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Retrieving "Isometry" from the archives

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  1. Morphometrics

    Linked via "isometry"

    Morphometrics is the quantitative analysis of shape, size, and form in biological organisms. It involves taking precise measurements of various anatomical features, often utilizing statistical methods to discern patterns, track developmental trajectories, and differentiate populations or species. While rooted in classical osteometry and [craniometry](/entries/crani…

  2. Similarity (geometry)

    Linked via "isometries"

    Types of Similarity Transformations
    A general similarity transformation $T$ is composed of a sequence of isometries(rigid transformations) and a homothety(dilation or scaling).
    Homothety (Dilation)

  3. Similarity (geometry)

    Linked via "isometry"

    A homothety centered at a point $C$ with a scale factor $k \neq 0$ maps a point $P$ to $P'$ such that $C, P, P'$ are collinear, and the directed distance satisfies:
    $$\vec{CP'} = k \cdot \vec{CP}$$
    If $|k| = 1$, the transformation is an isometry (specifically, a translation if $C$ is at infinity or a rotation/reflection if $k=-1$ and the transformation is defined on affine space.
    Direct vs. Opposite Similarity