worldToLocal

worldToLocal is a transformation operation that converts coordinates from world space into an object's local coordinate space. It is typically realized by applying the inverse of the object's world transform matrix. If a point in world space is P_world, the corresponding local coordinates are obtained as P_local = M_world^{-1} * P_world, where M_world is the 4x4 matrix representing the object's position, rotation, and scale in the world. For directions or vectors, you use a homogeneous coordinate with a zero w component to avoid translating the vector.

In practice, many graphics and game engines provide utilities to perform this operation directly, such as inverse transform functions. The concept is the reverse of localToWorld, which maps local coordinates to world space. The worldToLocal operation requires careful handling of coordinate conventions, including the matrix convention (row-major vs column-major) and the handedness of the coordinate system. Non-uniform scale or complex rotations can affect the simplicity of the results, and in some cases additional steps may be needed to extract pure rotational components.

Common uses include hit testing and raycasting in local space, transforming points for physics calculations, animation skinning, and utility scripts that need to interpret world-origin data relative to an object’s local frame. In many engines, equivalent functions exist, such as Transform.InverseTransformPoint in Unity or similar reverse transforms in other frameworks.

Overall, worldToLocal is a fundamental tool for interpreting world-position data within the context of an individual object’s local coordinate system.