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The intersection of a collection of half-planes describes a convex polygon, whose vertices can be constructed in $O(n \log n)$ time using a divide-and-conquer approach (e.g., intersect each half-plane with a bounding box and recursively merge the resulting polygons)polygons pairwise).

Suppose, however, that I'm interested only in the area of this polygon. Are there known algorithms for computing the area that are either 1. asymptotically faster (I'm doubtful) or 2. simpler (I'm hopeful) than those used to explicitly construct the vertices? Also of interest are algorithms that are 3. more stable in finite-precision.

Thanks!

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Area of a Convex Polygon (Described via Half-Planes)

The intersection of a collection of half-planes describes a convex polygon, whose vertices can be constructed in $O(n \log n)$ time using a divide-and-conquer approach (e.g., intersect each half-plane with a bounding box and recursively merge the resulting polygons).

Suppose, however, that I'm interested only in the area of this polygon. Are there known algorithms for computing the area that are either 1. asymptotically faster (I'm doubtful) or 2. simpler (I'm hopeful) than those used to explicitly construct the vertices? Also of interest are algorithms that are 3. more stable in finite-precision.

Thanks!