A can be written as... $y = a$
B can be written as... $y = bx + a$
C can be written as... $y = cx^2 + bx + a$
1) How can I write D? I was looking at implementing bezier curves into some code but is there something similar which could be computed much quicker?
2) C is a quadratic... what is the name for D?
Perhaps if I explain what I'm doing.... I am trying to build a decent servo controller. I have a servo which will move from servo position 30 to 0. I want it to move in a more elegant way than B (above)... ideally like in the picture. I will come up with a way of defining the movement between 2 positions when I send a command to the controller. Perhaps this is a quadratic equation which could be calculated easily for each x (time) between y (servo angles)... this would mean I would only need to pass a, b and c to the controller along with the time (length) and both positions.
I figured it would be better to have it able to be more irregular... but still super quick to compute. I considered bezier curves as a definition for the line, but they seem overcomplicated and slow to compute... if there anything else I could use?