Generating Distance Fields from Parametric Plane Curves
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Abstract
Distance fields have been presented as a general representation for both
curves and surfaces [4]. Using space partitioning, adaptive distance fields
(ADF) found their way into various applications, such as real-time font rendering
[5].
Computing approximate distance fields for implicit representations and
mesh objects received much attention. Parametric curves and surfaces, however,
are usually not part of the discussion directly. There are several algorithms
that can be used for their conversion into distance fields. However,
most of these are based converting parametric representations to piecewise
linear approximations [7].
This paper presents two algorithms to directly compute distance fields
from arbitrary parametric plane curves. One method is based on the rasterization
of general parametric curves, followed by a distance propagation using
fast marching. The second proposed algorithm uses the differential geometric
properties of the curve to generate simple geometric proxies, segments of osculating
circles, that are used to approximate the distance from the original
curve