Updated

Documentation/doc/biblio/geom.bib

@@ -4167,7 +4167,7 @@ cell neighborhood in $O(m)$ time."
 , succeeds =	"aarx-clgta-96"
 , update =	"98.07 rote, 98.03 mitchell, 97.03 rote"
 , abstract =	"Exploiting the concept of so-called light edges, we introduce
-		a new way of defining the greedy triangulation GT(S) of a point 
+		a new way of defining the greedy triangulation GT(S) of a point
 		set S.  It provides a decomposition of
 		GT(S) into levels, and the number of levels allows us to
 		bound the total edge length of GT(S). In particular, we show
@@ -12292,9 +12292,9 @@ method that uses very different techniques."
 , pages =	"201--290"
 , url =	"http://wwwpi6.fernuni-hagen.de/Publikationen/tr198.pdf"
 , succeeds =	"ak-vd-96"
-, cites =	"ahknu-vdcfc-95, abms-claho-94, aesw-emstb-91, agss-ltacv-89, ahl-sqrpc-90, aiks-fkpmd-91, a-dppuv-82, aaag-ntsp-95, aa-skfgpf-95, aacktrx-tin-96, a-nemts-83, as-vdco-95, ay-aampt1-90, ay-aampt2-90, ar-cvddp-96, a-gvdps-89, a-lbvdc-98, abky-cabmm-88, abcw-cpdts-88, ab-rdt-85, a-sdcgp-85, a-pdpaa-87, a-rpccc-87, a-iadbu-88, a-lcpd-88, a-ndrcv-90, a-vdsfg-91, ae-oacwv-84, aha-mttls-92, ai-grvd-88, as-solri-92, abi-cvus-88, br-rasas-90, bo-arcgi-79, bs-dcms-76, bwy-oetac-80, be-mgot-92i, beg-pgmg-94, b-bnvd, bt-gatuf-85, bmt-dppbp-96, bcdt-osc3d-91i, bdsty-arsol-92, bg-tdrcs-93, bsty-vdhdc-95, bt-rcdt-93, bh-cpcoe-88, b-rgsdd-89, b-vdch-79, b-gtfga-80, bms-hcvdl-94, b-gog-55, c-vmpmp-85, cd-svd-88, crw-gc-91, csy-oscpf-95, cdns-nsrgs-95, c-ochaa-93, ce-iacko-87, cgt-ecabs-95, cx-alesw-96, c-bvdcp-86, c-cdt-89, c-tapga-89, c-gqmgc-93, 
+, cites =	"ahknu-vdcfc-95, abms-claho-94, aesw-emstb-91, agss-ltacv-89, ahl-sqrpc-90, aiks-fkpmd-91, a-dppuv-82, aaag-ntsp-95, aa-skfgpf-95, aacktrx-tin-96, a-nemts-83, as-vdco-95, ay-aampt1-90, ay-aampt2-90, ar-cvddp-96, a-gvdps-89, a-lbvdc-98, abky-cabmm-88, abcw-cpdts-88, ab-rdt-85, a-sdcgp-85, a-pdpaa-87, a-rpccc-87, a-iadbu-88, a-lcpd-88, a-ndrcv-90, a-vdsfg-91, ae-oacwv-84, aha-mttls-92, ai-grvd-88, as-solri-92, abi-cvus-88, br-rasas-90, bo-arcgi-79, bs-dcms-76, bwy-oetac-80, be-mgot-92i, beg-pgmg-94, b-bnvd, bt-gatuf-85, bmt-dppbp-96, bcdt-osc3d-91i, bdsty-arsol-92, bg-tdrcs-93, bsty-vdhdc-95, bt-rcdt-93, bh-cpcoe-88, b-rgsdd-89, b-vdch-79, b-gtfga-80, bms-hcvdl-94, b-gog-55, c-vmpmp-85, cd-svd-88, crw-gc-91, csy-oscpf-95, cdns-nsrgs-95, c-ochaa-93, ce-iacko-87, cgt-ecabs-95, cx-alesw-96, c-bvdcp-86, c-cdt-89, c-tapga-89, c-gqmgc-93,
-		cd-vdbcd-85, ckstw-vdl3s-95, csw-fmasp-95, c-wcanh-76, cms-mfdca-94, c-narsc-87, c-agmst-89, cms-frric-93, cs-arscg-89, cmrs-tspvd-93, cw-pspp-86, dj-wtacg-89, ds-oiti-89, bms-plpco-93, dfnp-stdt-91, d-eaclm-77, dk-savd-87, dk-bspwa-97, dn-cgacp-85, d-slsv-34, d-pp-44, d-rysoa-92, dv-cprac-77, dds-saeid-92, de-apphd-96, d-nhndt-87, d-tdt-90, d-fhcdt-92, d-udrdp-50, dl-cvdrp-91, ddg-fsp-83, dfs-dgaag-90, dl-pmtds-89, dl-msp-76, d-ec-83, d-fdcac-87, d-hdvdl-91, e-acg-87, e-atccd-90, e-ubids-95, egs-ueplf-89, egs-oplms-86, eks-sspp-83, em-tdas-94, eos-calha-86, es-vda-86, ess-ztha-93, es-itfwr-96, es-otatd-91, et-qtaml-93, et-ubcdt-93, etw-otama-92, ei-drmwc-79, f-sodt-90, f-iwatd-86, f-nsa2d-92, f-vddt-92, f-savd-87, gs-nsagv-69, gj-cigtn-79, g-3dmud-95, g-agt-85, grr-vdlsm-95, grss-sracp-95, 
