x = vx * t
y = vy * t + c * t²
sqr( vx² + vy² ) = 1
c >= 0
t >= 0 (in practice t >= abs( x ))
Note: vx and vy ARE NOT v*x and v*y - they are unique variables.
When the numbers c, x and y are known,
for a given value of t,
how do I determine if the equation can be solved?
if the equation can be solved,
how do I determine the values of vx and vy?
Nice to know:
x,y = position (relative to origin)
vx,vy = direction (normalized)
c = curvature
t = time