@node Surface, Table, Strings, Commands

@iftex
@syntax Surface.
@end iftex
@pindex Surface
@example
Syntax: SURFACE type z1 z2
or      SURFACE type z1 z2 @r{WORD WORD}
@end example

   Draw a wire-frame surface of the current @code{IMAGE} from the point
defined by @code{VIEWPOINT}. If the WORDs
are omitted a line in the surface will be drawn for each row and column
of the image; if the WORDs are present they will be taken to be the
@code{x}- and @code{y}- coordinates of the desired lines, and SM will
interpolate in the image to determine
the corresponding values (see also the hundreds digit of type, below).

The command @code{VIEWPOINT} specifies the position of the observer
and the type of projection used (@pxref{Viewpoint}).

   The last digit of TYPE is used to determine which surface to draw:
@example
        0       no hidden line removal
        1       draw top surface
        2       draw bottom surface
        3       draw both top and bottom surfaces
@end example

If @code{type}'s tens digit is set, @code{SURFACE} will use the current
limits (as set with @code{LIMITS}) rather than autoscaling them from the
data.

If @code{type}'s hundreds digit is set, the two @code{WORD}s are taken to
be the @code{x}- and @code{y}- coordinates corresponding to the rows and
columns of the IMAGE, but no interpolation is done. For example, after
@example
IMAGE (11,11)
SET ix=0,10
set xs=0,10,2
do y=0,10 @{
   SET IMAGE(ix,$y) = cos(0.2*ix)*sin(0.4*$y)
@}
VIEWPOINT 30 -10 -1
SURFACE 3 -1.1 1.1 xs xs
@end example
@noindent
will draw a 2-sided surface, drawing 21 lines in each direction on
the surface. If, on the other hand, the data were really only known on
at irregular set of @code{x}- and @code{y}-values, you could say something
like
@example
IMAGE (11,11)
SET ix=0,10
SET x = @{ 0 1.3 2.4 3 4 4.5 4.6 6.7 8.2 9.6 10 @}
SET y = @{ 0 0.4 0.9 1.2 2.718 3.14 4.2 5.4 6.667 9.1 10 @}
do i=0,10 @{
   SET IMAGE(ix,$i) = cos(0.2*x)*sin(0.4*y[$i])
@}
CTYPE cyan
SURFACE 103 -1.1 1.1 x y
CTYPE default
@end example
@noindent
to draw the same surface.

@code{z1} and @code{z2} are the limits used for the z-axis;
you might want to set them with @code{MINMAX}. The surface drawn will
be truncated at @code{z1} and @code{z2} unless you are using an
axonometric projection (@pxref{Viewpoint}).

There are some useful macros in the file @file{surfaces}; say
@code{load surfaces} to read them. If VERBOSE is one or more, a helpful
header will be printed when you load the file.