+		cd-vdbcd-85, ckstw-vdl3s-95, csw-fmasp-95, c-wcanh-76, cms-mfdca-94, c-narsc-87, c-agmst-89, cms-frric-93, cs-arscg-89, cmrs-tspvd-93, cw-pspp-86, dj-wtacg-89, ds-oiti-89, bms-plpco-93, dfnp-stdt-91, d-eaclm-77, dk-savd-87, dk-bspwa-97, dn-cgacp-85, d-slsv-34, d-pp-44, d-rysoa-92, dv-cprac-77, dds-saeid-92, de-apphd-96, d-nhndt-87, d-tdt-90, d-fhcdt-92, d-udrdp-50, dl-cvdrp-91, ddg-fsp-83, dfs-dgaag-90, dl-pmtds-89, dl-msp-76, d-ec-83, d-fdcac-87, d-hdvdl-91, e-acg-87, e-atccd-90, e-ubids-95, egs-ueplf-89, egs-oplms-86, eks-sspp-83, em-tdas-94, eos-calha-86, es-vda-86, ess-ztha-93, es-itfwr-96, es-otatd-91, et-qtaml-93, et-ubcdt-93, etw-otama-92, ei-drmwc-79, f-sodt-90, f-iwatd-86, f-nsa2d-92, f-vddt-92, f-savd-87, gs-nsagv-69, gj-cigtn-79, g-3dmud-95, g-agt-85, grr-vdlsm-95, grss-sracp-95,
-		goy-cvdsl-93, gs-cdtp-78, gks-ricdv-92, gmr-vdmpp-92, gs-pmgsc-85, h-ca-75, h-rvdlp-92, h-gbitp-91, hkp-itnc-91, hn-sc-89, hns-psscp-88, h-pcprn-91, hks-uevsi-93, h-oarms-79, iklm-cdf3s-93, iki-awvdr-94, iss-nriac-92, j-3dtlt-89, j-ctddt-91, j-gspgm-91, jrz-ccdt-91, km-accvd-91, km-icdmc-92, kk-cdtmb-88, kg-cgwac-92, k-csmwt-94, ks-tpscv-93, k-eccs-79, k-ndot-80, k-osps-83, kr-fcm-85, k-cddvd-80, k-cavd-89, kl-ltrab-93, kl-fsc-95, kl-mpsp-95, kmm-ricav-93a, kw-vdbgm-88, k-sssgt-56, kl-fsacl-95, l-dtmmi-94, l-esta-94, l-scsi-77, l-vdlmh-94, l-ricsa-95, l-tdvdl-80, l-matps-82, l-knnvd-82, ld-gvdp-81, ll-gdtpg-86, lw-vdllm-80, lk-qgtam-96, l-ltcrn-94, msw-sblp-92, ms-pggrg-80, m-dtchn-84, mr-vdcdg-90, mks-cplvd-96, m-tdird-76, m-mnfcp-70, m-lpltw-84, mmo-cavd-91, m-zkav-93, 
+		goy-cvdsl-93, gs-cdtp-78, gks-ricdv-92, gmr-vdmpp-92, gs-pmgsc-85, h-ca-75, h-rvdlp-92, h-gbitp-91, hkp-itnc-91, hn-sc-89, hns-psscp-88, h-pcprn-91, hks-uevsi-93, h-oarms-79, iklm-cdf3s-93, iki-awvdr-94, iss-nriac-92, j-3dtlt-89, j-ctddt-91, j-gspgm-91, jrz-ccdt-91, km-accvd-91, km-icdmc-92, kk-cdtmb-88, kg-cgwac-92, k-csmwt-94, ks-tpscv-93, k-eccs-79, k-ndot-80, k-osps-83, kr-fcm-85, k-cddvd-80, k-cavd-89, kl-ltrab-93, kl-fsc-95, kl-mpsp-95, kmm-ricav-93a, kw-vdbgm-88, k-sssgt-56, kl-fsacl-95, l-dtmmi-94, l-esta-94, l-scsi-77, l-vdlmh-94, l-ricsa-95, l-tdvdl-80, l-matps-82, l-knnvd-82, ld-gvdp-81, ll-gdtpg-86, lw-vdllm-80, lk-qgtam-96, l-ltcrn-94, msw-sblp-92, ms-pggrg-80, m-dtchn-84, mr-vdcdg-90, mks-cplvd-96, m-tdird-76, m-mnfcp-70, m-lpltw-84, mmo-cavd-91, m-zkav-93,
 		m-uuam-28, m-rcvdp-93, m-spop-93, mmp-dgp-87, ms-getcc-88, mp-fitcp-78, m-osclv-90, m-lavd-91, osy-gvdl-86, osy-gvdl-87, oy-rmpmd-85, oim-iimvd-84, obs-stcav-92, p-etspi-77, pl-ecgvd-95, p-kpudz-82, p-mrpdt-92, ps-cgi-85, p-scnsg-57, r-odtr-91, rr-oprav-94, r-aiv-94, r-mrpdt-90, r-tbvdm-93, rsl-ashts-77, st-pwvt-88, s-cvdhd-82, s-mplbc-85, s-chdch-86, s-nfhdv-87, s-cdtvd-88, s-sdlpc-91, s-barga-93, s-cg-78, sh-cpp-75, s-icpps-85, s-atubl-94, s-let-78, s-vidt-80, s-sagdt-91, s-facdt-87, s-mmdpsl-91a, sd-csdta-95, s-smane-92, si-cvdom-92, soi-toari-90, s-rngam-83, si-atpvd-86, t-otdt-93, too-natdv-83, t-gcvdm-86, t-rngfp-80, v-mstkd-88, v-sgagc-91, v-dmrsl-09, v-nadpc-08, w-eucdt-93, ws-oacdt-87, w-cnddt-81, w-sedbe-91a, www-sdpfo-87, y-cmstk-82, y-amp-87, y-oavds-87, zm-sdnah-91, ZZZ"
 , update =	"00.11 smid, 00.03 bibrelex, 99.03 bibrelex, 98.11 bibrelex, 98.07 mitchell, 98.03 bibrelex, 97.03 icking"
 , annote =	"Chapter 5 of su-hcg-00"
@@ -12847,9 +12847,9 @@ method that uses very different techniques."
 , url =	"http://www.ifor.math.ethz.ch/staff/fukuda/fukuda.html"
 , update =	"98.03 houle, 97.03 pocchiola, 96.05 fukuda"
 , annote =	"Reverse search is a general exhaustive search technique
-which came out of the new convex hull algorithm by the authors. 
+which came out of the new convex hull algorithm by the authors.
 This technique can be applied to many enumeration problems in computer
-science, operations research and geometry.  
+science, operations research and geometry.
 It is highly suitable for parallelization."
 }
 
