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Aufgabenblatt 1

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Anton Ertl
2022-03-14 11:12:15 +01:00
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Die Angabe für die 1. Aufgabe finden Sie in
* angabe/Aufgabenblatt1.md
die zugehörigen .java-Dateien in src
Entsprechend für die weiteren Aufgaben.

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# Aufgabenblatt 1
## Allgemeine Anmerkungen
Ihre Lösung für dieses Aufgabenblatt ist bis Montag, 21.3.2022 11:00 Uhr durch `git commit` und `push` abzugeben. Mit der Angabe werden folgende Dateien mitgeliefert, die sie gemäß der Angabe verändern müssen: `Simulation.java`, `Vector3.java`, `Body.java` und zum Testen `Aufgabe1Test.java`. Die zusätzliche Datei `CodeDraw.jar` wird nur zum Zeichnen verwendet und sollte nicht entfernt oder verändert werden. Die zusätzliche Datei `SpaceDraw.java` enthält Methoden, die in der Simulation benötigt werden. Diese Methoden können Sie auch in Ihrer Lösung aufrufen.
Vorgegebene Programmteile dürfen nur an den Stellen verändert werden, die mit TODO markiert sind. Zusätzliche Klassen, Interfaces, Methoden und Variablen dürfen aber eingefügt werden. Wenn Sie zusätzlich zu den gefragten Klassen weitere Klassen definieren, achten Sie darauf, dass die Klassennamen mit `My` beginnen, um Konflikte mit späteren Aufgabenblättern zu vermeiden.
## Verwendung in IntelliJ
Diese Aufgabenstellung ist ein vollständiges IntelliJ-Projekt, das Sie bereits in IntelliJ öffnen können. Sie müssen daher kein eigenes Projekt anlegen. Öffnen Sie nach dem Klonen des Repos in IntelliJ einfach den entsprechenden Ordner. Gegebenenfalls muss noch folgender Schritt ausgeführt werden:
- Einstellen des _Project SDK_: Öffnen Sie dazu in IntelliJ die Projekteinstellungen (_File_ -> _Project Structure..._) und wählen Sie ein JDK unter _Project | Project SDK_ aus.
## Thema
Das allgemeine Thema dieses und der kommenden Aufgabenblätter ist der Weltraum und die Simulation der physikalischen Gesetze, die für Himmelskörper gelten. Obwohl ein möglichst exaktes physikalisches Modell wünschenswert ist, ist bei der Implementierung die Genauigkeit der physikalischen Modelle sekundär. Konzeptuelle Fehler bei den physikalischen Berechnungen spielen keine Rolle bei der Bewertung. Schwerpunkt sind die Konzepte der Programmiersprache.
## Ziel
Ziel der Aufgabe ist die Anwendung der Konzepte: Objekt- vs. Klassenmethode, Datensatz, Data Hiding, Konstruktoren (siehe Skriptum Seiten 31-50).
## Aufgaben
1. Lesen Sie sich die Kommentare in den Dateien durch und führen Sie die Klasse `Simulation` aus.
2. Data hiding:
1. Machen Sie in den Klassen `Vector3` und `Body` alle Objektvariablen `private`.
2. Definieren Sie entsprechende Konstruktoren, um die Objektvariablen zu initialisieren. `Simulation` soll nur noch diese nutzen und nicht mehr direkt auf die Objektvariablen zugreifen dürfen. Testen Sie zunächst die vervollständigten Klassen `Vector3` und `Body` mit der Klasse `Aufgabe1Test`. Entfernen Sie dazu die Kommentarzeichen in der Klassendefinition.
