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Механизм интерактивного обозначения площадей в геоинформационных системах.

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ВЕСТНИК
МГСУ
6/2011
ɆȿɏȺɇɂɁɆ ɂɇɌȿɊȺɄɌɂȼɇɈȽɈ ɈȻɈɁɇȺɑȿɇɂə
ɉɅɈɓȺȾȿɃ ȼ ȽȿɈɂɇɎɈɊɆȺɐɂɈɇɇɕɏ ɋɂɋɌȿɆȺɏ
INTERACTIVE AREA DEFINITION IN GEOGRAPHIC
INFORMATION SYSTEMS
Ⱥ.ȼ. Ɇɢɯɚɣɥɢɱɟɧɤɨ, Ⱥ.ȼ. Ⱥɡɚɪɨɜɚ
A.V. Mikhailicheko, A.V. Azarova
ɎȽȻɈɍ ȼɉɈ «ɆȽɋɍ»
ɋɬɚɬɶɹ ɨɩɢɫɵɜɚɟɬ ɚɥɝɨɪɢɬɦ ɨɛɨɡɧɚɱɟɧɢɹ ɩɥɨɳɚɞɟɣ ɜ ɝɟɨɢɧɮɨɪɦɚɰɢɨɧɧɵɯ ɫɢɫɬɟɦɚɯ ɱɟɪɟɡ ɢɧɬɟɪɚɤɬɢɜɧɨɟ ɨɩɪɟɞɟɥɟɧɢɟ ɩɨɥɨɠɟɧɢɹ ɞɨɛɚɜɥɹɟɦɨɣ ɜ ɩɨɥɢɝɨɧ ɬɨɱɤɢ.
Article describes an area definition algorithm and interactive evaluating the polygon
point position.
ɋɬɚɥɤɢɜɚɹɫɶ ɫ ɡɚɞɚɱɟɣ ɧɚɩɨɥɧɟɧɢɹ ɝɟɨɢɧɮɨɪɦɚɰɢɨɧɧɵɯ ɫɢɫɬɟɦ, ɨɞɧɢɦ ɢɡ ɧɚɢɛɨɥɟɟ ɱɚɫɬɨ ɢɫɩɨɥɶɡɭɟɦɵɯ ɨɩɟɪɚɰɢɣ ɹɜɥɹɟɬɫɹ ɨɩɟɪɚɰɢɹ ɝɟɨɦɟɬɪɢɱɟɫɤɨɝɨ ɨɛɨɡɧɚɱɟɧɢɹ
ɨɛɥɚɫɬɟɣ. Ɍɚɤɢɦɢ ɨɛɥɚɫɬɹɦɢ ɦɨɝɭɬ ɹɜɥɹɬɶɫɹ ɩɥɨɳɚɞɢ ɛɭɞɭɳɟɣ ɡɚɫɬɪɨɣɤɢ, ɩɚɪɤɢ, ɜɨɟɧɧɵɟ ɱɚɫɬɢ ɢ ɦɧɨɝɨɟ ɞɪɭɝɨɟ.
Ɉɩɪɟɞɟɥɟɧɢɟ ɨɛɥɚɫɬɢ ɦɨɠɟɬ ɩɪɨɢɫɯɨɞɢɬɶ ɪɚɡɧɵɦɢ ɫɩɨɫɨɛɚɦɢ. Ɉɞɧɢɦ ɢɡ ɬɚɤɢɯ
ɫɩɨɫɨɛɨɜ ɦɨɠɟɬ ɹɜɥɹɬɶɫɹ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɟ ɞɨɛɚɜɥɟɧɢɟ ɬɨɱɟɤ ɜ ɨɛɨɡɧɚɱɚɸɳɢɣ ɨɛɥɚɫɬɶ
ɦɧɨɝɨɭɝɨɥɶɧɢɤ. Ⱦɪɭɝɢɦ ɫɩɨɫɨɛɨɦ ɦɨɠɟɬ ɛɵɬɶ ɢɧɬɟɪɚɤɬɢɜɧɨɟ ɨɩɪɟɞɟɥɟɧɢɟ ɛɥɢɠɚɣɲɟɝɨ ɤ ɞɚɧɧɨɣ ɬɨɱɤɟ ɪɟɛɪɚ ɦɧɨɝɨɭɝɨɥɶɧɢɤɚ ɢ ɞɨɛɚɜɥɟɧɢɟ ɧɨɜɨɣ ɬɨɱɤɢ ɦɟɠɞɭ ɜɟɪɲɢɧɚɦɢ,
ɨɛɪɚɡɭɸɳɢɦɢ ɛɥɢɠɚɣɲɟɟ ɪɟɛɪɨ.
