Laboratorium 8 - województwa, powiaty, gminy, miejscowości (kontynuacja)

Napisz docelową klasę BoundingBox. Jest to prostokąt otaczający jednostkę. Do zdefiniowania prostokąta wystarczą dwa przeciwległe punkty, zamiast pięciu.

Zaprojektuj BoundingBox tak, aby miał dwa stany:

• BoundingBox może być pusty
• albo definiuje prostokąt (w tym zdegenerowany do pojedynczego punktu)

Sam(a) zadecyduj, jak je odróżnić, np. stosując specjalne wartości Double.NaN albo dodając flagę pusty/niepusty.

public class BoundingBox {
    double xmin = ???;
    double ymin = ???;
    double xmax = ???;
    double ymax = ???;
 
    /**
     * Powiększa BB tak, aby zawierał punkt (x,y)
     * Jeżeli był wcześniej pusty - wówczas ma zawierać wyłącznie ten punkt  
     * @param x - współrzędna x
     * @param y - współrzędna y
     */
    void addPoint(double x, double y){
 
    }
 
    /**
     * Sprawdza, czy BB zawiera punkt (x,y)
     * @param x
     * @param y
     * @return
     */
    boolean contains(double x, double y){
        return false;
    }
 
    /**
     * Sprawdza czy dany BB zawiera bb 
     * @param bb
     * @return
     */
    boolean contains(BoundingBox bb){
        return false;
    }
 
    /**
     * Sprawdza, czy dany BB przecina się z bb
     * @param bb
     * @return
     */
    boolean intersects(BoundingBox bb){
        return false;
    }
    /**
     * Powiększa rozmiary tak, aby zawierał bb oraz poprzednią wersję this
     * Jeżeli był pusty - po wykonaniu operacji ma być równy bb
     * @param bb
     * @return
     */
    BoundingBox add(BoundingBox bb){
        return this;
    }
    /**
     * Sprawdza czy BB jest pusty
     * @return
     */
    boolean isEmpty(){
        return true;
    }
 
    /**
     * Sprawdza czy 
     * 1) typem o jest BoundingBox 
     * 2) this jest równy bb
     * @return
     */
    boolean equals(Object o){
        return true;
    }
 
    /**
     * Oblicza i zwraca współrzędną x środka
     * @return if !isEmpty() współrzędna x środka else wyrzuca wyjątek
     * (sam dobierz typ)
     */
    double getCenterX(){
        throw new RuntimeException("Not implemented");
    }
    /**
     * Oblicza i zwraca współrzędną y środka
     * @return if !isEmpty() współrzędna y środka else wyrzuca wyjątek
     * (sam dobierz typ)
     */
    double getCenterY(){
        throw new RuntimeException("Not implemented");
    }
 
    /**
     * Oblicza odległość pomiędzy środkami this bounding box oraz bbx
     * @param bbx prostokąt, do którego liczona jest odległość
     * @return if !isEmpty odległość, else wyrzuca wyjątek lub zwraca maksymalną możliwą wartość double
     * Ze względu na to, że są to współrzędne geograficzne, zamiast odległości użyj wzoru haversine
     * (ang. haversine formula)
     *
     * Gotowy kod można znaleźć w Internecie...
     */
    double distanceTo(BoundingBox bbx){
        throw new RuntimeException("Not implemented");
    }
 
}

• Uzupełnij wartości BoundingBox podczas odczytu.
• Nie ustawiaj współrzędnych bezpośrednio, ale wywołaj metodę addPoint()
• Dodaj w klasie BoundingBox metodę toString() i uwzględnij jej wywołanie w AdminUnit.toString()
• Sprawdź, czy wartości współrzędnych czytane są poprawnie

Podczas czytania rekordów wydrukuj

System.out.printf(Locale.US,"LINESTRING(%f %f, %f %f, %f %f, %f %f,%f %f)", 
reader.getDouble("x1"),
reader.getDouble("y1"),
reader.getDouble("x2"),
reader.getDouble("y2"),
reader.getDouble("x3"),
reader.getDouble("y3"),
reader.getDouble("x4"),
reader.getDouble("y4"),
reader.getDouble("x1"),
reader.getDouble("y1")
);

