The Geometry of the Dot Product
The Geometry of the Dot Product
... and Applications to Visibility Modeling
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.
My article provides an introductory exploration of the theory of the dot product and its geometric interpretation.
An example involving field-of-view-calculations illustrates how the dot product can simplify visibility modeling and decision-making in games.
Additional proofs establish key lemmas that support further applications of the dot product and related operations in both 2D and 3D.