Computational Geometry through the Information Lens
نویسندگان
چکیده
A central issue in computational geometry is the discrepancy between the idealized geometric view of points and lines with infinite precision, and the realistic computational view that everything is represented by (finitely many) bits. The geometric view is inspired by Euclidean geometric constructions from circa 300 BC. The computational view matches the reality of digital computers as we know them today and as set forth by Turing in 1936. This discrepancy is traditionally seen as negative: theoretically simple algorithms with infinite precision become difficult to implement in practice with finite precision. A new body of research views the finite-precision reality to be a feature, not a bug, and analyzes the extent to which it can be exploited to obtain faster algorithms than possible for infinite precision.
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