ȼɨ ɜɬɨɪɨɦ ɫɥɭɱɚɟ ɩɪɨɝɪɚɦɦɟ ɧɟɨɛɯɨɞɢɦɨ ɪɟɲɢɬɶ ɝɟɨɦɟɬɪɢɱɟɫɤɭɸ ɡɚɞɚɱɭ, ɭɱɢɬɵɜɚɸɳɢɟ ɪɚɡɧɵɟ ɜɚɪɢɚɧɬɵ ɩɨɥɨɠɟɧɢɹ ɬɨɱɤɢ ɢ ɮɨɪɦɵ ɨɩɪɟɞɟɥɹɟɦɨɝɨ ɦɧɨɝɨɭɝɨɥɶɧɢɤɚ.
Ⱦɚɧɧɵɣ ɚɥɝɨɪɢɬɦ ɩɪɟɞɩɨɥɚɝɚɟɬ ɜɵɩɨɥɧɟɧɢɟ ɫɥɟɞɭɸɳɢɯ ɞɟɣɫɬɜɢɣ:
ɉɟɪɟɛɢɪɚɸɬɫɹ ɜɫɟ ɜɟɪɲɢɧɵ ɦɧɨɝɨɭɝɨɥɶɧɢɤɚ, ɢ ɧɚɯɨɞɢɬɫɹ ɪɚɫɫɬɨɹɧɢɟ ɞɨ ɡɚɞɚɧɧɨɣ
ɬɨɱɤɢ (ɪɢɫ. 1).
ȼɵɛɢɪɚɟɬɫɹ ɛɥɢɠɚɣɲɚɹ ɤ ɬɨɱɤɟ ɜɟɪɲɢɧɚ.
ɂɡ ɡɚɞɚɧɧɨɣ ɬɨɱɤɢ ɫɬɪɨɹɬɫɹ ɧɨɪɦɚɥɢ ɤɨ ɜɫɟɦ ɪɟɛɪɚɦ ɦɧɨɝɨɭɝɨɥɶɧɢɤɚ, ɢ ɜɵɛɢɪɚɸɬɫɹ ɬɟ ɪɟɛɪɚ, ɭ ɤɨɬɨɪɵɯ ɬɨɱɤɚ ɩɟɪɟɫɟɱɟɧɢɹ ɫ ɧɨɪɦɚɥɶɸ ɧɚɯɨɞɢɬɫɹ ɧɚ ɪɟɛɪɟ (ɪɢɫ. 2).
ȼ ɬɨɦ ɫɥɭɱɚɟ, ɟɫɥɢ ɬɚɤɢɟ ɪɟɛɪɚ ɧɚɲɥɢɫɶ, ɞɥɹ ɜɵɛɪɚɧɧɵɯ ɪɟɛɟɪ ɜɵɛɢɪɚɟɬɫɹ ɪɟɛɪɨ
ɫ ɧɚɢɦɟɧɶɲɟɣ ɞɥɢɧɨɣ ɧɨɪɦɚɥɢ.
ɋɪɚɜɧɢɜɚɟɬɫɹ ɪɚɫɫɬɨɹɧɢɟ ɞɨ ɛɥɢɠɚɣɲɟɣ ɜɟɪɲɢɧɵ ɫ ɞɥɢɧɨɣ ɧɨɪɦɚɥɢ, ɨɩɭɳɟɧɧɨɣ
ɛɥɢɠɚɣɲɟɦɭ ɪɟɛɪɭ.