@@ -16291,7 +16291,7 @@ rendering. Contains pseudocode."
 , number =	4
 , year =	1997
 , note =	"Special issue on parallel I/O.  An earlier version
-		  appears in Proc. of the 8th Annual 
+		  appears in Proc. of the 8th Annual
 		 ACM Symposium on Parallel Algorithms and
 		 Architectures (SPAA~'96), Padua, Italy, June 1996, 109--118"
 , update =	"97.03 murali"
@@ -18449,12 +18449,12 @@ the interior. Contains pseudocode."
 , succeeds =	"d-rld-89"
 , update =	"98.07 bibrelex, 98.03 mitchell, 93.09 held"
 , annote =	"He considers rectilinear paths in a rectilinear simple polygon.  In $O(n\log n)$
-		 preprocessing time and space, he builds a data structure that supports 
+		 preprocessing time and space, he builds a data structure that supports
-		 $O(\log n)$ time queries for distance between two points ($O(1)$ time between 
+		 $O(\log n)$ time queries for distance between two points ($O(1)$ time between
-		 two polygon vertices).  He is actually searching for paths that are``smallest'' in 
+		 two polygon vertices).  He is actually searching for paths that are``smallest'' in
-		 that they are shortest simultaneously in rectilinear link distance and 
+		 that they are shortest simultaneously in rectilinear link distance and
-		 $L_1$ length (which is always possible).  See improvements to $O(n)$ time and 
+		 $L_1$ length (which is always possible).  See improvements to $O(n)$ time and
-		 space by Lingas, Maheshwari, and Sack~\cite{lms-parld-95} and 
+		 space by Lingas, Maheshwari, and Sack~\cite{lms-parld-95} and
 		 Schuierer~\cite{s-odssr-96}."
 }
 
