Three transformations turn a 3D world into a pixel grid: extrinsics place the camera in the world, perspective projects 3D onto the image plane, and intrinsics map that to pixels. Drag the camera and watch points project live.
[R | t]. Rotation, translation. Lossless.K. Continuous → discrete; quantization + origin shift.That single equation is the entire camera model. Everything else — calibration, stereo, SfM, AR — is just solving for one of the variables given the others.
Cyan points are 3D world points. The green pyramid is the camera frustum. The right panel shows the projected pixels.
K = camera-to-pixel. fx, fy = focal length in pixels; cx, cy = principal point. Converts metric image plane → pixel grid.[R|t] = world-to-camera. Tells you where the camera is in the world.For checkerboard-style calibration, you collect many (world_pt, image_pt) pairs across poses and solve for K. Once K is fixed, given a single image of a known 3D pattern, cv2.solvePnP recovers (R, t) — the pose of the camera. That's perspective-n-point, and it's how AR markers, head-pose estimation, and robot tool localization all work under the hood.