Compact representation of triangulations

Overview & Synopsis

We consider the problem of representing compact geometric data structures maintaining an efficient implementation of navigation operations. For the case of planar triangulations with $m$ faces, we propose a compact representation of the connectivity information that improves to $2.175$ bits per triangle the asymptotic amount of space required and that supports navigation between adjacent triangles in constant time. For triangulations with $m$ faces of a surface with genus $g$, our representation requires asymptotically an extra amount of $36(g-1)\lgm$ bits. The structure also allows constant time access to vertex specific data, like coordinates, but the paper does not address the compression of this geometric information.