## Plot a path between 2 points, speed decelerating

Hi there,

I'm a programmer trying to plot the positions between two points. The number of steps from Point1 to Point2 is variable, as are the x,y positions of the two points.

I can do it if the speed is constant. The function is as follows:

Code:
PlotMotion(x1,y1,x2,y2,steps)

xinc = Beat(x1,x2)-Defeat(x1,x2)
xinc=xinc/(steps-2)

yinc = Beat(y1,y2)-Defeat(y1,y2)
yinc=yinc/(steps-2)

For a = 2 To steps
c(a)\x=Defeat(x1,x2)+(xinc*a)
c(a)\y=Defeat(y1,y2)+(yinc*a)
Next a

c(1)\x=x1
c(1)\y=y1
c(steps)\x=x2
c(steps)\y=y2
That's the program code (PureBasic). Forgive my ignorance but I believe the mathematical formula would be something like:

$\displaystyle Xn = (x2-x1) / steps * n$
$\displaystyle Yn = y2-y1) / steps * n$
assuming that x2 is greater than x1, and y2 is greater than y1.

However, can anyone tell me how to plot the path between two points if the speed is steadily decelerating?

At high school I could possibly have done this by myself but that's years ago and I'm reduced to googling for the formula. Hours later, I still can't find it, so any help would be greatly appreciated.