3. Datenkapselung: Anstelle der gegebenen statischen Methoden in der Datei `Simulation.java` sollen nur noch entsprechende Objektmethoden der Klassen `Body` und `Vector3` benutzt werden. (Ausnahme ist die Methode `main`. Die statischen Methoden der Klasse `SpaceDraw` müssen auch nicht verändert werden.) Implementieren Sie dazu die spezifizierten Methoden und bauen Sie `Simulation` so um, dass anstelle der Aufrufe statischer Methoden Objektmethoden genutzt werden. Sie sollen alle in `Body` und `Vector3` spezifizierten Methoden implementieren, auch wenn nicht alle von `Simulation` genutzt werden. Die in `Simulation.java` gegebenen statischen Methoden können dann entfernt werden (natürlich bis auf die erwähnten Ausnahmen). Nutzen Sie die implementierten Methoden auch in `Simulation.java`, um die Himmelskörper zu bewegen und zu zeichnen.
## Zusatzfragen
Beantworten Sie folgende Zusatzfragen als Kommentar in `Simulation.java`:
1. Was versteht man unter _Datenkapselung_? Geben Sie ein Beispiel, wo dieses Konzept in dieser Aufgabenstellung angewendet wird.
2. Was versteht man unter _Data Hiding_? Geben Sie ein Beispiel, wo dieses Konzept in dieser Aufgabenstellung angewendet wird.
3. Was steht bei einem Methodenaufruf links vom `.` (z.B. bei `SpaceDraw.massToColor(1e30)` oder
`body.radius()`)? Woran erkennt man dabei Objektmethoden?
### Denkanstöße (ohne Bewertung)
Folgende Fragen sind als Denkanstöße gedacht und bilden die Grundlage für eine Diskussion in der Übungseinheit zu diesem Aufgabenblatt.
1. Welche anderen oder weiteren Objektmethoden hätten Sie zur Verfügung gestellt, wenn es keine Vorgaben gegeben hätte?
2. Wann wäre es sinnvoll, die Klasse `SpaceDraw` so zu ändern, dass diese ebenfalls Objektmethoden
zur Verfügung stellt?
#### _Punkteaufteilung_
- Korrekte Sichtbarkeit von Objektvariablen in `Vector3` und `Body` und Initialisierung mittels Konstruktoren: 1 Punkt
- Korrekte Objektmethoden in `Vector3`: 1 Punkt
- Korrekte Objektmethoden in `Body`: 1.5 Punkte
- Korrekte Verwendung der Objektmethoden in `Simulation`: 1 Punkt
- Korrekte Beantwortung der Zusatzfragen: 0.5 Punkte
- Gesamt: 5 Punkte

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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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Also add information on how to contact you by electronic and paper mail.
If the program does terminal interaction, make it output a short
notice like this when it starts in an interactive mode:
<program> Copyright (C) <year> <name of author>
This program comes with ABSOLUTELY NO WARRANTY; for details type `show w'.
This is free software, and you are welcome to redistribute it
under certain conditions; type `show c' for details.
The hypothetical commands `show w' and `show c' should show the appropriate
parts of the General Public License. Of course, your program's commands
might be different; for a GUI interface, you would use an "about box".
You should also get your employer (if you work as a programmer) or school,
if any, to sign a "copyright disclaimer" for the program, if necessary.
For more information on this, and how to apply and follow the GNU GPL, see
<https://www.gnu.org/licenses/>.
The GNU General Public License does not permit incorporating your program
into proprietary programs. If your program is a subroutine library, you
may consider it more useful to permit linking proprietary applications with
the library. If this is what you want to do, use the GNU Lesser General
Public License instead of this License. But first, please read
<https://www.gnu.org/licenses/why-not-lgpl.html>.

21
lib/LICENSE Normal file
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@ -0,0 +1,21 @@
MIT License
Copyright (c) 2021 Niklas Kraßnig
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.

