# rigid-body motion using an orthogonal affine transformation

The use of an orthogonal matrix (R) in the affine transformation formula $$\left( x ^{\prime}= R x + A \right)$$ ensures that the transformation is a rigid-body motion. This means the object is only rotated and translated, and its intrinsic properties-specifically its shape, size, and internal distances-are perfectly preserved at all times during the animation. The animated demo is the fundamental relationship between linear algebra and geometry.

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