@@ -21011,10 +21011,10 @@ cubes with side-lengths not exceeding 1 in the $3$-dimensional
 euclidean space. Let $S$ and $T$ be two points lying outside
 the open cubes. Assume one needs to find a short path emanating
 from $S$ and terminating at $T$ avoiding the cubes of $\cal P$
-under the restriction that the cubes are not known prior to the search. 
+under the restriction that the cubes are not known prior to the search.
 In fact the positions and the side-lengths of the cubes become known
 to the searcher as the cubes are contacted. We give an algorithm to
-construct a path of length less than 
+construct a path of length less than
 $\frac 32 d + 3 \sqrt 3 \log d + 5$,
 where $d > 3 \sqrt 3$ denotes the distance between S and T."
 }
@@ -24325,7 +24325,7 @@ experimental results are given."
 , abstract =	"This  paper
 presents  the main algorithmic and design choices that have been
 made
-to implement triangulations in 
+to implement triangulations in
 the computational geometry algorithms library CGAL."
 }
 
@@ -25614,9 +25614,9 @@ present a polynomial-time exact algorithm to solve this problem."
 		rectangles floating in 3-space, with edges represented by
 		vertical lines of sight. We apply an extension of the
 		{Erd\H os}-Szekeres Theorem in a geometric setting to obtain an
-		upper bound of 56 for size of the largest complete graph which 
+		upper bound of 56 for size of the largest complete graph which
-		is representable. On the other hand, we construct a 
+		is representable. On the other hand, we construct a
-		representation of the complete graph with 22 vertices. 
+		representation of the complete graph with 22 vertices.
 		These are the best existing bounds."
 }
 
@@ -28630,7 +28630,7 @@ determinants."
 , year =	1993
 , update =	"98.03 mitchell"
 , abstract =	"We calculate the partition
- of the configuration space $I\!\!R^2 x S^1$ 
+ of the configuration space $I\!\!R^2 x S^1$
  of a car-like  robot, only moving forwards,  with respect  to the
  type of the  length optimal paths.  This kind  of robot is  subject to
  kinematic constraints on   its  path curvature and  its   orientation.
@@ -33590,35 +33590,35 @@ determinants."
 Given a set of polygonal obstacles of $n$ vertices in the plane,
 the problem of processing the all-pairs Euclidean {\em short} path
 queries is that of reporting an obstacle-avoiding path $P$ (or
-its length) between two arbitrary query points $p$ and $q$ in the 
+its length) between two arbitrary query points $p$ and $q$ in the
-plane, such that the length of $P$ is within a small factor of the 
+plane, such that the length of $P$ is within a small factor of the
 length of a Euclidean {\em shortest} obstacle-avoiding path between
 $p$ and $q$.  The goal is to answer each short path query quickly
-by constructing data structures that capture path information in 
+by constructing data structures that capture path information in
-the obstacle-scattered plane.  For the related all-pairs Euclidean 
+the obstacle-scattered plane.  For the related all-pairs Euclidean
-{\em shortest} path problem, the best known algorithms for even 
+{\em shortest} path problem, the best known algorithms for even
-very simple cases (e.g., {\em rectilinear} shortest paths among 
+very simple cases (e.g., {\em rectilinear} shortest paths among
 disjoint {\em rectangular} obstacles in the plane) require
 at least quadratic space and time to construct a data structure,
-so that a length query can be answered in polylogarithmic time.  
+so that a length query can be answered in polylogarithmic time.
-The previously best known solution to the all-pairs Euclidean 
+The previously best known solution to the all-pairs Euclidean
-{\em short} path problem also uses a data structure of quadratic 
+{\em short} path problem also uses a data structure of quadratic
-space and superquadratic construction time, in order to answer a 
+space and superquadratic construction time, in order to answer a
-length query in polylogarithmic time.  In this paper, we present a 
+length query in polylogarithmic time.  In this paper, we present a
-data structure that requires nearly linear space and takes subquadratic 
+data structure that requires nearly linear space and takes subquadratic
-time to construct.  Precisely, for any given $\epsilon$ satisfying 
+time to construct.  Precisely, for any given $\epsilon$ satisfying
 $0$ $<$ $\epsilon$ $\leq$ $1$, our data structure can be built
-in $o(q^{3/2})$ $+$ $O((n\log n)/\epsilon)$ time and 
+in $o(q^{3/2})$ $+$ $O((n\log n)/\epsilon)$ time and
-$O(n\log n+n/\epsilon)$ space, where $q$, $1$ $\leq$ $q$ $\leq$ $n$, 
+$O(n\log n+n/\epsilon)$ space, where $q$, $1$ $\leq$ $q$ $\leq$ $n$,
-is the minimum number of faces needed to cover all the vertices of 
+is the minimum number of faces needed to cover all the vertices of
-a certain planar graph we use.  This data structure enables us to 
+a certain planar graph we use.  This data structure enables us to
 report the length of a short path between two arbitrary query points
 in $O((\log n)/\epsilon+1/\epsilon^2)$ time and the actual path
-in $O((\log n)/\epsilon+1/\epsilon^2+L)$ time, where $L$ is the 
+in $O((\log n)/\epsilon+1/\epsilon^2+L)$ time, where $L$ is the
-number of edges of the output path.  The constant approximation 
+number of edges of the output path.  The constant approximation
-factor, $6+\epsilon$, for the short paths that we compute is quite 
+factor, $6+\epsilon$, for the short paths that we compute is quite
-small.  Our techniques are parallelizable and can also be used 
+small.  Our techniques are parallelizable and can also be used
-to improve the previously best known results on several related 
+to improve the previously best known results on several related
 graphic and geometric problems."
 }
 
