopppp defines the characteristics of the
       image shaping to be effected.  This latter command
       essentially specifies that a waveform whose wavelength is
       128 latitudes be employed, that the waveform be shifted so
       that latitude 63 becomes a node (as does -64, 191, -191,
       etc.), and maximum proportioning occurs at latitude 0.













                                  - 3 -



       Not only are the radii associated with latitude 63
       proportioned to 100 percent of their original value but,
       because neighboring latitudes immediately below are
       proportioned by values of the waveform approaching 100
       percent, the transition from the proportioned region to the
       unproportioned region is smooth and continuous.

       The behavior of rrrrccccoooosssspppprrrroooopppp is conceptually the same as
       rrrrssssiiiinnnnpppprrrroooopppp (indeed is the same when applied to rectilinear
       images) however, since the proportioning is achieved in an
       azimuthal sense, its influence is more reminiscent of graphs
       of sinusoidal functions plotted in polar coordinates.

       By analogy to the rrrrssssiiiinnnnpppprrrroooopppp example above, the commands

       llllggggrrrraaaannnnggggeeee 0000 111122227777

       and

       rrrrccccoooosssspppprrrroooopppp 111111118888 111122228888 0000

       essentially force the features associated with the first
       quadrant of the image to become more radially prominent as
       the center of the quadrant is approached from either
       quadrant boundary.  Over a relatively broad range of
       longitudes near the center, radii are adjusted to values at
       or near 118 percent of their original values.  On the other
       hand similarly broad longitude spans near the quadrant
       boundaries remain at or near their original values.  As is
       characteristic of sinusoidal behavior, the relative change
       in the proportioning effect, from longitude to neighboring
       longitude, is greatest midway between boundary and center at
       which point it passes through an inflection from increasing
       to decreasing relative change.

       CAVEATS

       These commands require careful coordination of the latitude
       and longitude range window boundaries with your selection of
       period and node in order to obtain smooth and continuous
       boundary transitions.


