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src/Aufgabe1Test.java Normal file
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import java.awt.*;
public class Aufgabe1Test {
public static void main(String[] args) {
//test classes Body and Vector3
/* TODO: remove this line
// create two bodies
Body sun = new Body(1.989e30,new Vector3(0,0,0),new Vector3(0,0,0));
Body earth = new Body(5.972e24,new Vector3(-1.394555e11,5.103346e10,0),new Vector3(-10308.53,-28169.38,0));
testValue(earth.distanceTo(sun), 1.4850000175024106E11);
testValue(sun.distanceTo(earth), 1.4850000175024106E11);
for(int i = 0; i < 3600*24; i++) {
Vector3 f1 = earth.gravitationalForce(sun);
Vector3 f2 = sun.gravitationalForce(earth);
earth.move(f1);
sun.move(f2);
}
// a dummy body to check the correct position after 24h of movement
Body targetPositionEarth = new Body(1, new Vector3(-1.403250141841815E11,
4.859202658875631E10, 0.0), new Vector3(0,0,0));
// check distance to target position (should be zero)
testValue(earth.distanceTo(targetPositionEarth), 0);
// TODO: remove this line */
}
public static void testComparison(Object first, Object second, boolean expected) {
boolean real = first == second;
if (real == expected) {
System.out.println("Successful comparison");
} else {
System.out.println("Comparison NOT successful! Expected value: " + expected + " / Given value: " + real);
}
}
public static void testValue(Object given, Object expected) {
if (given == expected) {
System.out.println("Successful test");
} else {
System.out.println("Test NOT successful! Expected value: " + expected + " / Given value: " + given);
}
}
public static void testValue(double given, double expected) {
if (given < expected + (expected+1)/1e12 && given > expected - (expected+1)/1e12) {
System.out.println("Successful test");
} else {
System.out.println("Test NOT successful! Expected value: " + expected + " / Given value: " + given);
}
}
}

79
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import codedraw.CodeDraw;
import java.awt.*;
// This class represents celestial bodies like stars, planets, asteroids, etc..
public class Body {
//TODO: change modifiers.
public double mass;
public Vector3 massCenter; // position of the mass center.
public Vector3 currentMovement;
//TODO: define constructor.
// Returns the distance between the mass centers of this body and the specified body 'b'.
public double distanceTo(Body b) {
//TODO: implement method.
return 0;
}
// Returns a vector representing the gravitational force exerted by 'b' on this body.
// The gravitational Force F is calculated by F = G*(m1*m2)/(r*r), with m1 and m2 being the
// masses of the objects interacting, r being the distance between the centers of the masses
// and G being the gravitational constant.
// Hint: see simulation loop in Simulation.java to find out how this is done.
public Vector3 gravitationalForce(Body b) {
//TODO: implement method.
return null;
}
// Moves this body to a new position, according to the specified force vector 'force' exerted
// on it, and updates the current movement accordingly.
// (Movement depends on the mass of this body, its current movement and the exerted force.)
// Hint: see simulation loop in Simulation.java to find out how this is done.
public void move(Vector3 force) {
//TODO: implement method.
}
// Returns the approximate radius of this body.
// (It is assumed that the radius r is related to the mass m of the body by r = m ^ 0.5,
// where m and r measured in solar units.)
public double radius() {
//TODO: implement method.
return 0d;
}
// Returns a new body that is formed by the collision of this body and 'b'. The impulse
// of the returned body is the sum of the impulses of 'this' and 'b'.
public Body merge(Body b) {
//TODO: implement method.
return null;
}
// Draws the body to the specified canvas as a filled circle.
// The radius of the circle corresponds to the radius of the body
// (use a conversion of the real scale to the scale of the canvas as
// in 'Simulation.java').
// Hint: call the method 'drawAsFilledCircle' implemented in 'Vector3'.
public void draw(CodeDraw cd) {
//TODO: implement method.
}
// Returns a string with the information about this body including
// mass, position (mass center) and current movement. Example:
// "5.972E24 kg, position: [1.48E11,0.0,0.0] m, movement: [0.0,29290.0,0.0] m/s."
public String toString() {
//TODO: implement method.
return "";
}
}

253
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import codedraw.CodeDraw;
import java.awt.*;
import java.util.Random;
// TODO: insert answers to questions (Zusatzfragen) in 'Aufgabenblatt1.md' as comment.
