Geometrie Leitseite URLhaftendorn.uni-lueneburg.de/mathe-lehramt/geo/geo.htm
[Geometrie] [Platonische Körper] 
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Geometrie Leitseite URL haftendorn.uni-lueneburg.de/mathe-lehramt/geo/geo.htm |
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[Geometrie] [Platonische Körper] |
 Ein Programm von  Albert Kluge, Bremen |
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Mathematisches Highlight: Kreuzprodukt der eine Fläche aufspannenden Vektoren bilden. Wenn Betrag der z-Koordinate positiv ist, dann Fläche anzeigen. |
Wuerfel2.java
import java.awt.*;
import java.applet.*;
public class Wuerfel2 extends Applet {
// 8 Eckpunkte 1-8
// mit je 3 Koordinaten 1,2,3
double p[][] = new double[9][4];
int x=1, y=2, z=3;
public void init() {
setBackground(new Color(255,255,255));
// 8 Eckpunkte im lokalen Würfel-Koordinatensystem
// Nullpunkt = Mittelpunkt
p[1][x] = -100; p[1][y] = -100; p[1][z] = -100;
p[2][x] = +100; p[2][y] = -100; p[2][z] = -100;
p[3][x] = +100; p[3][y] = -100; p[3][z] = +100;
p[4][x] = -100; p[4][y] = -100; p[4][z] = +100;
p[5][x] = -100; p[5][y] = +100; p[5][z] = -100;
p[6][x] = +100; p[6][y] = +100; p[6][z] = -100;
p[7][x] = +100; p[7][y] = +100; p[7][z] = +100;
p[8][x] = -100; p[8][y] = +100; p[8][z] = +100;
// 8 - - - - - 7
// / | / |
// 5 - - - - - 6 |
// | | | |
// | 4 - - - -|- 3
// | / | /
// 1 - - - - - 2
// y-Werte spiegeln
for (int i=1;i<9;i++) {
p[i][y] = -p[i][y];
}
}
// Rotationswinkel in rad
double angle_x = 0.01;
double angle_y = 0.0075;
double angle_z = 0.005;
Image buffer;
Graphics2D gBuffer;
double c[] = new double[9];
int w = 200; // -> Weltkoordinaten
public void paint(Graphics g) {
// Double-Buffering
if (buffer==null) {
buffer=createImage(this.getSize().width, this.getSize().height);
gBuffer=(Graphics2D)buffer.getGraphics();
}
gBuffer.clearRect(0,0,this.getSize().width, this.getSize().height);
// Antialiasing
gBuffer.setRenderingHint(RenderingHints.KEY_ANTIALIASING,
RenderingHints.VALUE_ANTIALIAS_ON);
// Perspektive: *1+z/1000
for (int i=1;i<9;i++) {
c[i] = 1+p[i][z]/1000;
}
// Kreuzprodukt der eine Fläche aufspannenden Vektoren bilden
// Wenn Betrag der z-Koordinate positiv: Fläche anzeigen
if((p[1][x]*c[1]-p[2][x]*c[2])*(p[3][y]*c[3]-p[2][y]*c[2])
-(p[1][y]*c[1]-p[2][y]*c[2])*(p[3][x]*c[3]-p[2][x]*c[2]) > 0) {
// |2->1 x 2->3| > 0
int xCoords1234[] = {(int)(p[1][x]*c[1])+w,(int)(p[2][x]*c[2])+w,
(int)(p[3][x]*c[3])+w,(int)(p[4][x]*c[4])+w};
int yCoords1234[] = {(int)(p[1][y]*c[1])+w,(int)(p[2][y]*c[2])+w,
(int)(p[3][y]*c[3])+w,(int)(p[4][y]*c[4])+w};
gBuffer.setColor(new Color(255,0,0));
gBuffer.fillPolygon(new Polygon(xCoords1234,yCoords1234,4));
}
else if((p[7][x]*c[7]-p[6][x]*c[6])*(p[5][y]*c[5]-p[6][y]*c[6])
-(p[7][y]*c[7]-p[6][y]*c[6])*(p[5][x]*c[5]-p[6][x]*c[6]) > 0) {
// |6->7 x 6->5| > 0
int xCoords5678[] = {(int)(p[5][x]*c[5])+w,(int)(p[6][x]*c[6])+w,
(int)(p[7][x]*c[7])+w,(int)(p[8][x]*c[8])+w};
int yCoords5678[] = {(int)(p[5][y]*c[5])+w,(int)(p[6][y]*c[6])+w,
(int)(p[7][y]*c[7])+w,(int)(p[8][y]*c[8])+w};
