Computing Mitered Offset Curves Based on Straight Skeletons

Abstract

We study the practical computation of mitered and beveled offset curves of planar straight-line graphs (PSLGs), i.e., of arbitrary collections of straight-line segments in the plane that do not intersect except possibly at common end points. The line segments can, but need not, form polygons. Similar to Voronoi-based offsetting, we propose to compute a straight skeleton of the input PSLG as a preprocessing step for mitered offsetting. For this purpose, we extend and adapt Aichholzer and Aurenhammer's triangulation-based straight-skeleton algorithm to make it process real-world data on a conventional finite-precision arithmetic.We implemented this extended algorithm in C and use our implementation for extensive experiments. All tests demonstrate the practical suitability of using straight skeletons for the offsetting of complex PSLGs. Our main practical contribution is strong experimental evidence that mitered offsets of PSLGs with 100 000 segments can be computed in about ten milliseconds on a standard PC once the straight skeleton is available and that our implementation clearly is the fastest code for mitered offsetting even if the computational costs of the straight-skeleton computation are included in the timings.

Skeletal Structures for Modeling Generalized Chamfers and Fillets in the Presence of Complex Miters

“…Nowadays it is generally uncontested that computing an appropriate skeletal data structure as preprocessing constitutes the premier choice for offsetting 2D polygons with regard to both speed and reliability. See, e.g., constant-radius offsets based on Voronoi diagrams [9] and mitered offsets based on straight skeletons [18]. Hence, it seems natural to apply a similar approach to mitered offsetting in three dimensions and to resort to 3D pendants of 2D straight skeletons.…”

Continuously Generalizing Buildings to Built-up Areas by Aggregating and Growing

“…Suppose that our input has n edges in total. Operations like growing, dilation, erosion, merge, and clip cost time O(n 2 ) [10,18]. We iteratively aggregate in Section 2.3.…”

Generalized offsetting of planar structures using skeletons

“…The approach is identical to how constantdistance offsets are computed based on Voronoi diagrams or straight skeletons [11,16]. Roughly, we iterate through all the arcs of VD v (S) and add offset elements in each face that contains points at distance t · σ .…”

“…Palfrader and Held [16] demonstrate that Aichholzer and Aurenhammer's triangulation-based algorithm [2] for computing unweighted straight skeletons can be implemented robustly on standard IEEE 754 double-precision floatingpoint arithmetic. Their experiments show that computing the straight skeleton of inputs of a million vertices takes under ten seconds, and that mitered offsets can be computed in fractions of a second if a straight skeleton is available.…”

“…This type of offset can be generated in linear time from a straight skeleton [16]. In order to avoid very sharp corners in the offset, the linear axis can be used in place of the straight skeleton [16], thus obtaining offsets with multi-segment bevels. See Fig.…”