• fullscreen
• steuerung_kurve.pde
• ```//steering along a curve:
//the curve is described with a paramter,
//that means: y=f(parameter), x=g(parameter)
//this way loops are possible.
//on setup,the the parameter is divided in 200
//steps and the according points are calculated and stored in an array,
//together with the distances between a point and the next point,
//because this might be used for some kind of steering.
//the vehicles looks for the nearest point and then is going to the next point on the curve
//following the numbering in the array. So there is a clear direction of the movement.
//we can keep the velocity at a constant level or adapt it
//at the distance of the points.
//this works very well in general, but there is a problem,
//when the curve is intersecting itself - which way to go for
// the vehicle?
//It would be easy to solve that problem, when the points on the
//curve where in a strictly rising order - but often it´s not like that,
//for example with some of the curves in polar coordinates (the angel as
// the parameter, going around from 0 to 4PI in two turns.

int z,a,altb=0;
float x,y,phi;
float[] punkte=new float[600];
PVector ort=new PVector(0,0,0);
PVector geschw=new PVector(0,0,0);

float faktor=1;
float tempo=5;//ab ca. 10 überspringen von punkten
int b=0;
int what=0;

void setup() {
size(600,600,P2D);
// frameRate(30);
smooth();
rectMode(CENTER);
getarray();
//starting point and speed for the vehicle
ort.x=punkte[0]+random(-300,300)-100;
ort.y=punkte[1]+random(-300,300)-100;
geschw.x=random(-13,13);
geschw.y=random(-13,13);
}

void draw() {
background(0);
stroke(0);
//drawing the stored points of the line if you want that
for(int i=0;i<198;i++){
stroke(0,30);
line(punkte[3*i%600],punkte[(3*i+1)%600],punkte[3*(i+1)%600],punkte[(3*(i+1)+1)%600]);
stroke(255,0,255);
point(punkte[3*i],punkte[3*i+1]);
}
stroke(255,0,0);
altb=b;
b=findnearest(ort.x,ort.y);

//the vehicle at ort.x/ort.y looks for the nearest point
//with index b on the curve. from there, steering() will send it
// to the next point with index b+1
steering(b%198);
display();
}
void display(){
translate(ort.x,ort.y);
rotate(atan2(geschw.y,geschw.x));
fill(255,255,0);
rect(0,0,30,15);
}

int findnearest(float ax, float by){
float b;
float c;
int zaehler=0;
b=dist(punkte[0],punkte[1],ort.x,ort.y);
for(int i=1;i<199;i=i+1){
c=dist(punkte[3*i],punkte[3*i+1],ort.x,ort.y);
if(b>c){
b=c;
zaehler=i;
}
}
if(abs(altb-zaehler)<5||abs(abs(altb-zaehler)-100)<5){
return zaehler;}else{
println(altb+"x"+zaehler);
return (altb+2)%200;

}
}

void steering(int i){
println(i);
PVector kraft=new PVector(0,0,0);

// kraft.set((2*punkte[3*(i+1)]+punkte[3*(i+2)])/3-ort.x,(2*punkte[3*(i+1)+1]+punkte[3*(i+2)+1])/3-ort.y,0);
// kraft.set(punkte[3*(i+1)]-ort.x,punkte[3*(i+1)+1]-ort.y,0);
kraft.set(punkte[3*(i+1)]-(ort.x+geschw.x),punkte[3*(i+1)+1]-(ort.y+geschw.y),0);
kraft.mult(faktor);
geschw.normalize();
geschw.mult(tempo);
}

void getarray(){
float incr=2*TWO_PI/200;
for(int i=0;i<200;i=i+1){
switch (what){
case 0:
phi=(float) i*incr+0.13;
punkte[3*i]=150*cos(phi)+100*cos(2*phi)+300;
punkte[3*i+1]=150*sin(phi)-100*sin(3*phi)+300;
break;
case 1:
phi=(float) i*incr;
punkte[3*i]=150*cos(phi)+100*cos(3*phi)+300;
punkte[3*i+1]=150*sin(phi)-100*sin(3*phi)+300;
break;
case 2:

phi=(float) i*incr+0.02;
punkte[3*i]=150*cos(phi)+100*cos(3*phi/2-1)+300;
punkte[3*i+1]=150*sin(phi)-100*sin(phi/2+1)+300;
break;
case 3:

phi=(float) i*incr+0.02;
punkte[3*i]=150*cos(phi/2)+100*cos(3*phi/2+1.1)+300;
punkte[3*i+1]=150*sin(phi+0.4)-100*sin(phi/2+2)+300;
break;

case 4:

phi=(float) i*incr+0.02;
punkte[3*i]=220*cos(phi/2+0.15)+300;
punkte[3*i+1]=150*sin(phi+0.4)-100*sin(phi/2+2)+300;
break;
case 5:
phi=(float) i*incr+0.13;
punkte[3*i]=200*cos(phi)+300;
punkte[3*i+1]=200*sin(phi+1)+300;
break;
case 6:
phi=(float) i*incr/2;
punkte[3*i]=50+50*(phi-PI)*(phi-7*PI/6);
punkte[3*i+1]=300+100*sin(phi);
;
break;
}
}
for(int i=0;i<199;i=i+1){
punkte[3*i+2]=dist(punkte[3*i],punkte[3*i+1],punkte[3*(i+1)],punkte[3*(i+1)+1]);
}
}

void mouseClicked(){
what=(what+1)%7;
getarray();
}

```

### tweaks (0)

This sketch is running as Java applet, exported from Processing.

## steering on a curve

3

click the mouse to try different curves. More explanation at the top of the code.

kaypel
21 Jan 2010
The car misses some loops.
Abel Dewitz
21 Jan 2010
Dear kaypel, that´s exactly the problem I described in the preface of my code.
Perhaps someone has an idea how to solve this.
The car doesn´t go from one point to the next, because this would limit the speed very strictly. One step could not be greater than the distance to the next point. To be more flexible, the car goes in the direction of the next point, but the program chooses speed. So you can reach for example two points ahead.
Then the car looks for the point, that is the nearest and continues from that point. If there is an intersection, it can happen that it chooses a point an the other loop.
Abel Dewitz
21 Jan 2010
Now the problem is solved: finding the next point, the program checks the difference of the indices to the previous point. If it is too big, it´s probably on the wrong loop and we take the point before (on the right loop) +2.
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