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2 posts tagged with "linear algebra"

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Rotations as a Special Case of Vector Transformations

· One min read
Thorsten Suckow-Homberg
Thorsten Suckow-Homberg

Rotations as a Special Case of Vector Transformations​

... with Applications to Game World Modeling​

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 Geometry of the Dot Product

· One min read
Thorsten Suckow-Homberg
Thorsten Suckow-Homberg

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.