Geo-Information and Computational Geometry
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Geo-information and computational geometry Peter J.M. van Oosterom and Marc J. van Kreveld (Editors) Geo-information and computational geometry Peter J.M. van Oosterom and Marc J. van Kreveld (Editors) NCG Nederlandse Commissie voor Geodesie Netherlands Geodetic Commission 44 Delft, September 2006 Geo-information and computational geometry Peter J.M. van Oosterom and Marc J. van Kreveld (Editors) Nederlandse Commissie voor Geodesie Netherlands Geodetic Commission 44, 2006 ISBN-10: 90 6132 299 5 ISBN-13: 978 90 6132 299 3 Published by: NCG, Nederlandse Commissie voor Geodesie, Netherlands Geodetic Commission, Delft, The Netherlands Printed by: Optima Grafische Communicatie, Optima Graphic Communication, Rotterdam, The Netherlands Cover illustration: Axel Smits NCG, Nederlandse Commissie voor Geodesie, Netherlands Geodetic Commission P.O. Box 5058, 2600 GB Delft, The Netherlands T: +31 (0)15 278 28 19 F: +31 (0)15 278 17 75 E: [email protected] W: www.ncg.knaw.nl The NCG, Nederlandse Commissie voor Geodesie, Netherlands Geodetic Commission is part of the Royal Netherlands Academy of Arts and Sciences (KNAW) Contents Editorial vii Peter van Oosterom and Marc van Kreveld Computational Geometry: Its objectives and relation to GIS 1 Marc van Kreveld ,2DQG&DFKH(I¿FLHQW$OJRULWKPVIRU6SDWLDO'DWD 0DUNGH%HUJ 4XDG(GJHVDQG(XOHU2SHUDWRUVIRU$XWRPDWLF%XLOGLQJ([WUXVLRQ8VLQJ/,'$5'DWD &KULVWRSKHU*ROGDQG5HEHFFD7VH $OJRULWKPVIRUFDUWRJUDPVDQGRWKHUVSHFLDOL]HGPDSV Bettina Speckmann &RQVWUDLQHGWHWUDKHGUDOPRGHOVDQGXSGDWHDOJRULWKPVIRUWRSRJUDSKLFGDWD )ULVR3HQQLQJD 7RZDUGVLPSURYHGVROXWLRQVFKHPHVIRU0RQWH&DUORVLPXODWLRQLQHQYLURQPHQWDO PRGHOLQJODQJXDJHV 'HUHN.DUVVHQEHUJDQG.RUGH-RQJ v vi Editorial *HRJUDSKLF,QIRUPDWLRQ6FLHQFH *,6 LVDPXOWLGLVFLSOLQDU\UHVHDUFKDUHD&RQWULEXWLRQVIURP WKHVSDWLDOVFLHQFHVFRPHIURPJHRGHV\JHRJUDSK\DQGFDUWRJUDSK\ZKHUHDVFRQWULEXWLRQVIURP FRPSXWHUVFLHQFHFRPHIURPGDWDEDVHVDUWL¿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µ*HR,QIRUPDWLRQDQG&RPSXWDWLRQDO*HRPHWU\¶RIWKH1HWKHUODQGV*HRGHWLF&RP- PLVVLRQ MRLQWO\RUJDQL]HGZLWK*HR,QIRUPDWLH1HGHUODQG ZDVGHYRWHGWRWKHUHODWLRQVKLSVEH- WZHHQ*,6DQGFRPSXWDWLRQDOJHRPHWU\,QD*,6FRPSXWDWLRQVZLWKFRRUGLQDWHVDUHQHHGHG