How to create cubic bezier curve using control points?

Question

How can I create the cubic bezier curve to (6,2) using control points (2,3.8) and (3.8,2)?

What I have tried:

I considered all the points as the control points P₀=(2,3.8) P₂=(6,2) P₁=(3.8,2)

Consider the below equation: ∑ p_i B_i,n (u)

where B is the basis function.

and

B_i,n(u)=ⁿC_iuⁱ(1-u)^n-i

SO I derived the equation:

=P₀B_0,2(u)+P₁B_1,2(u)+P₂B_2,2(u)

But I am not able to get anything using this equation. ANy Help?

Edit:

if I consider only two control points i.e P₀=(2,3.8) and P₁=(3.8,2) then what is the use of point (6,2) and how we determine how much curly the path is?

Answer 1

A cubic bezier curve starting from point $P_0$, ending at point $P_3$ with two control points $P_1$ and $P_2$ is represented by the following,

$$B(t) = P_0(1-t)^3 + 3(1-t)^2tP_1 + 3(1-t)t^2P_2 + t^3P_3, \ \ t \in [0,1]$$

In your question, $P_1, P_2, P_3$ are given but $P_0$ is not satisfied. May be it is $(0,0)$. Please check the source of the question.