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mathe-simulation-runder-bewegungen
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Added Abstand = Durchmesser Definition

This commit is contained in:
Justin Dretvic 2020-06-28 02:33:57 +02:00
parent de6dcebe77
commit aa01030e3e
5 changed files with 69 additions and 39 deletions
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5
Datensammlung.txt Normal file
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@ -0,0 +1,5 @@
Ort: START || Phi: 200° || Theta: 45°
Ort: END || Phi: 20° || Theta: -45°
Ort: Berlin || Phi: 52.52° || Theta: 13.37°
Ort: Tokyo || Phi: 139.76° || Theta: 35.68°
Ort: ? || Phi: ?° || Theta: ?°

6
src/app/_0_Constants.java
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@ -39,4 +39,10 @@ public class _0_Constants {
// Simulation // Simulation
public static double VELOCITY = 10; // Die Geschwindigkeit sollte Pi betragen public static double VELOCITY = 10; // Die Geschwindigkeit sollte Pi betragen
// Winkel vom Startpunkt & Endpunkt
public static double PHI_S = 139.72;
public static double THETA_S = 35.68;
public static double PHI_E = 52.52;
public static double THETA_E = 13.37;
} }

37
src/app/_0_Matrices.java
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@ -2,17 +2,17 @@ package app;
public class _0_Matrices { public class _0_Matrices {
// Anpassungs-Matrizen
public static double[][] M_JavaNormalized = new double[][] { public static double[][] M_JavaNormalized = new double[][] {
{ -(_0_Constants.S1) * Math.sin(_0_Constants.ALPHA), 1, 0, _0_Constants.START_X}, { -(_0_Constants.S1) * Math.sin(_0_Constants.ALPHA), 1, 0, _0_Constants.START_X},
{ -(_0_Constants.S1) * Math.cos(_0_Constants.ALPHA), 0, -1, _0_Constants.START_Y}, { -(_0_Constants.S1) * Math.cos(_0_Constants.ALPHA), 0, -1, _0_Constants.START_Y},
}; };
public static double[][] M_JavaNormalized_Umriss = new double[][] { public static double[][] M_JavaNormalized_Umriss = new double[][] {
{ -(_0_Constants.S1) * Math.sin(_0_Constants.ALPHA), 1, 0}, { -(_0_Constants.S1) * Math.sin(_0_Constants.ALPHA), 1, 0},
{ -(_0_Constants.S1) * Math.cos(_0_Constants.ALPHA), 0, -1}, { -(_0_Constants.S1) * Math.cos(_0_Constants.ALPHA), 0, -1},
}; };
// Dreh-Matrizen
public static double[][] DrehungX(double winkel) { public static double[][] DrehungX(double winkel) {
return new double[][] { return new double[][] {
{ 1, 0, 0}, { 1, 0, 0},
@ -34,19 +34,22 @@ public class _0_Matrices {
}; };
} }
public static double[][] START = new double[][] { // Vektoren
{_0_Constants.RADIUS * Math.cos( Math.toRadians(35.68) ) * Math.cos( Math.toRadians(139.76) )}, public static double[][] M_START = START(_0_Constants.PHI_S,_0_Constants.THETA_S);
{_0_Constants.RADIUS * Math.cos( Math.toRadians(35.68) ) * Math.sin( Math.toRadians(139.76) )}, public static double[][] START(double _phi, double _theta){
{_0_Constants.RADIUS * Math.sin( Math.toRadians(35.68) ) } return new double[][] {
}; {_0_Constants.RADIUS * Math.cos( Math.toRadians(_theta) ) * Math.cos( Math.toRadians(_phi) )},
public static double[][] END = new double[][] { {_0_Constants.RADIUS * Math.cos( Math.toRadians(_theta) ) * Math.sin( Math.toRadians(_phi) )},
{_0_Constants.RADIUS * Math.cos( Math.toRadians(13.37) ) * Math.cos( Math.toRadians(52.52) )}, {_0_Constants.RADIUS * Math.sin( Math.toRadians(_theta) ) }
{_0_Constants.RADIUS * Math.cos( Math.toRadians(13.37) ) * Math.sin( Math.toRadians(52.52) )}, };
{_0_Constants.RADIUS * Math.sin( Math.toRadians(13.37) ) } }