@@ -36888,7 +36888,7 @@ avoids overlap. This is useful in cartography."
 This paper shows that the $i$-level of an arrangement of hyperplanes in
 $E^d$ has at most ${{i+d-1}\choose {d-1}}$ local minima.
 This bound follows from ideas previously used to prove bounds on $(\leq k)$-sets.
-Using linear programming duality, 
+Using linear programming duality,
 the Upper Bound Theorem is obtained as a corollary,
 giving yet another proof of this
 celebrated bound on the number of vertices of a simple polytope
@@ -42606,10 +42606,10 @@ Contains C code."
 , succeeds =	"dp-olacd-91"
 , update =	"98.11 bibrelex, 98.07 bibrelex, 95.09 mitchell"
 , annote =	"In this paper you will find the definition of a Constrained
-		 Delaunay Triangulation, some theorems and the pseudocode of 
+		 Delaunay Triangulation, some theorems and the pseudocode of
-		 the algorithms to program it. On-Line means that you can 
+		 the algorithms to program it. On-Line means that you can
-		 insert points and required edges in any order. With this 
+		 insert points and required edges in any order. With this
-		 algorithm you can update an old CDT without retriangulating 
+		 algorithm you can update an old CDT without retriangulating
 		 the old data."
 }
 
@@ -44330,7 +44330,7 @@ Contains C code."
 
 @techreport{d-vrtdd-09
 ,  author      = "Olivier Devillers"
-,  title       = "Vertex Removal in Two Dimensional {Delaunay} Triangulation: 
+,  title       = "Vertex Removal in Two Dimensional {Delaunay} Triangulation:
                   Asymptotic Complexity is Pointless"
 , thanks = "triangles"
 ,  institution = "INRIA"
@@ -53249,17 +53249,17 @@ library."
 , update =	"98.11 bibrelex, 98.03 mitchell, 97.11 bibrelex, 97.03 rote"
 , abstract =	"We call a line $l$ a separator for a set $S$ of objects in
 		the plane if $l$ avoids all the objects and
-		partitions $S$ into two nonempty subsets, one consisting 
+		partitions $S$ into two nonempty subsets, one consisting
 		of objects lying above $l$ and the
-		other of objects lying below $l$. We present an 
+		other of objects lying below $l$. We present an
 		$O(n log n)$-time algorithm for
-		finding a separator line for a set of $n$ segments, provided 
+		finding a separator line for a set of $n$ segments, provided
-		the ratio between the diameter of the set of segments and 
+		the ratio between the diameter of the set of segments and
 		the length of the smallest segment is bounded.
-		No subquadratic algorithms are known for the general case. 
+		No subquadratic algorithms are known for the general case.
 		Our algorithm is based on the recent results of
-		Matousek, Pach, Sharir, Sifrony, and Welzl (1994) concerning 
+		Matousek, Pach, Sharir, Sifrony, and Welzl (1994) concerning
-		the union of fat triangles, but we also include an analysis 
+		the union of fat triangles, but we also include an analysis
 		which improves the bounds obtained by Matousek et al."
 }
 