ZKHUHDVFRPSXWDWLRQDOJHRPHWU\LVDERXWGHYHORSLQJPHWKRGVWRGRVR7KHVHPLQDUDLPHGWR LPSURYHWKHXQGHUVWDQGLQJRIWKHWZRUHVHDUFK¿HOGVVRWKDWLQWHUDFWLRQLQWKHIXWXUHLVIXUWKHU VWUHQJWKHQHG:HKRSHWKDWWKHVWXG\GD\KDVUHVXOWHGLQODVWLQJQHZFRQWDFWVEHWZHHQDOOSHRSOH LQWKH1HWKHUODQGVZLWKDQLQWHUHVWLQJHRPHWULFFRPSXWLQJLQ*,6 7KHFRQWULEXWLRQVUHÀHFWWKHGLYHUVLW\RIWKHSRVVLEOHLQWHUDFWLRQVEHWZHHQFRPSXWDWLRQDOJHRP- HWU\DQG*,67KHWRSLFVRIWKHFRQWULEXWLRQVUDQJHIURPRYHUYLHZVRIUHOHYDQWWHFKQLTXHVDQG WRROVWRVROYLQJVSHFL¿FVSDWLDOSUREOHPVLQHLWKHUWKHREMHFWEDVHG YHFWRU RU¿HOGEDVHG UDVWHU GRPDLQ7KLVSXEOLFDWLRQLVDUHÀHFWLRQRIWKHGLIIHUHQWVHPLQDUFRQWULEXWLRQV 7KH ¿UVW SDSHU µ&RPSXWDWLRQDO *HRPHWU\ ,WV REMHFWLYHV DQG UHODWLRQ WR *,6¶LV E\ 0DUF YDQ .UHYHOG 8WUHFKW8QLYHUVLW\ 7KHDQDO\VLVRIDOJRULWKPVLQYROYHVXQGHUVWDQGLQJKRZHI¿FLHQWO\ DQDOJRULWKPVROYHVDSUREOHP2QHRIWKHPDLQREMHFWLYHVRIFRPSXWDWLRQDOJHRPHWU\LV¿QGLQJ WKHPRVWHI¿FLHQWDOJRULWKPVIRUDOOVRUWVRIJHRPHWULFSUREOHPV+HLQWURGXFHVWKHPDLQFRQFHSWV DQGLGHDVLQFRPSXWDWLRQDOJHRPHWU\LQFOXGLQJHI¿FLHQF\DQDO\VLVLQWUDFWDELOLW\RXWSXWVHQVL- WLYHDOJRULWKPVDQGDSSUR[LPDWLRQDOJRULWKPV7KHEDVLFSUREOHPVRIFRPSXWDWLRQDOJHRPHWU\ DOOKDYHDGLUHFWRULQGLUHFWXVHWR*,6+HDOVRLQGLFDWHVZK\FRPSXWDWLRQDOJHRPHWU\LVQRWDV XVHIXOWR*,6DVLWFRXOGEH FRPSOLFDWHGDOJRULWKPVIRFXVRQZRUVWFDVHHI¿FLHQF\DQGRQZHOO GH¿QHGVLPSOHWRVWDWHSUREOHPV DQGKRZWKLVLVFXUUHQWO\LPSURYLQJ DYDLODEOHVRIWZDUHOLEUDU- LHVVLPSOHUDOJRULWKPVSURYDEO\HI¿FLHQWXQGHUUHDOLVWLFDVVXPSWLRQV 0DUNGH%HUJ 78(LQGKRYHQ DGGUHVVHVRQHRIWKHLVVXHVWRPDNHFRPSXWDWLRQDOJHRPHWU\WHFK- QLTXHVPRUHDSSOLFDEOHLQSUDFWLFHQDPHO\WKHKDQGOLQJRIODUJHGDWDVHWVWKDWGRQRW¿WLQPDLQ PHPRU\ DVRIWHQPRUHRUOHVVLPSOLFLWO\DVVXPHGLQWKHGHVFULSWLRQRIPDQ\GDWDVWUXFWXUHVDQG DOJRULWKPV ,QKLVSDSHUµ,2DQG&DFKHHI¿FLHQW$OJRULWKPVIRU6SDWLDO'DWD¶KHH[SODLQVKRZ WKHKLHUDUFKLFDOPHPRU\FRQVLVWLQJRIDGLVNPDLQPHPRU\DQGVHYHUDOOHYHOVRIFDFKHVKRXOGEH LQFOXGHGLQGDWDVWUXFWXUHDQGDOJRULWKPGHVLJQ7KHGLIIHUHQFHEHWZHHQWKHWLPHVWRDFFHVVWKHVH GLIIHUHQWOHYHOVRIPHPRU\LVTXLWHODUJHWKHGLVNLVW\SLFDOO\DERXWWLPHVVORZHUWKDQ DFFHVVLQJWKHPDLQPHPRU\,QWKHSDSHUVRPHRIWKHUHFHQWUHVXOWVWKDWKDYHEHHQREWDLQHGRQ ,2DQGFDFKHHI¿FLHQWDOJRULWKPVDUHGLVFXVVHGZLWKIRFXVRQVSDWLDOGDWD 2QHVSHFL¿FGDWDVWUXFWXUHEDVHGRQTXDGHGJHVDQGDSSOLHGWRFUHDWLQJDQGHGLWLQJWKUHHGL- PHQVLRQDOPRGHOVLVGHVFULEHGE\&KULVWRSKHU*ROGDQG5HEHFFD7VH 8QLYHUVLW\RI*ODPRUJDQ 8. 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