// Simulates the formation of a massive solar system.
public class Simulation {
// gravitational constant
public static final double G = 6.6743e-11;
// one astronomical unit (AU) is the average distance of earth to the sun.
public static final double AU = 150e9; // meters
// one light year
public static final double LY = 9.461e15; // meters
// some further constants needed in the simulation
public static final double SUN_MASS = 1.989e30; // kilograms
public static final double SUN_RADIUS = 696340e3; // meters
public static final double EARTH_MASS = 5.972e24; // kilograms
public static final double EARTH_RADIUS = 6371e3; // meters
// set some system parameters
public static final double SECTION_SIZE = 2 * AU; // the size of the square region in space
public static final int NUMBER_OF_BODIES = 22;
public static final double OVERALL_SYSTEM_MASS = 20 * SUN_MASS; // kilograms
// all quantities are based on units of kilogram respectively second and meter.
// The main simulation method using instances of other classes.
public static void main(String[] args) {
//TODO: change implementation of this method according to 'Aufgabenblatt1.md'.
// simulation
CodeDraw cd = new CodeDraw();
Body[] bodies = new Body[NUMBER_OF_BODIES];
Vector3[] forceOnBody = new Vector3[bodies.length];
Random random = new Random(2022);
for (int i = 0; i < bodies.length; i++) {
bodies[i] = new Body();
bodies[i].mass = Math.abs(random.nextGaussian()) * OVERALL_SYSTEM_MASS / bodies.length; // kg
bodies[i].massCenter = new Vector3();
bodies[i].currentMovement = new Vector3();
bodies[i].massCenter.x = 0.2 * random.nextGaussian() * AU;
bodies[i].massCenter.y = 0.2 * random.nextGaussian() * AU;
bodies[i].massCenter.z = 0.2 * random.nextGaussian() * AU;
bodies[i].currentMovement.x = 0 + random.nextGaussian() * 5e3;
bodies[i].currentMovement.y = 0 + random.nextGaussian() * 5e3;
bodies[i].currentMovement.z = 0 + random.nextGaussian() * 5e3;
}
double seconds = 0;
// simulation loop
while (true) {
seconds++; // each iteration computes the movement of the celestial bodies within one second.
// merge bodies that have collided
for (int i = 0; i < bodies.length; i++) {
for (int j = i + 1; j < bodies.length; j++) {
if (distance(bodies[j].massCenter, bodies[i].massCenter) <
SpaceDraw.massToRadius(bodies[j].mass) + SpaceDraw.massToRadius(bodies[i].mass)) {
bodies[i] = merge(bodies[i], bodies[j]);
Body[] bodiesOneRemoved = new Body[bodies.length - 1];
for (int k = 0; k < bodiesOneRemoved.length; k++) {
bodiesOneRemoved[k] = bodies[k < j ? k : k + 1];
}
bodies = bodiesOneRemoved;
// since the body index i changed size there might be new collisions
// at all positions of bodies, so start all over again
i = -1;
j = bodies.length;
}
}
}
// for each body (with index i): compute the total force exerted on it.
for (int i = 0; i < bodies.length; i++) {
forceOnBody[i] = new Vector3(); // begin with zero
for (int j = 0; j < bodies.length; j++) {
if (i != j) {
Vector3 forceToAdd = gravitationalForce(bodies[i], bodies[j]);
forceOnBody[i] = plus(forceOnBody[i], forceToAdd);
}
}
}
// now forceOnBody[i] holds the force vector exerted on body with index i.
// for each body (with index i): move it according to the total force exerted on it.
for (int i = 0; i < bodies.length; i++) {
move(bodies[i], forceOnBody[i]);
}
// show all movements in the canvas only every hour (to speed up the simulation)
if (seconds % (3600) == 0) {
// clear old positions (exclude the following line if you want to draw orbits).
cd.clear(Color.BLACK);
// draw new positions
for (Body body : bodies) {
draw(cd, body);
}
// show new positions
cd.show();
}
}
}
//TODO: remove static methods below.
