projectionsrays

Projectionsrays is a term occasionally used in computer vision and computer graphics to denote the family of rays that originate from a camera or light source and pass through the image plane, thereby linking three-dimensional scene points to two-dimensional image coordinates. The phrase is not universally standardized; many texts refer to camera rays, projection rays, or image rays. Nevertheless, the concept is widely used as a convenient abstraction for describing how scene geometry projects into an image.

In the standard pinhole camera model, each image pixel p corresponds to a projectionsray with origin at the camera center C and direction d determined by the camera intrinsics and the pixel coordinate. A common formulation is d = K^{-1} p̃, where p̃ is the homogeneous image coordinate. The ray can be written as X(t) = C + t d for t ≥ 0. The collection of rays for all pixels constitutes the ray space or projection space; intersections of these rays with 3D geometry yield projected image points, subject to occlusion and shading.

Projectionsrays are fundamental to many algorithms and pipelines. In ray tracing and ray casting, they are traced through a scene to determine visibility and lighting. In multiview geometry and structure from motion, correspondences between projectionsrays across views are used to estimate camera motion and 3D structure. In volume and image-based rendering, signals are sampled along projectionsrays to synthesize images.

Variants and challenges include lens distortion, non-pinhole camera models, and wide-angle or fisheye projections, which alter the ray directions. Orthographic projection, by contrast, uses parallel projections, a special case with d fixed for all rays. See also camera model, ray tracing, and projection.