Originally Posted by

**hollywood** It is the same as the other thread, except you have both x and y to solve, and you have variables instead of numbers.

Let $\displaystyle p_0=(x_0,y_0)\text{, }p_1=(x_1,y_1)\text{, and }p_2=(x_2,y_2)$.

Also, let $\displaystyle C(t)=(x(t),y(t))$.

So we are looking for:

$\displaystyle x(t)\text{ satisfying }x(t_0)=x_0\text{, }x(t_1)=x_1\text{, and }x(t_2)=x_2$, and

$\displaystyle y(t)\text{ satisfying }y(t_0)=y_0\text{, }y(t_1)=y_1\text{, and }y(t_2)=y_2$.

Each of these is solved by the same process as the other thread. For the x-coordinate:

$\displaystyle x(t)=x_0\ \frac{t-t_1}{t_0-t_1}\ \frac{t-t_2}{t_0-t_2}+x_1\ \frac{t-t_0}{t_1-t_0}\ \frac{t-t_2}{t_1-t_2}+x_2\ \frac{t-t_0}{t_2-t_0}\ \frac{t-t_1}{t_2-t_1}$

and of course the y-coordinate is similar.

- Hollywood