# How to solve a polynomial of the form y = ax^3 + bx^2 + cx + d using the incremental algorithm in computer graphics

I am studying Computer Graphics and need to design an incremental algorithm for solving the polynomial $y = ax^3 + bx^2 + cx + d$, and then implement that in OpenGL. The input will be the values of $a, b,c,d$ and the desired output is a line/curve to be drawn. The values of $x$ would be in the range $1\leq x\leq100$. The algorithm needs to be very efficient hence I am required to use only addition operation, as multiplication is less efficient.

It would be similar to this technique, but here the polynomial to be considered is the one given above. I have searched a lot on the Internet but cannot find the required solution, because most of the examples solve the equation $y = mx+b$.

Can anyone kindly guide me how to solve it or which method should be applied to solve it?

• Can you clarify what you mean by solving it? What are the inputs, and what is the desired output? Are you given the value of $a,b,c,d,y$ and you want to find a value $x$ such that $ax^3+bx^2+cx+d=y$? Can you edit the question to clarify? Also, what do you mean by "not using multiplication"? I don't even know what that means. What does that mean, and where does that requirement come from? Is there some context that would help us understand your needs? – D.W. Mar 14 '18 at 18:38
• @D.W. I have edited my question. The inputs will the values of a, b, c, d, and the output would be a line to be drawn. And for making it efficient, we cannot use multiplication but can use addition only. – swdeveloper Mar 15 '18 at 2:44