article published yes Herbert Edelsbrunner author 3FB178DA-F248-11E8-B48F-1D18A9856A870000-0002-9823-6833 Emo Welzl author For H a set of lines in the Euclidean plane, $A(H)$ denotes the induced dissection, called the arrangement of H. We define the notion of a belt in $A(H)$, which is bounded by a subset of the edges in $A(H)$, and describe two algorithms for constructing belts. All this is motivated by applications to a host of seemingly unrelated problems including a type of range search and finding the minimum area triangle with the vertices taken from some finite set of points. SIAM1986 eng 0097-5397 1095-711110.1137/0215019 151271 - 284 yes H. Edelsbrunner, E. Welzl, SIAM Journal on Computing 15 (1986) 271–284. Edelsbrunner, H., &#38; Welzl, E. (1986). Constructing belts in two-dimensional arrangements with applications. <i>SIAM Journal on Computing</i>. SIAM. <a href="https://doi.org/10.1137/0215019">https://doi.org/10.1137/0215019</a> Edelsbrunner H, Welzl E. 1986. Constructing belts in two-dimensional arrangements with applications. SIAM Journal on Computing. 15(1), 271–284. H. Edelsbrunner and E. Welzl, “Constructing belts in two-dimensional arrangements with applications,” <i>SIAM Journal on Computing</i>, vol. 15, no. 1. SIAM, pp. 271–284, 1986. Edelsbrunner, Herbert, and Emo Welzl. “Constructing Belts in Two-Dimensional Arrangements with Applications.” <i>SIAM Journal on Computing</i>. SIAM, 1986. <a href="https://doi.org/10.1137/0215019">https://doi.org/10.1137/0215019</a>. Edelsbrunner H, Welzl E. Constructing belts in two-dimensional arrangements with applications. <i>SIAM Journal on Computing</i>. 1986;15(1):271-284. doi:<a href="https://doi.org/10.1137/0215019">10.1137/0215019</a> Edelsbrunner, Herbert, and Emo Welzl. “Constructing Belts in Two-Dimensional Arrangements with Applications.” <i>SIAM Journal on Computing</i>, vol. 15, no. 1, SIAM, 1986, pp. 271–84, doi:<a href="https://doi.org/10.1137/0215019">10.1137/0215019</a>. 41102018-12-11T12:07:00Z2022-02-01T09:34:20Z