LookAt

LookAt is a common function in 3D graphics used to create a view matrix that positions and orients a camera so that it looks at a specified target point. Given the camera position (eye), a center or target point (center), and an up direction (up), lookAt returns a 4x4 matrix that transforms world coordinates into camera (view) space, enabling rendering from the camera’s perspective.

The typical construction computes three orthogonal axes: forward, right, and true up. Let f be the normalized vector from eye to center (the viewing direction), s be the normalized cross product of f and up (the camera's right vector), and u be the cross product of s and f (the corrected up vector). The rotation portion of the view matrix is built from s, u, and −f (signs vary with convention), and the translation portion encodes the camera position via dot products with eye. The exact arrangement of these components depends on row-major versus column-major storage and on the graphics API’s conventions (OpenGL, DirectX, etc.).

Conventions differ across systems. OpenGL-style pipelines typically use a right-handed system with the camera looking toward −Z in world space, yielding a view matrix compatible with GLM’s lookAt. DirectX commonly uses a left-handed system with forward toward +Z. The concept is implemented in many libraries, such as glm::lookAt in GLM, XMMatrixLookAtRH/LH in DirectX, and Camera.LookAt in various engines.

Notes and pitfalls: eye and center must not coincide; up should not be parallel to the viewing direction. If up is not orthogonal to f, it is orthogonalized during computation. LookAt only produces a view transformation; it does not project the scene.