1. P0_1 = PVector.sub(P1, P0);
2. P0_1.mult(t);
3. P0_1.add(P0);

I tested and it is correct but i have no clue what is going on :)

All I have done is use basic algebra to reorganise your equation to simplify the computation.

Start with the original problem
P0_1 = (1 - t)*P0 + t*P1               now expand the brackets
P0_1 = P0 - t*P0 + t*P1                collect terms in 't'
P0_1 = P0  + t * (P1 - P0)             have swapped last 2 terms

Now converting this into Java for Processing gives

1. P0_1 = PVector.sub(P1, P0); 
   
2. P0_1.mult(t);
3. P0_1.add(P0);

PVector.sub is a class method that creates a new PVector object that is the difference between two other PVector object.

HTH

I have no  basic algebra knowledge it appears.

I have no  basic algebra knowledge it appears.

Hope you didn't take offence, none was intended. Everyone has different strengths and weaknesses, one of mine strengths is maths and I don't have the time to list my weaknesses.

O no didn't take it as a offence.