}; public static double[][] M_END = END(_0_Constants.PHI_E,_0_Constants.THETA_E);
// Ort: START || Phi: 180° || Theta: 45° public static double[][] END(double _phi, double _theta){
// Ort: END || Phi: 30° || Theta: -45° return new double[][] {
// Ort: Berlin || Phi: 52.52° || Theta: 13.37° {_0_Constants.RADIUS * Math.cos( Math.toRadians(_theta) ) * Math.cos( Math.toRadians(_phi) )},
// Ort: Tokyo || Phi: 139.76° || Theta: 35.68° {_0_Constants.RADIUS * Math.cos( Math.toRadians(_theta) ) * Math.sin( Math.toRadians(_phi) )},
// Ort: ? || Phi: ?° || Theta: ?° {_0_Constants.RADIUS * Math.sin( Math.toRadians(_theta) ) }
};
}
} }

23
src/app/_1_GeoAnimation_DrawingOperations.java
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@ -38,20 +38,19 @@ public class _1_GeoAnimation_DrawingOperations extends JPanel{
// Objekt-Attribute // Objekt-Attribute
_2_Methods Meth = new _2_Methods(); _2_Methods Meth = new _2_Methods();
double[][] bewegung = Meth.drehBewegung(0); double[][] bewegung = new double[3][1];
ArrayList<Integer> WegX = new ArrayList<Integer>(); ArrayList<Integer> WegX = new ArrayList<Integer>();
ArrayList<Integer> WegY = new ArrayList<Integer>(); ArrayList<Integer> WegY = new ArrayList<Integer>();
double newTime; double newTime;
double distance = Meth.RadiusStartToEnd(); double distance = Meth.RadiusStartToEnd();
double differencePhi = Meth.getPhi(_0_Matrices.END) - Meth.getPhi(_0_Matrices.START); double differencePhi = Meth.getPhi(_0_Matrices.M_END) - Meth.getPhi(_0_Matrices.M_START);
double differenceTheta = Meth.getTheta(_0_Matrices.END) - Meth.getTheta(_0_Matrices.START); double differenceTheta = Meth.getTheta(_0_Matrices.M_END) - Meth.getTheta(_0_Matrices.M_START);
boolean planeLanded = false; boolean planeLanded = false;
boolean firstPoint = true; boolean firstPoint = true;
// DRAWING OPERATIONS IN HERE // DRAWING OPERATIONS IN HERE
@Override protected void paintComponent(Graphics g) { @Override protected void paintComponent(Graphics g) {
super.paintComponent(g);
// Zeit-Korrektur // Zeit-Korrektur
time = t.GetTimeInSeconds(); time = t.GetTimeInSeconds();
if (firstPoint) { if (firstPoint) {
@ -60,6 +59,7 @@ public class _1_GeoAnimation_DrawingOperations extends JPanel{
} }
actualTime = time - deltaTime; actualTime = time - deltaTime;
super.paintComponent(g);
Graphics2D g2d; Graphics2D g2d;
g2d = (Graphics2D) g; g2d = (Graphics2D) g;
g2d.setRenderingHint(RenderingHints.KEY_ANTIALIASING, RenderingHints.VALUE_ANTIALIAS_ON); g2d.setRenderingHint(RenderingHints.KEY_ANTIALIASING, RenderingHints.VALUE_ANTIALIAS_ON);
@ -134,23 +134,22 @@ public class _1_GeoAnimation_DrawingOperations extends JPanel{
// Start- & Endpunkt Zeichnen // Start- & Endpunkt Zeichnen
g2d.setColor(Color.YELLOW); g2d.setColor(Color.YELLOW);
g2d.setFont(new Font("Arial", Font.BOLD, 20)); g2d.setFont(new Font("Arial", Font.BOLD, 20));
g2d.fillOval(Meth.getCoords(Meth.normVector(_0_Matrices.START), "x")-(_0_Constants.RADIUS_KUGEL), Meth.getCoords(Meth.normVector(_0_Matrices.START), "y")-(_0_Constants.RADIUS_KUGEL), _0_Constants.DIAMETER_KUGEL, _0_Constants.DIAMETER_KUGEL); g2d.fillOval(Meth.getCoords(Meth.normVector(_0_Matrices.M_START), "x")-(_0_Constants.RADIUS_KUGEL), Meth.getCoords(Meth.normVector(_0_Matrices.M_START), "y")-(_0_Constants.RADIUS_KUGEL), _0_Constants.DIAMETER_KUGEL, _0_Constants.DIAMETER_KUGEL);
