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Change of Coordinates and Applications to View Matrices

· One min read

Change of Coordinates​

... and Applications to View Matrices​

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.

The derivation is built from from fundamental linear algebra principles, beginning with the interpretation of the matrix-vector product as projections onto an orthonormal basis. This leads to formal treatment of coordinate system changes using change-of-coordinates matrices. By applying these concepts, we can construct a 4×44 \times 4 revealing the precise geometric meaning of both its rotational as well as translational components.

To complement the theoretical derivation, I also provide an interactive application as a hands-on experience, enabling readers to visualize the effects of these transformations in real-time.

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