@@ -57348,18 +57348,18 @@ a simple polygon with vertex set P. We prove that it is NP-complete
 to find a minimum weight polygon or a maximum weight polygon for a
 given vertex set, resulting in a proof of NP-completeness for the
 corresponding area optimization problems. This answers a generalization
-of a question stated by Suri in 1989. 
+of a question stated by Suri in 1989.
 We give evidence that it is unlikely that the minimization
-problem can be approximated. 
+problem can be approximated.
 For the maximiation problem, we show that we can find in optimal
 time O(n log n) a polygon
 of more than half the area AR(conv(P)) of the convex hull conv(P)
 of P, yielding a fast 1/2 approximation method for the problem.
 We demonstrate that it is NP-complete to decide whether there
-is a simple polygon of at least (2/3+eps)(AR(conv(P)). 
+is a simple polygon of at least (2/3+eps)(AR(conv(P)).
 We also sketch an NP-hardness proof for the problem of finding a minimum-link
 searating polygon for two finite point sets in the plane.
-Finally, we turn to higher dimensions, where we prove that for 
+Finally, we turn to higher dimensions, where we prove that for
 0<k<d+1, 1<d, it is
 NP-hard to minimize the volume of the k-dimensional faces of a
 d-dimensional simple nondegenerate polyhedron with a given vertex
@@ -57467,7 +57467,7 @@ set, answering a generalization of a question stated by O'Rourke in 1980."
 , update =	"98.03 mitchell"
 , abstract =	"For a given set $A\subseteq\ (-\pi;+\pi]$ of angles, the problem ``Angle-Restricted Tour'' (ART) is to decide whether a set $P$ of $n$ points in the
 Euclidean plane allows a closed directed tour consisting of straight line segments, such that all angles between consecutive line segments are from the
-set $A$. 
+set $A$.
 \par
 We present a variety of combinatorial and algorithmic results on this problem. In particular, we show that any finite set of at least 5 points allows a
 ``pseudoconvex'' tour, where all angles are nonnegative."
@@ -93036,7 +93036,7 @@ and implement some of them."
 , nickname =	"IWCIA '01"
 , year =	2001
 , pages =	"139--151"
-, comments =	"Appears also in Electronic Notes in Theoretical 
+, comments =	"Appears also in Electronic Notes in Theoretical
                  Computer Science, Volume 46,
                  www.elsevier.nl/locate/entcs/volume46.html"
 , update =	"01.11 smid"
@@ -97147,7 +97147,7 @@ exclusive read exclusive write parallel random-access machine (EREW
 PRAM). Let $P$ be a trapezoided rectilinear simple polygon with $n$
 vertices. In $O(\log n)$ time using $O(n/{\log n})$ processors we can
 optimally compute
-\begin{enumerate} 
+\begin{enumerate}
 \item minimum rectilinear link paths, or shortest paths in the $L_1$
 metric from any point in $P$ to all vertices of $P$,
 \item minimum rectilinear link paths from any segment inside $P$ to
@@ -105738,22 +105738,22 @@ and robustness is significantly improved; the implementation has no numerical
 tolerances and does not exhibit cycling problems. The algorithm also handles
 penetrating polyhedra, making it useful for nonconvex polyhedral collision
 detection. This paper presents the theoretical principles of V-clip, and gives
-a pseudocode description of the algorithm. It also documents various tests 
+a pseudocode description of the algorithm. It also documents various tests
-that compare V-clip, Lin-Canny, and the Enhanced Gilbert-Johnson-Keerthi 
+that compare V-clip, Lin-Canny, and the Enhanced Gilbert-Johnson-Keerthi
-algorithm, a simplex-based algorithm that is widely used for the same 
+algorithm, a simplex-based algorithm that is widely used for the same
-application. The results show V-clip to be a strong contender in this field, 
+application. The results show V-clip to be a strong contender in this field,
-comparing favorably with the other algorithms in most of the tests, in terms 
+comparing favorably with the other algorithms in most of the tests, in terms
 of both performance and robustness.
 \par
 From the V-Clip Collision Detection WWW page:
 \par
 V-Clip is a low-level collision detection algorithm. The basic operation
-provided to the application is that of performing a collision check between 
+provided to the application is that of performing a collision check between
-two objects. The decisions of when to perform the checks between which object 
+two objects. The decisions of when to perform the checks between which object
-pairs are left to the application. In particular, the V-Clip library does not 
+pairs are left to the application. In particular, the V-Clip library does not
-include facilities for higher level collision check culling, using bounding 
+include facilities for higher level collision check culling, using bounding
-boxes or spheres, for example. If this is required, consider writing one 
+boxes or spheres, for example. If this is required, consider writing one
-yourself, or consider using a complete collision detection package such as 
+yourself, or consider using a complete collision detection package such as
 I-Collide or V-Collide.
 \par
 V-Clip is designed for objects that are bounded by closed surfaces, and not
@@ -106549,9 +106549,9 @@ problems in computational geometry is presented."
 , cites =	"rwzw-cksck-91, rw-cckgp-92, eorw-fmakg-92"
 , update =	"98.03 mitchell, 97.11 bibrelex, 97.03 rote"
 , abstract =	"Given a set $S$ of $n$ points in the plane, we compute in time
-		$O(n^3)$ the total number of convex polygons whose vertices are 
+		$O(n^3)$ the total number of convex polygons whose vertices are
-		a subset of $S$. We give an $O(m n^3)$ algorithm for computing 
+		a subset of $S$. We give an $O(m n^3)$ algorithm for computing
-		the number of convex $k$-gons with vertices in $S$, for all 
+		the number of convex $k$-gons with vertices in $S$, for all
 		values $k=3,\ldots,m$."
 }
 
