My article introduces the mathematical derivation of the lookAt view matrix commonly used in computer graphics APIs like OpenGL.
As part of the graphics pipeline, the purpose of this matrix is to perform the view transformation, converting global world coordinates into a coordinate system defined by position and direction of an observer.
Rotations, as a class of affine vector transformations, represent rigid body transformations that change the direction of a vector within a given plane.
Efficient and accurate handling of such transformations poses challenges not only for game and animation engines, but also for simulations and real-time systems, where the limitations of floating-point arithmetic and operation throughput can negatively impact the computational outcomes.
The Dot Product is a fundamental building block for vector operations in video games and simulations. A solid understanding is crucial for applications involving view-related coordinate transformations and even physical modeling within a game world. For many practical use cases, the dot product offers an elegant alternative to constructing explicit visibility cones or relying on computationally expensive raytracing algorithms.