g2d.drawString("START", Meth.getCoords(Meth.normVector(_0_Matrices.START), "x"),Meth.getCoords(Meth.normVector(_0_Matrices.START), "y")-15); g2d.drawString("START", Meth.getCoords(Meth.normVector(_0_Matrices.M_START), "x"),Meth.getCoords(Meth.normVector(_0_Matrices.M_START), "y")-15);
g2d.fillOval(Meth.getCoords(Meth.normVector(_0_Matrices.END), "x")-(_0_Constants.RADIUS_KUGEL), Meth.getCoords(Meth.normVector(_0_Matrices.END), "y")-(_0_Constants.RADIUS_KUGEL), _0_Constants.DIAMETER_KUGEL, _0_Constants.DIAMETER_KUGEL); g2d.fillOval(Meth.getCoords(Meth.normVector(_0_Matrices.M_END), "x")-(_0_Constants.RADIUS_KUGEL), Meth.getCoords(Meth.normVector(_0_Matrices.M_END), "y")-(_0_Constants.RADIUS_KUGEL), _0_Constants.DIAMETER_KUGEL, _0_Constants.DIAMETER_KUGEL);
g2d.drawString("END", Meth.getCoords(Meth.normVector(_0_Matrices.END), "x"),Meth.getCoords(Meth.normVector(_0_Matrices.END), "y")-15); g2d.drawString("END", Meth.getCoords(Meth.normVector(_0_Matrices.M_END), "x"),Meth.getCoords(Meth.normVector(_0_Matrices.M_END), "y")-15);
// Ausgaben: Zeit //TODO Delete in the end? // Ausgaben: Zeit
System.out.println("---------------------------"); System.out.println("---------------------------");
System.out.println("time: " + time); System.out.println("time: " + time);
System.out.println("actual time: " + (actualTime) ); System.out.println("actual time: " + (actualTime) );
System.out.println("finish time: " + Meth.zeitGrenze() ); System.out.println("finish time: " + Meth.zeitGrenze() );
System.out.println("---------------------------");
// Wegpunkt & Streckenverlauf Zeichnen // Wegpunkt & Streckenverlauf Zeichnen
g2d.setColor(Color.CYAN); g2d.setColor(Color.CYAN);
bewegung = Meth.drehBewegung(Math.toRadians(actualTime)); bewegung = Meth.drehBewegung(Math.toRadians(actualTime));
System.out.println("Phi: "+ Meth.getPhi(Meth.normVector(bewegung)) ); // System.out.println("Phi: "+ Meth.getPhi(Meth.normVector(bewegung)) );
System.out.println("Theta: " + Meth.getTheta(Meth.normVector(bewegung)) ); // System.out.println("Theta: " + Meth.getTheta(Meth.normVector(bewegung)) );
for(int i = 0; i < WegX.size(); i++) for(int i = 0; i < WegX.size(); i++)
g2d.drawLine(WegX.get(i), WegY.get(i), WegX.get(i), WegY.get(i)); g2d.drawLine(WegX.get(i), WegY.get(i), WegX.get(i), WegY.get(i));
if(actualTime <= Meth.zeitGrenze() && planeLanded == false) { if(actualTime <= Meth.zeitGrenze() && planeLanded == false) {

37
src/app/_2_Methods.java
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@ -1,8 +1,10 @@
package app; package app;
//import java.util.Arrays;
public class _2_Methods { public class _2_Methods {
// Objektattribute
double[][] startpunkt = _0_Matrices.START(_0_Constants.PHI_S,_0_Constants.THETA_S);
double[][] endpunkt = _0_Matrices.END(_0_Constants.PHI_E,_0_Constants.THETA_E);
// Gibt X oder Y Koordinate aus einem normierten Vektor zurück, abhängig vom String Parameter // Gibt X oder Y Koordinate aus einem normierten Vektor zurück, abhängig vom String Parameter
protected int getCoords(double[][] _vector, String _axe) { protected int getCoords(double[][] _vector, String _axe) {
@ -45,17 +47,22 @@ public class _2_Methods {
// Trennlinie P_Dach // Trennlinie P_Dach
double[][] p_dach = new double[3][1]; double[][] p_dach = new double[3][1];
for(int i = 0; i < 3; i++) for(int i = 0; i < 3; i++)
p_dach[i][0] = _0_Matrices.START[i][0]; p_dach[i][0] = startpunkt[i][0];
for(int i = 0; i < 3; i++) for(int i = 0; i < 3; i++)
p_dach[i][0] /= betrag(_0_Matrices.START); p_dach[i][0] /= betrag(startpunkt);
// Trennlinie N_Dach // Trennlinie N_Dach
