Efficient offset trimming for planar rational curves using biarc trees

We present an efficient algorithm for trimming both local and global self-intersections in planar offset curves. The algorithm is based on a G1G1-continuous biarc approximation of the given planar curves. We first consider an implementation that employs a distance map which can be stored in the graphics hardware depth buffer. The depth-buffer approach is easier to implement than a different approach that is based on a biarc-tree, a hierarchical data structure for the biarc approximation of the given planar curves. Though more involved technically, the biarc-tree algorithm is more efficient both in computing time and in memory space needed for storing the data structure. We demonstrate the real-time performance of our algorithm using several experimental results.

► Efficient algorithm for planar curve offset trimming.
► Real-time performance even for complicated planar rational curves.
► Efficient representation of the distance map for planar rational curves using the biarc tree data structure.