Rt. Farouki et R. Ramamurthy, SPECIFIED-CENTER-DOT-PRECISION COMPUTATION OF CURVE CURVE BISECTORS/, International journal of Computational geometry and applications, 8(5-6), 1998, pp. 599-617
Citations number
33
Categorie Soggetti
Mathematics,"Computer Science Theory & Methods",Mathematics,"Computer Science Theory & Methods
The bisector of two plane curve segments (other than lines and circles
) has, in general, no simple - i.e., rational - parameterization, and
must therefore be approximated by the interpolation of discrete data.
A procedure for computing ordered sequences of point/tangent/curvature
data along the bisectors of polynomial or rational plane curves is de
scribed, with special emphasis on (i) the identification of singularit
ies (tangent-discontinuities) of the bisector; (ii) capturing the exac
t rational form of those portions of the bisector with a terminal foot
point on one curve; and (iii) geometrical criteria that characterize e
xtrema of the distance error for interpolants to the discretely-sample
d data. G(1) piecewise-parabolic and G(2) piecewise-cubic approximatio
ns (with O(h(4)) and O(h(6)) convergence) are described which, used in
adaptive schemes governed by the exact error measure, can be made to
satisfy any prescribed geometrical tolerance.