double[][] n_dach = kreuzprodukt(_0_Matrices.START, _0_Matrices.END); double[][] n_dach = kreuzprodukt(startpunkt, endpunkt);
for(int i = 0; i < 3; i++) for(int i = 0; i < 3; i++)
n_dach[i][0] /= betrag(n_dach); n_dach[i][0] /= betrag(n_dach);
// Trennlinie U_Dach // Trennlinie U_Dach
double[][] u_dach = kreuzprodukt(n_dach, p_dach); double[][] u_dach = kreuzprodukt(n_dach, p_dach);
for(int i = 0; i < 3; i++) for(int i = 0; i < 3; i++)
u_dach[i][0] /= betrag(u_dach); u_dach[i][0] /= betrag(u_dach);
// Trennlinie Check NaN
if( Double.isNaN((p_dach[0][0])) || Double.isNaN((p_dach[1][0])) || Double.isNaN((p_dach[2][0])) || Double.isNaN((n_dach[0][0])) || Double.isNaN((n_dach[1][0])) || Double.isNaN((n_dach[2][0])) ) {
startpunkt = _0_Matrices.START(_0_Constants.PHI_S+0.01,_0_Constants.THETA_S);
return drehBewegung(_time);
}
// Trennlinie Ergebnismatrix // Trennlinie Ergebnismatrix
return new double[][] { return new double[][] {
{ ( _0_Constants.RADIUS * Math.cos(_time * _0_Constants.VELOCITY) * p_dach[0][0] ) + ( _0_Constants.RADIUS * Math.sin(_time * _0_Constants.VELOCITY) * u_dach[0][0] ) }, { ( _0_Constants.RADIUS * Math.cos(_time * _0_Constants.VELOCITY) * p_dach[0][0] ) + ( _0_Constants.RADIUS * Math.sin(_time * _0_Constants.VELOCITY) * u_dach[0][0] ) },
@ -100,22 +107,31 @@ public class _2_Methods {
if(_u[1][0] < 0) { if(_u[1][0] < 0) {
winkel = Math.toRadians(360) + ( winkel * (-1) ); winkel = Math.toRadians(360) + ( winkel * (-1) );
} }
return Math.toDegrees(winkel); return Math.toDegrees(winkel);
} }
// Berechnet die Entfernung vom Start bis zum Endpunkt // Berechnet die Entfernung vom Start bis zum Endpunkt
protected double WinkelstartToEnd() { protected double WinkelstartToEnd() {
return (Math.acos( ( skalarprodukt (_0_Matrices.START,_0_Matrices.END) ) / ( betrag(_0_Matrices.START) * betrag(_0_Matrices.END) ) ) ) ; double variable = ( skalarprodukt (startpunkt,endpunkt) ) / ( betrag(startpunkt) * betrag(endpunkt)) ;
if(variable < -1)
variable -= (variable + 1);
if(variable > 1)
variable += (variable - 1);
return (Math.acos( variable ) ) ;
} }
// Berechnet die Entfernung vom Start bis zum Endpunkt // Berechnet die Entfernung vom Start bis zum Endpunkt als Radius
protected double RadiusStartToEnd() { protected double RadiusStartToEnd() {
return (Math.acos( ( skalarprodukt (_0_Matrices.START,_0_Matrices.END) ) / ( betrag(_0_Matrices.START) * betrag(_0_Matrices.END) ) ) ) * _0_Constants.RADIUS; double variable = ( skalarprodukt (startpunkt,endpunkt) ) / ( betrag(startpunkt) * betrag(endpunkt)) ;
if(variable < -1)
variable -= (variable + 1);
if(variable > 1)
variable += (variable - 1);
return Math.acos( variable ) * _0_Constants.RADIUS;
} }
protected double zeitGrenze() { protected double zeitGrenze() {
return Math.toDegrees( (WinkelstartToEnd() / (_0_Constants.VELOCITY)) ); return Math.toDegrees( (WinkelstartToEnd() / (_0_Constants.VELOCITY) ) );
} }
// Bestimmt, ob sich das Objekt im negativen Bereich der x-Achse befindet // Bestimmt, ob sich das Objekt im negativen Bereich der x-Achse befindet
@ -133,6 +149,7 @@ public class _2_Methods {
return Math.atan( _0_Constants.S1 * Math.sin(_0_Constants.ALPHA) ); return Math.atan( _0_Constants.S1 * Math.sin(_0_Constants.ALPHA) );
} }
// Bestimmt den Winkel Theta der Umrissellipse
protected double umrissTheta(double _phi) { protected double umrissTheta(double _phi) {
return Math.atan( -_0_Constants.S1 * Math.cos(_0_Constants.ALPHA) * Math.cos(_phi) ); return Math.atan( -_0_Constants.S1 * Math.cos(_0_Constants.ALPHA) * Math.cos(_phi) );
} }