Graphics Reference
In-Depth Information
When working with floating-point formats, perform operations centered on the
origin to avoid wasting the extra bit of precision offered by the sign bit. The same
applies to signed integers.
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11.7
Summary
Many parts of a collision detection system are sensitive to robustness issues. This
chapter has discussed the sources of these issues, focusing on the sources of floating-
point errors. To understand where the floating-point errors are coming from, it is
important to understand how real numbers are represented as floating-point num-
bers. Today, the IEEE-754 floating-point formats are ubiquitous, and they were
presented here.
The chapter further discussed how to perform robust computations using floating-
point arithmetic. Three tactics were suggested. One is to work with tolerances that
are large enough to effectively hide any error buildup. Commonly, tolerances are
seen in the use of thick planes. Another tactic is to ensure sharing of calculations,
ensuring values are not recomputed (in subtly different ways). A third tactic is to work
exclusively with fat objects, allowing errors to be safely ignored.
Interval arithmetic was introduced as a failsafe approach to maintain bounds of
the errors of computations. Last, the option of using exact arithmetic was explored.
The next chapter also deals with robustness, discussing how to remove problematic
features such as cracks and concave geometry from the input geometry before they
cause problems at runtime.