// Draws a body in the 'cd' canvas showing a projection onto the (x,y)-plane. The body's mass
// center coordinates and its radius are transformed into canvas coordinates. The color of
// the body corresponds to the temperature of the body, assuming the relation of mass and
// temperature of a main sequence star.
// The canvas is assumed to show a quadratic SECTION_SIZE x SECTION_SIZE
// section of space centered arround (x, y) = (0, 0).
public static void draw(CodeDraw cd, Body b) {
cd.setColor(SpaceDraw.massToColor(b.mass));
drawAsFilledCircle(cd, b.massCenter, SpaceDraw.massToRadius(b.mass));
}
// Draws a filled circle in the 'cd' canvas unsing the (x,y)-coordinates of 'center'
// Coordinates and 'radius' are transformed into canvas coordinates. The canvas is assumed
// to show a quadratic SECTION_SIZE x SECTION_SIZE projection of space centered arround (x, y) =
// (0, 0).
public static void drawAsFilledCircle(CodeDraw cd, Vector3 center, double radius) {
double x = cd.getWidth() * (center.x + Simulation.SECTION_SIZE / 2) / Simulation.SECTION_SIZE;
double y = cd.getWidth() * (center.y + Simulation.SECTION_SIZE / 2) / Simulation.SECTION_SIZE;
radius = cd.getWidth() * radius / Simulation.SECTION_SIZE;
cd.fillCircle(x, y, Math.max(radius, 1.5));
}
// Returns a vector representing the gravitational force exerted by body 'b2' on body 'b1'.
// The gravitational Force F is calculated by F = G*(m1*m2)/(r*r), with m1 and m2 being the masses of the objects
// interacting, r being the distance between the centers of the masses and G being the gravitational constant.
// To calculate the force exerted on b1, simply multiply the normalized vector pointing from b1 to b2 with the
// calculated force.
public static Vector3 gravitationalForce(Body b1, Body b2) {
Vector3 direction = minus(b2.massCenter, b1.massCenter);
double distance = length(direction);
normalize(direction);
double force = G * b1.mass * b2.mass / (distance * distance);
return times(direction, force);
}
// Returns a new body that is formed by the collision of 'b1' and 'b2'. The impulse
// of the returned body is the sum of the impulses of 'b1' and 'b2'.
public static Body merge(Body b1, Body b2) {
Body result = new Body();
result.mass = b1.mass + b2.mass;
result.massCenter = times(plus(times(b1.massCenter, b1.mass), times(b2.massCenter,
b2.mass)),
1 / result.mass);
result.currentMovement =
times(plus(times(b1.currentMovement, b1.mass), times(b2.currentMovement, b2.mass)),
1.0 / result.mass);
return result;
}
// Move the body 'b' according to the 'force' excerted on it.
public static void move(Body b, Vector3 force) {
Vector3 newPosition = plus(
plus(b.massCenter,
times(force, 1 / b.mass)
// F = m*a -> a = F/m
),
b.currentMovement
);
// new minus old position.
Vector3 newMovement = minus(newPosition, b.massCenter);
// update body state
b.massCenter = newPosition;
b.currentMovement = newMovement;
}
// Returns the norm of v1-v2.
public static double distance(Vector3 v1, Vector3 v2) {
double dX = v1.x - v2.x;
double dY = v1.y - v2.y;
double dZ = v1.z - v2.z;
return Math.sqrt(dX * dX + dY * dY + dZ * dZ);
}
// Returns v1+v2.
public static Vector3 plus(Vector3 v1, Vector3 v2) {
Vector3 result = new Vector3();
result.x = v1.x + v2.x;
result.y = v1.y + v2.y;
result.z = v1.z + v2.z;
return result;
}
// Returns v1-v2.
public static Vector3 minus(Vector3 v1, Vector3 v2) {
Vector3 result = new Vector3();
result.x = v1.x - v2.x;
result.y = v1.y - v2.y;
result.z = v1.z - v2.z;
return result;
}
// Returns v*d.
public static Vector3 times(Vector3 v, double d) {
Vector3 result = new Vector3();
result.x = v.x * d;
result.y = v.y * d;
result.z = v.z * d;
return result;
}
// Returns the norm of 'v'.
public static double length(Vector3 v) {
return distance(v, new Vector3()); // distance to origin.