@@ -113828,7 +113828,7 @@ small) triangulation of a convex polyhedron is NP-complete. Their 3SAT-reduction
 , update =	"98.07 bibrelex, 97.07 orourke"
 , annote =	"A new polygon visibility graph is introduced.  It is
                  demonstrated that it encodes more geometric
-		 information about the polygon than does the vertex 
+		 information about the polygon than does the vertex
                  visibility graph.  For example, it determines the
                  shortest path tree for each vertex."
 }
@@ -113856,7 +113856,7 @@ small) triangulation of a convex polyhedron is NP-complete. Their 3SAT-reduction
 , annote =	"Vertex-edge visibility graphs of pseudo-polygons
 		are characterized combinatorially, showing that the
 		decision problem for them is in P.  This also establishes
-		that the decision problem for vertex-vertex 
+		that the decision problem for vertex-vertex
 		visibility graphs of pseudo-polygons is in NP."
 }
 
@@ -124693,7 +124693,7 @@ Previous title:  On-Line Navigation Through Regions of Variable
 		points and we are able to report an approximation of the width
 		of this dynamic point set. Our data structure takes linear space
 		and allows for reporting the approximation with relative
-		accuracy $\epsilon$ in $O(sqrt(1/\epsilon)log n)$ time; and the 
+		accuracy $\epsilon$ in $O(sqrt(1/\epsilon)log n)$ time; and the
 		update time is $O(\log^2 n)$. The method uses the tentative
 		prune-and-search strategy of Kirkpatrick and Snoeyink."
 }
@@ -130003,12 +130003,12 @@ Contains C code."
 , update =	"98.07 bibrelex+rote, 98.03 mitchell, 97.03 rote"
 , abstract =	"We consider the problem of approximating a convex figure
 		in the plane by a pair $(r,R)$ of homothetic (i. e., similar and
-		parallel) rectangles with $r$ contained in $C$ and $R$ 
+		parallel) rectangles with $r$ contained in $C$ and $R$
-		containing $C$. We show the existence of such pairs where the 
+		containing $C$. We show the existence of such pairs where the
-		sides of the outer rectangle have length at most double the 
+		sides of the outer rectangle have length at most double the
-		length of the inner rectangle, thereby solving a problem posed 
+		length of the inner rectangle, thereby solving a problem posed
 		by P\'{o}lya and Szeg\H{o}.
-		If the $n$ vertices of a convex polygon $C$ are given as a 
+		If the $n$ vertices of a convex polygon $C$ are given as a
 		sorted array, such an approximating pair of rectangles can be
 		computed in time $O(log^2 n)$."
 }
@@ -130891,7 +130891,7 @@ Contains C code."
 , year =	1995
 , pages =	"1976--1982"
 , comments =	"also contains an interesting algorithm for the Fortune-Wilfong
-		problem, to find a minimal-length curvature-constrained 
+		problem, to find a minimal-length curvature-constrained
 		path in a polygonal environment."
 , update =	"96.05 mitchell"
 }
@@ -145397,6 +145397,17 @@ of geometric optics."
 		 any other by flips."
 }
 
+@article{w-sf-76
+, author =	{Neal R. Wagner}
+, title =       {The Sofa Problem}
+, year =        {1976}
+, journal =     {The American Mathematical Monthly}
+, volume =      {83}
+, number =         {3}
+, pages =       {188--189}
+, doi =         {10.2307/2977022}
+}
+
 @inproceedings{ww-oedca-00
 , author =	"Uli Wagner and Emo Welzl"
 , title =	"Origin-Embracing Distributions, or A Continuous Analogue of the Upper Bound Theorem"
@@ -151805,13 +151816,13 @@ amplification and suppression of local contrast. Contains C code."
 
