LINE MONOTONIC PARTITIONING OF PLANAR CUBIC B-SPLINES

This paper describes the line-monotonic partitioning of curves. A set of sufficient conditions for line-monotonicity is provided, along with a method for partitioning closed, periodic, planar, cubic B-splines into line-monotone pieces. A new B-spline control polygon classification is introduced as a framework for discussing B-spline shape behavior, extending and reinterpreting the work of Yates, Wang, and Su and Liu. Line-monotone pieces of cubic B-spline curve segments are identified for each control polygon shape class. Every segment is either line-monotone, or can be partitioned into two line-monotone pieces, a result that extends to all parametric cubics. Line-monotonic partitioning of closed curves is useful in applications such as filling.