Rather than building up the rendering pixel by pixel,
the rendering may be built up row by row, or column by column.
Each row, or column, is visited once.
Consider rendering y = g(x), where 
.
An example rendering follows:
denotes a rendering produced using
column, or row, testing.
The function g is evaluated for each column.
An example evaluation follows:
is evaluated,
pixels of R may be appropriately set.
If spans a
single pixel, that pixel may be set to 
;
pixels untouched by
may be set to 
.
Another example rendering follows:
Finer tests may be performed, as with pixel-based testing. Using sample testing, g is evaluated for a portion of each partially undetermined column. An example rendering follows:
denotes a rendering produced using sub-column, or sub-row,
sample testing.
The portions chosen for the above rendering lay on the left
side of each pixel column. Another pass, choosing portions
on the right side of each pixel column, would set
the remaining undetermined pixels to .
An example rendering, produced using sub-column continuity-based testing, follows:
with a single test.
With continuity-based testing, 
and
are computed; if g is continuous over
then g is known to smoothly pass
from 
to 
if 
;
g is known to smoothly pass
from 
to 
if 
.
The following diagram illustrates a portion of a single column from the
preceding rendering:
, for any 
,
may be set to ; determining such pixels is straight-forward.
Such determination mimics the rules behind determining
; see section 
.
With continuity information, g must smoothly
pass from 
to 
if 
;
g must smoothly pass from 
to 
if 
.
Of course, row and column testing may be used on specifications containing inequalities. Logical combinations of equations and relations are easily accommodated, by passing row or column descriptions along with evaluation results when evaluating the upper levels of S.
| Jeff Tupper | March 1996 |