I have this concrete problem where I know the 3 coordinates of a triangle $ABC$ in a $xyz$ frame reference and I need to estimate the position $P$ and direction $\vec{n_{p}}$ of a stationary camera with known focal distance $f$. For this purpose I have the image from the camera where I know $H$, $W$ and the respective 2D positions $a$, $b$, $c$ in pixels.
My questions:
- Is this possible by knowing only 3 points $ABC$?
- Does make difference if triangle $ABC$ is equilateral or not since I know the map $ABC => abc$?
- How to estimate $P$ and $\vec{n_{P}}$ relative to frame $xyz$?
I read already Camera Pose Estimation from Vanishing Points, Step by Step Camera Pose Estimation for Visual Tracking and Planar Markers and How to compute camera pose from Homography matrix? but sincerily I couldn't realize how to solve my problem.