Algorithms

Ralf Meier wrote:

In fact I enjoyd this discussion very much.

1. For N "control points", you have N-1 cubic functions.
2. Each function is of the form f(x) = ax^3 + bx^2 +cx + d
3. The 1^st derivative of each function is the velocity f'(x) = 3ax^2 + 2bx + c, and it will be continuous (no abrupt velocity changes)
4. The 2^nd derivative of each function is the acceleration f''(x) = 6ax + 2bx, and it will be continuous (no jerks)
5. f₀(t₀) = x₀
6. f₀'(t₀) = v₀
7. f_N-1(t_N) = x_N
8. f_N-1'(t_N) = v_N

Joan M wrote:

I've tried to make my own which works perfectly when the values allow the motor to reach the maximum speed "plateau" but it is not working well when is not possible to achieve this speed

Joan M wrote:

What you suggest changes the acceleration... I would like to change the speed and find the lowest permissible speed without changing the acceleration.

u_vmax	3000 mm/s
u_v0	2200 mm/s  <--------- the important different one
u_vf	0 mm/s	
u_a	2000 mm/s^2	
u_x0	3000 mm	
u_xf	6000 mm	
c_dist	3000 mm
c_vmax	2901,250001 mm

u_vmax	3000 mm/s	
u_v0	0 mm/s  <--------- the important different one	
u_vf	0 mm/s	
u_a	2000 mm/s^2	
u_x0	3000 mm	
u_xf	6000 mm	
c_dist	3000 mm	
c_vmax	2449,489743 mm	

u_vmax	3000 mm/s	
u_v0	2600 mm/s  <--------- the important different one
u_vf	0 mm/s	
u_a	2000 mm/s^2	
u_x0	3000 mm	
u_xf	6000 mm	
c_dist	3000 mm	
c_vmax	3000 mm	

LimitIterations = 1000

LimitIterations = vmax

Member 10566089 wrote:

I have to write a program that

Member 10566089 wrote:

I can't find an algorithm that solves this problem in O(n). Do you have any idea?

int l, l_max, u_max, u;
int A[N+1] =  // array input
l_max= l =1;
u_max= u =1;


int i;
for (i=2;i<N;i++)
{
    if (A[i] >= A[u])
        u = i;
    else if (A[i] < A[l])
    {
        if (u-l > u_max-l_max)
        {
            l_max = l;
            u_max = u;
        }
        l = u = i;
    }
}
if (u-l > u_max - l_max)
{
    l_max = l;
    u_max = u;
}
printf("%d    %d", l_max,u_max);

	public static void main(String[] args) {
		int [] arr=  //input
		int N=arr.length;
		LinkedList <Subarray> subarrays=new LinkedList<Subarray> ();
		Subarray s=new Subarray();
		s.setStart(0);
		s.setEnd(0);
		for (int i=1;i<N;i++)
		{
			if (arr[i] < arr[i-1])
			{
				s.setEnd(i-1);
				subarrays.add(s);
				s=new Subarray();
				s.setStart(i);
				s.setEnd(i);
			}
		}
		s.setEnd(N-1);
		subarrays.add(s);
		Iterator<Subarray> iterator = subarrays.iterator();
		s=iterator.next();
		Subarray nxt;
		while (iterator.hasNext()) {
			nxt=iterator.next();
			if (arr[nxt.getEnd()]>=arr[s.getEnd()] && arr[s.getStart()]<=arr[nxt.getStart()])
				nxt.setStart(s.getStart());
			s=nxt;
		}
		iterator = subarrays.iterator();
		s=iterator.next();
		while (iterator.hasNext())
		{
			nxt=iterator.next();
			if ((nxt.getEnd()-nxt.getStart()) > (s.getEnd()-s.getStart())){
				s=nxt;
			}
		}
		System.out.print("+s.getStart()+""+s.getEnd());
	}
}

public static void main(String[] args) {
		int [] input=//input
		int max = input.length - 1;
		int[] aux = new int[input.length];	//Array con i valori massimi
		for(int i = input.length; i>0; i--){
		    if(input[i-1] > input[max])
		    {
		        max = i - 1;
		    }
		    aux[i-1] = max;
		}


		int l = 0;
		int u = 0;
		max = 0;
		int lMax = 0;
		int uMax = 0;
		
		for (int i=0;i<aux.length;i++)
			System.out.print(aux[i]+" ");
		for(int i = 0; i< input.length; i++){

			System.out.println(""+input[i]+",l: "+l+",u: "+u);
			
			if (input[i] >= input[l] && aux[l] >= i)
			{
		        u = i;
		    }
		    else
		    {
		        if(u-l > max)
		        {
		            lMax = l;
		            uMax = u;
		            max = u-l;
		        }
		        l = i;
		        u = i;
		    }
		}
		if(u-l > max){
		    lMax = l;
		    uMax = u;
		}
		System.out.println("l "+l+" u "+u);
	}