Generating Distance Fields from Parametric Plane Curves

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

Rasterization of Nonparametric Curves

We examine a class of algorithms for rasterizing algebraic curves based on an implicit form that can be evaluated cheaply in integer arithmetic using finite differences. These algorithms run fast and produce "optimal" digital output, where previously known algorithms have had serious limitations. We extend previous work on conic sections to the cubic and higher order curves, and we solve an important undersampling problem