gBuffer.setColor(new Color(255,0,0));
gBuffer.fillPolygon(new Polygon(xCoords5678,yCoords5678,4));
}
if((p[6][x]*c[6]-p[2][x]*c[2])*(p[1][y]*c[1]-p[2][y]*c[2])
-(p[6][y]*c[6]-p[2][y]*c[2])*(p[1][x]*c[1]-p[2][x]*c[2]) > 0) {
// |2->6 x 2->1| > 0
int xCoords1265[] = {(int)(p[1][x]*c[1])+w,(int)(p[2][x]*c[2])+w,
(int)(p[6][x]*c[6])+w,(int)(p[5][x]*c[5])+w};
int yCoords1265[] = {(int)(p[1][y]*c[1])+w,(int)(p[2][y]*c[2])+w,
(int)(p[6][y]*c[6])+w,(int)(p[5][y]*c[5])+w};
gBuffer.setColor(new Color(0,255,0));
gBuffer.fillPolygon(new Polygon(xCoords1265,yCoords1265,4));
}
else if((p[4][x]*c[4]-p[3][x]*c[3])*(p[7][y]*c[7]-p[3][y]*c[3])
-(p[4][y]*c[4]-p[3][y]*c[3])*(p[7][x]*c[7]-p[3][x]*c[3]) > 0) {
// |3->4 x 3->7| > 0
int xCoords4378[] = {(int)(p[4][x]*c[4])+w,(int)(p[3][x]*c[3])+w,
(int)(p[7][x]*c[7])+w,(int)(p[8][x]*c[8])+w};
int yCoords4378[] = {(int)(p[4][y]*c[4])+w,(int)(p[3][y]*c[3])+w,
(int)(p[7][y]*c[7])+w,(int)(p[8][y]*c[8])+w};
gBuffer.setColor(new Color(0,255,0));
gBuffer.fillPolygon(new Polygon(xCoords4378,yCoords4378,4));
}
if((p[3][x]*c[3]-p[2][x]*c[2])*(p[6][y]*c[6]-p[2][y]*c[2])-(p[3][y]*c[3]
-p[2][y]*c[2])*(p[6][x]*c[6]-p[2][x]*c[2]) > 0) {
// |2->3 x 2->6| > 0
int xCoords2376[] = {(int)(p[2][x]*c[2])+w,(int)(p[3][x]*c[3])+w,
(int)(p[7][x]*c[7])+w,(int)(p[6][x]*c[6])+w};
int yCoords2376[] = {(int)(p[2][y]*c[2])+w,(int)(p[3][y]*c[3])+w,
(int)(p[7][y]*c[7])+w,(int)(p[6][y]*c[6])+w};
gBuffer.setColor(new Color(0,0,255));
gBuffer.fillPolygon(new Polygon(xCoords2376,yCoords2376,4));
}
else if((p[5][x]*c[5]-p[1][x]*c[1])*(p[4][y]*c[4]-p[1][y]*c[1])
-(p[5][y]*c[5]-p[1][y]*c[1])*(p[4][x]*c[4]-p[1][x]*c[1]) > 0) {
// |1->5 x 1->4| > 0
int xCoords1485[] = {(int)(p[1][x]*c[1])+w,(int)(p[4][x]*c[4])+w,
(int)(p[8][x]*c[8])+w,(int)(p[5][x]*c[5])+w};
int yCoords1485[] = {(int)(p[1][y]*c[1])+w,(int)(p[4][y]*c[4])+w,
(int)(p[8][y]*c[8])+w,(int)(p[5][y]*c[5])+w};
gBuffer.setColor(new Color(0,0,255));
gBuffer.fillPolygon(new Polygon(xCoords1485,yCoords1485,4));
}
g.drawImage (buffer, 0, 0, this);
// Verzögerung
try {Thread.sleep(20);}
catch (InterruptedException e) {}
double px, py, pz;
for (int i=1;i<9;i++) {
px = p[i][x];
py = p[i][y];
pz = p[i][z];
// Rotation um x-Achse
p[i][y] = py*Math.cos(angle_x)-pz*Math.sin(angle_x);
p[i][z] = py*Math.sin(angle_x)+pz*Math.cos(angle_x);
py = p[i][y];
pz = p[i][z];
// Rotation um y-Achse
p[i][x] = px*Math.cos(angle_y)+pz*Math.sin(angle_y);
p[i][z] =-px*Math.sin(angle_y)+pz*Math.cos(angle_y);
px = p[i][x];
// Rotation um z-Achse
p[i][x] = px*Math.cos(angle_z)-py*Math.sin(angle_z);
p[i][y] = py*Math.cos(angle_z)+px*Math.sin(angle_z);
}
repaint();
}
public void update(Graphics g) {paint(g);}
}
Schema der Berechnung des Kreuzprodukts der Fläche. Dabei sind p und q die eine Fläche aufspannenden Vektoren.
[ p1 ] [ q1 ] [ p2*q3 - p3*q2 ] [ p2 ] x [ q2 ] = [ p3*q1 - p1*q3 ] [ p3 ] [ q3 ] [ p1*q2 - p2*q1 ]Download ©Albert Kluge www.jjam.de
| [Computer] [DGS] [Geometrie] [Platonische Körper] |
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