ȿɫɥɢ ɞɥɢɧɚ ɧɨɪɦɚɥɢ ɦɟɧɶɲɟ ɪɚɫɫɬɨɹɧɢɹ ɞɨ ɬɨɱɤɢ, ɬɨ ɪɟɡɭɥɶɬɚɬɨɦ ɪɚɛɨɬɵ ɚɥɝɨɪɢɬɦɚ ɹɜɥɹɟɬɫɹ ɪɟɛɪɨ ɫ ɧɚɢɦɟɧɶɲɟɣ ɞɥɢɧɨɣ ɧɨɪɦɚɥɢ.
ȿɫɥɢ ɪɟɛɪɚ ɫ ɬɨɱɤɨɣ ɩɟɪɟɫɟɱɟɧɢɹ ɧɨɪɦɚɥɢ, ɧɚɯɨɞɹɳɟɣɫɹ ɦɟɠɞɭ ɨɛɪɚɡɭɸɳɢɦɢ
ɜɟɪɲɢɧɚɦɢ ɧɟ ɛɵɥɢ ɧɚɣɞɟɧɵ ɢɥɢ ɪɚɫɫɬɨɹɧɢɟ ɞɨ ɛɥɢɠɚɣɲɟɣ ɬɨɱɤɢ ɦɟɧɶɲɟ ɞɥɢɧɵ
ɧɨɪɦɚɥɢ ɬɨ ɪɟɡɭɥɶɬɚɬɨɦ ɹɜɥɹɟɬɫɹ ɨɞɧɨ ɢɡ ɪɟɛɟɪ, ɜɟɪɲɢɧɨɣ ɤɨɬɨɪɵɯ ɹɜɥɹɟɬɫɹ ɛɥɢɠɚɣɲɚɹ ɬɨɱɤɚ.
450
6/2011
ВЕСТНИК
МГСУ
Ⱦɥɹ ɨɩɪɟɞɟɥɟɧɢɹ, ɤɚɤɨɝɨ ɢɦɟɧɧɨ ɪɟɛɪɚ – ɫɬɪɨɢɬɫɹ ɨɬɪɟɡɨɤ, ɫɨɟɞɢɧɹɸɳɢɣ ɡɚɞɚɧɧɭɸ ɬɨɱɤɭ ɢ ɛɥɢɠɚɣɲɭɸ ɜɟɪɲɢɧɭ, ɢ ɨɩɪɟɞɟɥɹɟɬɫɹ ɭɝɨɥ ɦɟɠɞɭ ɷɬɢɦ ɨɬɪɟɡɤɨɦ ɢ ɪɟɛɪɚɦɢ, ɫɨɞɟɪɠɚɳɢɦɢ ɛɥɢɠɚɣɲɭɸ ɬɨɱɤɭ.
Ɋɟɛɪɨ ɫ ɧɚɢɦɟɧɶɲɢɦ ɭɝɥɨɦ ɢ ɛɭɞɟɬ ɹɜɥɹɬɶɫɹ ɛɥɢɠɚɣɲɢɦ (ɪɢɫ 3).
Ɋɟɡɭɥɶɬɚɬ ɞɨɛɚɜɥɟɧɢɹ ɬɨɱɤɢ ɩɨɤɚɡɚɧ ɧɚ ɪɢɫ.
Ⱦɥɹ ɫɨɤɪɚɳɟɧɢɹ ɨɩɟɪɚɰɢɣ, ɜɵɩɨɥɧɹɟɦɵɯ ɗȼɆ ɞɥɹ ɷɬɨɝɨ ɚɥɝɨɪɢɬɦɚ ɦɨɠɧɨ ɩɪɢɦɟɧɢɬɶ ɫɥɟɞɭɸɳɢɟ ɨɩɬɢɦɢɡɚɰɢɢ:
ȼ ɫɜɹɡɢ ɫ ɬɟɦ, ɱɬɨ ɪɚɫɱɟɬ ɪɚɫɫɬɨɹɧɢɣ ɧɟɨɛɯɨɞɢɦ ɬɨɥɶɤɨ ɞɥɹ ɫɪɚɜɧɟɧɢɹ ɢɯ ɦɟɠɞɭ ɫɨɛɨɣ, ɦɨɠɧɨ ɧɟ ɜɵɱɢɫɥɹɬɶ ɤɨɪɟɧɶ ɢɡ ɫɭɦɦɵ ɤɜɚɞɪɚɬɨɜ ɪɚɡɧɨɫɬɟɣ ɤɨɨɪɞɢɧɚɬ ɜ ɮɨɪɦɭɥɟ:
݀‫ ݔ‬ൌ ඥሺ‫ݔ‬ଶ െ ‫ݔ‬ଵ ሻଶ ൅ ሺ‫ݕ‬ଶ െ ‫ݕ‬ଵ ሻଶ [2].
