/* ---- This file is part of SECONDO. Copyright (C) 2015, University in Hagen, Department of Computer Science, Database Systems for New Applications. SECONDO is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. SECONDO is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with SECONDO; if not, write to the Free Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA ---- //paragraph [1] Title: [{\Large \bf \begin{center}] [\end{center}}] //paragraph [2] Filename: [{\tt \begin{center}] [\end{center}}] [1] Implementation of the Euclidean Distance Operator [2] EuclideanDistance.cpp \tableofcontents \noindent 1 Introduction This file implements and registers the Euclidean distance operator for point sequences as described in \cite[section 2]{COO05}. 1.1 Operator ~dist\_euclidean~ The operator $dist\_euclidean : SEQ \times SEQ\ [\times geoid] \rightarrow real$ with $SEQ \in \{pointseq,\ tpointseq\}$ determines the Euclidean distance $D_{Eu}$ between two point sequences $P,\ Q$ of type ~SEQ~ that have the same number $n>0$ of points. The Euclidean distance of two point sequences is defined as $$D_{Eu}(P,\thinspace Q) := \sqrt{\sum_{i=1}^{n}d^{2}(p_{i},\thinspace q_{i})},$$ where $d^{2} : point \times point \rightarrow real$ is the squared Euclidean distance of two points, defined as $$d^{2}(p,\thinspace q) := (p_{x}-q_{x})^{2}+(p_{y}-q_{y})^{2}.$$ The temporal components of ~tpointseq~ objects are ignored. The computation takes the ~geoid~ into account, if specified. If any of the two sequences is ~undefined~ or empty (i.e. it contains no point) or if the sequences have different numbers of points, the result is ~undefined~. 2 Includes */ #include "PointSeq.h" #include "TrajectorySimilarity.h" #include "VectorTypeMapUtils.h" #include "Algebras/Geoid/Geoid.h" #include "QueryProcessor.h" namespace tsa { /* 3 Registration of Operators 3.1 ~dist\_euclidean~ This function expects two non-empty sequences with the same number of points. */ template double dist_euclidean(const SEQ& seq1, const SEQ& seq2, const Geoid* geoid) { double dist = 0.0; for (size_t i = 0; i < seq1.GetNoComponents(); ++i) { const Point p1 = seq1.get(i); const Point p2 = seq2.get(i); dist += sqrEuclideanDistance(p1, p2, geoid); } return sqrt(dist); } template int EuclideanDistValueMap( Word* args, Word& result, int /*message*/, Word& /*local*/, Supplier s) { const SEQ& seq1 = *static_cast(args[0].addr); const SEQ& seq2 = *static_cast(args[1].addr); const Geoid* geoid = HAS_GEOID ? static_cast(args[2].addr) : nullptr; result = qp->ResultStorage(s); // CcReal CcReal& dist = *static_cast(result.addr); /* Require defined and non-empty sequences of equal length. */ if (seq1.GetNoComponents() != seq2.GetNoComponents() || seq1.GetNoComponents() == 0) { dist.SetDefined(false); return 0; } dist.Set(dist_euclidean(seq1, seq2, geoid)); return 0; } ValueMapping dist_euclidean_functions[] = { EuclideanDistValueMap, EuclideanDistValueMap, EuclideanDistValueMap, EuclideanDistValueMap, nullptr }; struct DistEuclideanInfo : OperatorInfo { DistEuclideanInfo() : OperatorInfo() { name = "dist_euclidean"; signature = PointSeq::BasicType() + " x " + PointSeq::BasicType() + " -> " + CcReal::BasicType(); appendSignature( PointSeq::BasicType() + " x " + PointSeq::BasicType() + " x " + Geoid::BasicType() + " -> " + CcReal::BasicType()); appendSignature( TPointSeq::BasicType() + " x " + TPointSeq::BasicType() + " -> " + CcReal::BasicType()); appendSignature( TPointSeq::BasicType() + " x " + TPointSeq::BasicType() + " x " + Geoid::BasicType() + " -> " + CcReal::BasicType()); syntax = "dist_euclidean(_, _[, _])"; meaning = "Euclidean distance of two point sequences, that is the square " "root of the sum of squared Euclidean distances between " "corresponding points of the sequences. The geoid is taken " "into account, if specified. If any of the sequences is not " "defined or empty or if the sequences have different numbers " "of points, the result is undefined.\n" "The time complexity is O(n)."; } }; const mappings::VectorTypeMaps dist_euclidean_maps = { /*0*/ {{PointSeq::BasicType(), PointSeq::BasicType()}, /* -> */ {CcReal::BasicType()}}, /*1*/ {{PointSeq::BasicType(), PointSeq::BasicType(), Geoid::BasicType()}, /* -> */ {CcReal::BasicType()}}, /*2*/ {{TPointSeq::BasicType(), TPointSeq::BasicType()}, /* -> */ {CcReal::BasicType()}}, /*3*/ {{TPointSeq::BasicType(), TPointSeq::BasicType(), Geoid::BasicType()}, /* -> */ {CcReal::BasicType()}} }; ListExpr DistEuclideanTypeMap(ListExpr args) { return mappings::vectorTypeMap(dist_euclidean_maps, args); } int DistEuclideanSelect(ListExpr args) { return mappings::vectorSelect(dist_euclidean_maps, args); } void TrajectorySimilarityAlgebra::addEuclideanDistOp() { AddOperator( DistEuclideanInfo(), dist_euclidean_functions, DistEuclideanSelect, DistEuclideanTypeMap); } } //-- namespace tsa /* \begin{thebibliography}{ABCD99} //[Oe] [\"{O}] \bibitem[C[Oe]O05]{COO05} Lei Chen, M.\ Tamer [Oe]zsu, and Vincent Oria. \newblock {Robust and Fast Similarity Search for Moving Object Trajectories}. \newblock In Fatma [Oe]zcan, editor, {\em {Proceedings of the {ACM} {SIGMOD} International Conference on Management of Data, Baltimore, Maryland, USA, June 14-16, 2005}}, pages 491--502. {ACM}, 2005, http://doi.acm.org/10.1145/1066157.1066213; http://dblp.uni-trier.de/rec/bib/conf/sigmod/ChenOO05. \end{thebibliography} */