= Jonathan Richard Shewchuk
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<Jonathan Richard Shewchuk> developed adaptive exact arithmetic methods for robust <computational geometry> predicates. Orientation and incircle tests depend on the sign of a <determinant>; an incorrectly rounded sign near zero can corrupt the geometric decisions of an <algorithm>. His method spends additional precision only when needed to establish the correct sign.<Adaptive Precision Floating-Point Arithmetic and Fast Robust Geometric Predicates by Jonathan Richard Shewchuk>[author explanation, determinant signs and adaptive arithmetic]{ref}
For example, three nearly collinear points may give an orientation <determinant> extremely close to zero even when their coordinates are individually unexceptional. A fast approximate evaluation can resolve an easy case, while a difficult case triggers more exact work. This connects numerical accuracy to a discrete geometric decision, not merely to the number of printed decimal places.
Homepage: https://people.eecs.berkeley.edu/~jrs/
\Image[https://people.eecs.berkeley.edu/~jrs/head2.gif]
{title=Portrait of <Jonathan Richard Shewchuk>}
{source=https://people.eecs.berkeley.edu/~jrs/}
{width=220}
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