Ⱦɥɹ ɛɵɫɬɪɨɝɨ ɨɩɪɟɞɟɥɟɧɢɹ ɬɢɩɚ ɩɟɪɟɫɟɱɟɧɢɹ ɨɬɪɟɡɤɨɜ ɢ ɬɨɱɤɢ ɩɟɪɟɫɟɱɟɧɢɹ ɦɨɠɧɨ
ɜɨɫɩɨɥɶɡɨɜɚɬɶɫɹ ɚɥɝɨɪɢɬɦɨɦ FasterLineSegmentIntersection [1]:
ȼ ɨɛɳɟɦ ɫɥɭɱɚɟ ɩɨɥɨɠɟɧɢɟ ɬɨɱɤɢ ɩɟɪɟɫɟɱɟɧɢɹ ɦɨɠɧɨ ɨɩɢɫɚɬɶ ɫɥɟɞɭɸɳɢɦ ɨɛɪɚɡɨɦ:
ܲ‫ כ‬ൌ ܲଵ ൅ ߙሺܲଶ െ ܲଵ ሻ
ܲ‫ כ‬ൌ ܲଷ ൅ ߚሺܲସ െ ܲଷ ሻ
ȿɫɥɢ ɜɵɱɟɫɬɶ ɨɞɧɨ ɢɡ ɷɬɢɯ ɭɪɚɜɧɟɧɢɣ ɢɡ ɞɪɭɝɨɝɨ ɩɨɥɭɱɚɟɬɫɹ:
Ͳ ൌ ሺܲଵ െ ܲଷ ሻ ൅ ߙሺܲଶ െ ܲଵ ሻ ൅ ߚሺܲଷ െ ܲସ ሻ
Ɍɚɤɢɦ ɨɛɪɚɡɨɦ
ሺ‫ݕ‬ଷ െ ‫ݕ‬ସ ሻ ‫ כ‬ሺ‫ݔ‬ଵ െ ‫ݔ‬ଷ ሻ െ ሺ‫ݔ‬ଷ െ ‫ݔ‬ସ ሻ ‫ כ‬ሺ‫ݕ‬ଵ െ ‫ݕ‬ଷ ሻ
ߙൌ
ሺ‫ݕ‬ଶ െ ‫ݕ‬ଵ ሻ ‫ כ‬ሺ‫ݔ‬ଷ െ ‫ݔ‬ସ ሻ െ ሺ‫ݔ‬ଶ െ ‫ݔ‬ଵ ሻ ‫ כ‬ሺ‫ݕ‬ଷ െ ‫ݕ‬ସ ሻ
ሺ‫ݕ‬ଵ െ ‫ݕ‬ଷ ሻ ‫ כ‬ሺ‫ݔ‬ଶ െ ‫ݔ‬ଵ ሻ െ ሺ‫ݔ‬ଵ െ ‫ݔ‬ଷ ሻ ‫ כ‬ሺ‫ݕ‬ଶ െ ‫ݕ‬ଵ ሻ
ߚൌ
ሺ‫ݕ‬ଶ െ ‫ݕ‬ଵ ሻ ‫ כ‬ሺ‫ݔ‬ଷ െ ‫ݔ‬ସ ሻ െ ሺ‫ݔ‬ଶ െ ‫ݔ‬ଵ ሻ ‫ כ‬ሺ‫ݕ‬ଷ െ ‫ݕ‬ସ ሻ
ȿɫɥɢ ɞɟɥɢɬɟɥɶ ɪɚɜɟɧ 0, ɡɧɚɱɢɬ ɥɢɧɢɢ - ɩɚɪɚɥɥɟɥɶɧɵ. ȿɫɥɢ ɞɟɥɢɬɟɥɶ ɛɨɥɶɲɟ 0 ɢ ɱɢɫɥɢɬɟɥɶ ߙɦɟɧɶɲɟ 0 ɢɥɢ ɛɨɥɶɲɟ ɞɟɥɢɬɟɥɹ, ɬɨ ɨɬɪɟɡɤɢ ɜ ɝɪɚɧɢɰɚɯ ɜɟɪɲɢɧ ɧɟ ɩɟɪɟɫɟɤɚɸɬɫɹ.