}
// Normalizes the specified vector 'v': changes the length of the vector such that its length
// becomes one. The direction and orientation of the vector is not affected.
public static void normalize(Vector3 v) {
double length = length(v);
v.x /= length;
v.y /= length;
v.z /= length;
}
}

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import java.awt.*;
public class SpaceDraw {
// Returns the approximate radius of a celestial body with the specified mass.
// (It is assumed that the radius r is related to the mass m of the body by r = m ^ 0.5,
// where m and r measured in solar units.)
public static double massToRadius(double mass) {
return Simulation.SUN_RADIUS * (Math.pow(mass / Simulation.SUN_MASS, 0.5));
}
// Returns the approximate color of a celestial body with the specified mass. The color of
// the body corresponds to the temperature of the body, assuming the relation of mass and
// temperature of a main sequence star.
public static Color massToColor(double mass) {
Color color;
if (mass < Simulation.SUN_MASS / 10) {
// not a star-like body below this mass
color = Color.LIGHT_GRAY;
} else {
// assume a main sequence star
color = SpaceDraw.kelvinToColor((int) (5500 * mass / Simulation.SUN_MASS));
}
return color;
}
// Returns the approximate color of temperature 'kelvin'.
private static Color kelvinToColor(int kelvin) {
double k = kelvin / 100D;
double red = k <= 66 ? 255 : 329.698727446 * Math.pow(k - 60, -0.1332047592);
double green = k <= 66 ? 99.4708025861 * Math.log(k) - 161.1195681661 : 288.1221695283 * Math.pow(k - 60, -0.0755148492);
double blue = k >= 66 ? 255 : (k <= 19 ? 0 : 138.5177312231 * Math.log(k - 10) - 305.0447927307);
return new Color(
limitAndDarken(red, kelvin),
limitAndDarken(green, kelvin),
limitAndDarken(blue, kelvin)
);
}
// A transformation used in the method 'kelvinToColor'.
private static int limitAndDarken(double color, int kelvin) {
int kelvinNorm = kelvin - 373;
if (color < 0 || kelvinNorm < 0) return 0;
else if (color > 255) return 255;
else if (kelvinNorm < 500) return (int) ((color / 256D) * (kelvinNorm / 500D) * 256);
else return (int) color;
}
}

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import codedraw.CodeDraw;
import java.awt.*;
// This class represents vectors in a 3D vector space.
public class Vector3 {
//TODO: change modifiers.
public double x;
public double y;
public double z;
//TODO: define constructor.
// Returns the sum of this vector and vector 'v'.
public Vector3 plus(Vector3 v) {
//TODO: implement method.
return null;
}
// Returns the product of this vector and 'd'.
public Vector3 times(double d) {
//TODO: implement method.
return null;
}
// Returns the sum of this vector and -1*v.
public Vector3 minus(Vector3 v) {
//TODO: implement method.
return null;
}
// Returns the Euclidean distance of this vector
// to the specified vector 'v'.
public double distanceTo(Vector3 v) {
//TODO: implement method.
return -1d;
}
// Returns the length (norm) of this vector.
public double length() {
//TODO: implement method.
return 0;
}
// Normalizes this vector: changes the length of this vector such that it becomes 1.
// The direction and orientation of the vector is not affected.
public void normalize() {
//TODO: implement method.
}
// Draws a filled circle with a specified radius centered at the (x,y) coordinates of this vector
// in the canvas associated with 'cd'. The z-coordinate is not used.
public void drawAsFilledCircle(CodeDraw cd, double radius) {
//TODO: implement method.
}
// Returns the coordinates of this vector in brackets as a string
// in the form "[x,y,z]", e.g., "[1.48E11,0.0,0.0]".
public String toString() {
//TODO: implement method.
return "";
}
}