 
 @article{hh-esplp-08
-, author = "I. Haran and D. Halperin" 
+, author = "I. Haran and D. Halperin"
-, title = "An experimental study of point location in planar arrangements in CGAL" 
+, title = "An experimental study of point location in planar arrangements in CGAL"
-, journal = "ACM Journal of Experimental Algorithmics" 
+, journal = "ACM Journal of Experimental Algorithmics"
-, volume = "13" 
+, volume = "13"
-, year = 2008 
+, year = 2008
-, pages = "" 
+, pages = ""
-} 
+}
 
 @article{hkh-iiplgtds-12
 , author = {{Hemmer}, M. and {Kleinbort}, M. and {Halperin}, D.}
@@ -151900,7 +151911,7 @@ pages = {179--189}
  acmid = {939190},
  publisher = {IEEE Computer Society},
  address = {Washington, DC, USA},
-} 
+}
 
 @inproceedings{Arthur2007Kmeans,
  author = {Arthur, David and Vassilvitskii, Sergei},
@@ -151916,7 +151927,7 @@ pages = {179--189}
  acmid = {1283494},
  publisher = {Society for Industrial and Applied Mathematics},
  address = {Philadelphia, PA, USA},
-} 
+}
 
 @book{botsch2010polygon,
   title={Polygon mesh processing},
@@ -151955,7 +151966,7 @@ pages = {179--189}
  publisher = {ACM},
  address = {New York, NY, USA},
  keywords = {Design and analysis of algorithms, computational geometry, shortest path problems},
-} 
+}
 
 
 @inproceedings{schnabel2007efficient,

Set_movable_separability_2/doc/Set_movable_separability_2/Set_movable_separability_2.txt

@@ -9,18 +9,39 @@ namespace CGAL {
 
 \section sms_sec_intro Introduction
 
+Problems of moving sets of objects, such as polygons in the plane and
+polyhedra in three dimensions, without allowing collisions between the
+objects are ubiquitous in many fields including motion planning,
+computer graphics, VLSI layout, and manufacturing. One class of such
+problems, referred to as <em>Movable Separability of Sets</em>
+\cgalCite{t-mss-85}, considers the separability of sets of objects
+under different kinds of motions and various definitions of
+separation. The <em>moving sofa problem</em> or <em>sofa problem</em>
+(see <a
+href="https://en.wikipedia.org/wiki/Moving_sofa_problem">Moving sofa
+problem</a> is a classic member of this class. It is a two-dimensional
+idealisation of real-life furniture-moving problems; it asks for the
+rigid two-dimensional shape of largest area \f$A\f$ that can be
+maneuvered through an L-shaped planar region with legs of unit width
+\cgalCite{w-sf-76}. The area \f$A\f$ thus obtained is referred to as
+the sofa constant. The exact value of the sofa constant is an open
+problem.  These problems become progressively more challenging as the
+allowable separation motions becomes more complex (have more degrees
+of freedom), the number of objects involved grows, or the shape of the
+objects becomes more complicated.
+
+\cgalFigureBegin{sms_2_fig_sofa_problem,sofa_problem.png} The
+Hammersley sofa has area 2.2074 but is not the largest solution.
+\cgalFigureEnd
+
+\section sms_sec_casting Casting
+
 Casting is a manufacturing process where liquid material is poured
 into a cavity inside a mold, which has the shape of a desired
 product. After the material solidifies, the product is pulled out of
 the mold. Typically a mold is used to manufacture numerous copies of a
-product, in which case we need to make sure that the solidified
+product. The challenge is design a proper mold, such that the solidified
-product can be separated from its mold without breaking it.  The
+product can be separated from its mold without breaking it.
-challenge of designing a proper mold belongs to a larger topic termed
-<em>Movable Separability of Sets</em>; see \cgalCite{t-mss-85}
-These problems become progressively more challenging as the allowable
-separation motions becomes more complex (have more degrees of
-freedom), the number of objects involved grows, or the shape of the
-objects becomes more complicated.
 
 This package provides a function called
 `single_mold_translational_casting_2()` that given a simple closed