ȿɫɥɢ ɱɢɫɥɢɬɟɥɶ ߚɛɨɥɶɲɟ 0 ɢɥɢ ɦɟɧɶɲɟ ɡɧɚɦɟɧɚɬɟɥɹ, ɬɨ ɨɬɪɟɡɤɢ ɬɚɤɠɟ ɧɟ ɩɟɪɟɫɟɤɚɸɬɫɹ ɜ
ɝɪɚɧɢɰɚɯ. ȼɨ ɜɫɟɯ ɨɫɬɚɥɶɧɵɯ ɫɥɭɱɚɹɯ ɬɨɱɤɚ ɩɟɪɟɫɟɱɟɧɢɹ ɥɟɠɢɬ ɧɚ ɨɬɪɟɡɤɚɯ.
Ʌɢɬɟɪɚɬɭɪɚ
1. Ⱥɧɬɨɧɢɨ, Ɏ. «Ȼɵɫɬɪɨɟ ɨɩɪɟɞɟɥɟɧɢɟ ɩɟɪɟɫɟɱɟɧɢɣ ɨɬɪɟɡɤɨɜ», ɝɥ. 4-6, «Ⱦɪɚɝɨɰɟɧɧɵɟ
ɤɚɦɧɢ ɝɪɚɮɢɤɢ» ɩɨɞ ɪɟɞ. ɗɞ. Ⱦ. Ʉɢɪɤɚ. ɋɚɧ-Ⱦɢɟɝɨ, Ⱥɤɚɞɟɦɢɤ-ɉɪɟɫɫ, 1992.
2. ɇɢɤɭɥɢɧ ȿ.Ⱥ. «Ʉɨɦɩɶɸɬɟɪɧɚɹ ɝɟɨɦɟɬɪɢɹ ɢ ɚɥɝɨɪɢɬɦɵ ɦɚɲɢɧɧɨɣ ɝɪɚɮɢɤɢ», ɋɉɛ.,
Ȼɏȼ-ɉɟɬɟɪɛɭɪɝ, 2005.
Reference
1. Antonio, F. "Faster Line Segment Intersection. Ch. IV.6 in Graphics Gems III” (Ed. D. Kirk).
San Diego: Academic Press, pp. 199-202 and 500-501, 1992.
2. Nikulin E.A., “Computer geometry and machine graphics algorithms”, St. Peterburg, BHVPeterburg, 2005
Ʉɥɸɱɟɜɵɟ ɫɥɨɜɚ: ɢɧɠɟɧɟɪɧɵɟ ɫɟɬɢ, ɝɢɞɪɚɜɥɢɱɟɫɤɚɹ ɰɟɩɶ, ɩɨɬɟɪɢ ɞɚɜɥɟɧɢɹ, ɫɯɟɦɧɨɫɬɪɭɤɬɭɪɧɚɹ ɨɩɬɢɦɢɡɚɰɢɹ
Keywords: engineering networks, hydraulic circuit, pressure los, scheme-structural optimization
129337, Ɋɨɫɫɢɹ, ɝ. Ɇɨɫɤɜɚ, əɪɨɫɥɚɜɫɤɨɟ ɲɨɫɫɟ, ɞɨɦ 26;
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