The basic framework of the plane sweep algorithm has been extended to numerous related problems in computational geometry such as the counting of the k intersections of n segments in provably optimal O(n log n+ k) time (Chazelle and Edelsbrunner, 1992), and reporting the regions of intersection of polygons in the plane (Nievergelt and Preparata, 1982).
After obtaining all layers representing HPs based on two SVs separately, spatial intersections of polygons representing HPs of both variables per each ground sample plot were also created (p95 × pFRAMe (Intersection)).
This approach represents the uncertainty in measurement of a structural variant as a polygon in the plane, and identifies measurements supporting the same variant by computing intersections of polygons.
The chapter also discusses some useful algorithms such as checking whether a point is enclosed in a given polygon, computing the intersection of two polygons, and computing the area of a polygon.
Let c be the left upper corner of rectangle s. s adds a new intersection to all polygons below c, the polygon containing c is split into two and the cover-variables of all of them increase by one.
The polygon intersection verification algorithm from Vatti [24] is strong enough to process irregular polygons with holes.
The polygon intersection point set (PIPS) is refined to identify finite candidate sites.
These algorithms are based on a "decomposition rule" for evaluating polygon intersection area, which has been used extensively for rezoning in hydrocodes over the past decades.
Polygons are simply defined by their corners and their intersections with other polygons.For solid hard objects, such as a box, polygons are easier to handle; but for complex, deforming objects, such as a person's expressive face, there is no substitute for complex curves that "know" how to bend by themselves, without an animator having to calculate each position.
The last part of the algorithm which is remapping of the volume materials from the Lagrangian grid to the original one is performed by a series of polygon intersection procedures.
