Rida T. Farouki, Takis Sakkalis
Computer Aided Geometric Design
The bisector of a fixed point p and a smooth plane curve C-i.e., the locus traced by a point that remains equidistant with respect to p and C-is investigated in the case that C admits a regular polynomial or rational parameterization. It is shown that the bisector may be regarded as (a subset of) a "variable-distance" offset curve to C which has the attractive property, unlike fixed-distance offsets, of being generically a rational curve. This "untrimmed bisector" usually exhibits irregular points and self-intersections similar in nature to those seen on fixed-distance offsets. A trimming procedure, which identifies the parametric subsegments of this curve that constitute the true bisector, is described in detail. The bisector of the point p and any finite segment of the curve C is also discussed. © 1994.
Rida T. Farouki, Takis Sakkalis
Computer Aided Geometric Design
Rida T. Farouki, Manoj Dalvie, et al.
Journal of Applied Physics
Rida T. Farouki, Takis Sakkalis
Advances in Computational Mathematics
Thomas W. Sederberg, Rida T. Farouki
IEEE Computer Graphics and Applications