[Ether]

Originally Posted by theNerd

what if the current heading angle was a slope of infinity?

Pick a coordinate system whose origin is the starting point and whose positive X axis aligns with the starting direction of motion.

Compute the ending point (X₂,Y₂) and slope m₂ in that coordinate system.

Then the cubic becomes simply Y = aX³ + bX²

and the formulas for a and b are simply

a = (m₂X₂ - 2Y₂)/X₂³

b = (3Y₂ - m₂X₂)/X₂²