I need to have a parametric formula that given a start point (Lat, Long), end point (Lat, Long) and center and a parameter t gives me a point in the arc between those 2 points. I need to calculate all the given points in the arc to after that draw it in a map.
I researched the equations for the circle, arcs can't seem to adapt to my specific circumstances. Can anyone help?
Thanks in advance!
Assuming the center lies in $(0,0)$. You should know how to calculate the radius. The parametrisation of the circle itself is $t \mapsto R \cdot (\cos(t), \sin(t))$. Calculate which $t$ get mapped to the first and second point; say those values are $1$ and $2.5$, then your parametrisation is simply $\gamma: [1; 2.5] \to Circle: t \mapsto R \cdot (\cos(t), \sin(t))$.
If the center does not line in the origin,but in $(a,b)$, first translate all your points (center, start, end) by the vector $-(a,b)$. Now the center does lie in the origin. Calculate your parametrisation, and then add $(a,b)$ to it to get the parametrisation for the circle arc with center at $(a,b)$