Np. dla Krakowa będzie to

LINESTRING(19.7922353426102 49.9676667885393,19.7922353426102 50.1261382575516,20.2173454438402 50.1261382575516,20.2173454438402 49.9676667885393,19.7922353426102 49.9676667885393)

Skopiuj wynik i wklej na stronie

• http://arthur-e.github.io/Wicket/sandbox-gmaps3.html albo
• https://wktmap.com/

Kraków i Wieliczka

MULTILINESTRING((19.7922353426102 49.9676667885393,19.7922353426102 50.1261382575516,20.2173454438402 50.1261382575516,20.2173454438402 49.9676667885393,19.7922353426102 49.9676667885393),
(20.0027443903341 49.9709019769598,20.0027443903341 50.004649838968,20.0889354062256 50.004649838968,20.0889354062256 49.9709019769598,20.0027443903341 49.9709019769598))

Oczywiście możesz też wypisać odpowiedni tekst na podstawie współrzędnych w BoundingBox, a nawet dodać metodę, która to robi do klasy. Metoda np. może nazywać się getWKT() - WKT (Well Known Text) to format reprezentacji wektorów https://en.wikipedia.org/wiki/Well-known_text.

Możesz też obejrzeć dokładne granice

W pliku w admin_units_full.csv w archiwum admin_units.zip w ostatniej kolumnie są umieszczone dokładne granice jednostek administracyjnych. Dla Krakowa mają one postać:

POLYGON((19.7922355 50.011797,19.7923785 50.0110354,19.7927128 50.0102349,19.7930247 50.0096241,19.7936089 50.0086068,19.7937978 50.0082797,19.7943382 50.0072117,19.7946374 50.0062161,19.7946877 50.0060496,19.7947394 50.0056837,19.7948491 50.0048508,19.7952237 50.0032388,19.7951771 50.0027712,19.7954508 50.0021169,19.7957414 50.0007648,19.7961741 49.9993573,19.7963763 49.9982317,19.7966312 49.9973688,19.7963871 49.9965839,19.7963595 49.9965181,19.7961802 49.9960949,19.7960591 49.9958085,19.7959591 49.9956764,19.795856 49.995539,19.7956655 49.9952854,19.7961725 49.9951365,19.796227 49.9948993,19.7962304 49.9948776,19.7963481 49.9946581,19.796474 49.9945366,19.7966412 49.9946089,19.7970882 49.9947869,19.797529 49.9949711,19.7978465 49.9950632,19.7979768 49.9951466,19.7983182 49.9953214,19.7982156 49.995366,19.7983427 49.9955142,19.7984363 49.9956415,19.7987405 49.99584,19.7987104 49.9958754,19.7987503 49.995922,19.7987871 49.9959671,19.7988649 49.9959743,19.7989484 49.9959747,19.7991224 49.9959382,19.7993316 49.9958014,19.7994488 49.9957835,19.7997119 49.9957893,19.7998422 49.9957706,19.800006 49.9957834,19.800228 49.9957366,19.8005772 49.9955868,19.8006882 49.9955196,19.800776 49.995484,19.8008044 49.9954248,19.8007502 49.9953702,19.8006602 49.9953174,19.8008527 49.9951096,19.8009049 49.9950842,19.8009454 49.9950572,19.8009499 49.9950146,19.8009421 49.9949603,19.8009084 49.9949149,19.8008604 49.9948732,19.8007496 49.9948295,19.8006098 49.9948146,19.8006958 49.9947307,19.8007346 49.9946621,19.8007294 49.9946031,19.8007001 49.9945565,19.8007274 49.9944023,19.8009271 49.9942001,19.8009301 49.9941709,19.8008887 49.9939901,19.8011039 49.9939431,19.801243 49.9939846,19.8013641 49.9939082,19.8015185 49.9937534,19.8016667 49.9935393,19.8017101 49.9934322,19.8018456 49.9933932,19.8020356 49.9933629,19.8022334 49.9933732,19.802333 49.9934209,19.8024338 49.9936365,19.8025224 49.9938703,19.8025769 49.9939617,19.8026388 49.9940311,19.8027699 49.9941184,19.8030459 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Zdefiniujmy wpierw pojęcie sąsiada. W typowym przypadku sąsiadem danej jednostki ma być jednostka

