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Subpixel sample testing rarely verifies one-dimensional
elements of graphs.
Consider a graph G[g = 0], with
.
Consider
,
.
If
then we set
to
,
since
so
The corners of
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:
Continuity-based testing fares poorly with
,
as
is non-negative for all (x,y).
Next: 4.2.7 Linear Interval Arithmetic
Up: 4.2 Basic Rendering
Previous: 4.2.5 Exhaustive Subpixel Testing