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キーワード:
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要旨:
This thesis presents an exact and complete approach for visualization of
segments and points of real plane algebraic curves given in implicit form
$f(x,y) = 0$. A curve segment is a distinct curve branch consisting of regular
points
only. Visualization of algebraic curves having self-intersection and isolated
points constitutes the main challenge. Visualization of curve segments involves
even more
difficulties since here we are faced with a problem of discriminating
different curve branches, which can pass arbitrary close to each other.
Our approach is robust and efficient (as shown by our benchmarks), it
combines the advantages both of curve tracking and
space subdivision methods and is able to correctly rasterize segments of
arbitrary-degree algebraic curves using double, multi-precision or exact
rational arithmetic.