• na tym samym poziomie hierarchii (czyli sąsiadami województw mają być województwa, powiatów – powiaty, gmin – gminy, a miejscowości - leżące w pobliżu miejscowości
• podstawowym kryterium (dla województw, powiatów i gmin) ma być pokrywanie się BoundingBox testowane za pomocą metody intersects()

Miejscowości mogą być oddalone i ich granice nie będą się pokrywały. Stąd kryterium pokrywania nie wystarczy. Przyjmiemy więc, że sąsiadujące miejscowości położone są w odległości mniejszej niż pewien konfigurowalny parametr maxdistance, np. równy 15 km. Odległości mają być liczone od środków BoundingBox

Napisz funkcję klasy AdminUnitList

   /**
     * Zwraca listę jednostek sąsiadujących z jendostką unit na tym samym poziomie hierarchii admin_level. 
     * Czyli sąsiadami wojweództw są województwa, powiatów - powiaty, gmin - gminy, miejscowości - inne miejscowości
     * @param unit - jednostka, której sąsiedzi mają być wyznaczeni
     * @param maxdistance - parametr stosowany wyłącznie dla miejscowości, maksymalny promień odległości od środka unit, 
     *                    w którym mają sie znaleźć punkty środkowe BoundingBox sąsiadów
     * @return lista wypełniona sąsiadami
     */
    AdminUnitList getNeighbors(AdminUnit unit, double maxdistance){
        throw new RuntimeException("Not implemented");
    }

Zademonstruj w kodzie (np. testach), że jesteś w stanie:

• znaleźć wybraną jednostkę na danym poziomie hierarchii
• wyznaczyć i wypisać listę sąsiadów
• sprawdź wyniki na mapie…

Oblicz czas wyszukiwania sąsiadów

        double t1 = System.nanoTime()/1e6;
        // wywołanie funkcji
        double t2 = System.nanoTime()/1e6;
        System.out.printf(Locale.US,"t2-t1=%f\n",t2-t1);

Najprostsza metoda realizacji algorytmu wyszukiwania sąsiadów polega na iteracji przez wszystkie elementy listy i sprawdzenie, czy są sąsiadami (zgodnie ze zdefiniowanymi kryteriami). Gdybyśmy chcieli wyznaczyć sąsiadów dla wszystkich obiektów AdminUnit złożoność obliczeniowa będzie $O(n^2)$. Biorąc pod uwagę, że n~15_000–20_000, da to 225_000_000–400_000_000 testów sąsiedztwa, czyli raczej dużo…

Dysponujemy jednak hierarchią obiektów (parent→children) - potencjalnie drzewem z nieistniejącym korzeniem, którego potomkami są województwa, dalej powiaty i gminy. Jeżeli z niej skorzystamy - pozwoli to nam zapewne przyspieszyć obliczenia.

Uwaga - nie musimy tworzyć nieistniejącego korzenia. Wystarczy poprawnie zainicjować algorytm przeszukiwania. Zastosuj rozwiązania znane z przedmiotu Algorytmy i struktury danych.

Zaimplementuj algorytm wyszukiwania podobny do dla R-tree opisany w Wikipedii (sekcja Search).

1. Dla województwa, powiatu lub gminy użyj zdefiniowanego BoundingBox.
2. Dla miejscowości - po prostu rozszerz środek o maxdistance w każdym kierunku (ale zastosuj kryterium odległości).
3. Porównaj czasy wykonania dla wersji liniowej i wykorzystującej drzewo parent→children.
4. Warto przetestować sąsiadów dla gmin położonych na granicy województw, np. gmina Brzeszcze: https://geoportal360.pl/12/oswiecimski/brzeszcze-121302/ lub https://geoportal360.pl/24/bielski/wilamowice-240209/
5. Wypróbuj także działanie po usunięciu korzeni drzew niebędących województwami (Metropolia katowicka i inne…)