Subpixel sample testing rarely verifies one-dimensional
elements of graphs.
Consider a graph G[g = 0], with 
.
Consider 
,
.
If
to 
,
since
are common initial choices
for 
and 
.
Continuity-based testing is often used in place of
subpixel sample testing where = occurs in a specification.
Compare the following two 
renderings
of 
, produced using, and not using, continuity-based testing:
denotes a rendering produced using
continuity-based testing.
With sample testing, a sample must be chosen which lies
within a graph; with continuity-based testing, a pair
of samples must be chosen such that the graph lies between
the two samples.
If each sample is a point within 
,
and the samples are chosen
uniformly and independently, the outer pixels of each step have a 25% chance
of being verified as , while the inner pixel of each step has a 50% chance
of being verified as .
With subpixel sample testing, each pixel has a 0% chance of being
verified as .
Consider the following two renderings, both of which employ continuity-based testing:
,
as 
is non-negative for all (x,y).
| Jeff Tupper | March 1996 |