Next: 4.2.4 Subpixel Testing
Up: 4.2 Basic Rendering
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From the interval inclusion property we know that
so setting to ,
for each pixel ,
will generate a rendering of .
An example rendering follows:
The solid line depicts the associated graph.
denotes a rendering produced using pixel testing.
For each pixel ,
is computed and is then set accordingly.
An example evaluation follows:
Another example rendering follows:
An example evaluation of S,
using notation, follows:
We have chosen to take into account the lack of knowledge
of when evaluating ;
an alternative evaluation of S, which defers this accounting,
follows:
Although the evaluation result is ,
we do not know , so we
must assume that .
We must therefore set to
using either accounting approach.
The two approaches differ when rendering
The two renderings follows:
An example evaluation, using early accounting,
follows:
the corresponding evaluation
using deferred accounting is as follows:
Two renderings, corresponding to
the preceding renderings,
follow:
Superior inequality renderings
are possible using
instead of .
For discontinuous equations, renderings
are often superior to renderings. Consider
the following renderings:
With discontinuous specifications, set-based interval arithmetics
may sharply bound discontinuous pieces; without this ability
to use several bounds, the discontinuous pieces must be bound
with a single interval.
Next: 4.2.4 Subpixel Testing
Up: 4.2 Basic Rendering
Previous: 4.2.2 Sequential Rendering