Some Aspects of the Tangent-Angle vs. Arc Length Representation of Contours

Raudseps, Juris G.

doi:10.21236/ad0462877

Cited by 9 publications

(2 citation statements)

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“…Notably, the tangent angle function, 𝜙(𝑡), describes the angle of the tangent at a landmark as a function of distance traveled along the specimen's outline (Zahn and Roskies, 1972;MacLeod, 2012). While the concept of 𝜙 (sensu Zahn and Roskies, 1972) is equivalent to the one described in Section 3, the tangent angle function appears to have been derived without reference to differential geometry (Raudseps, 1965). Though we are interested specifically in the curvature of shapes, the tangent angle function was developed as a means to quantify shapes in their entirety-curvature is incidental.…”

Section: A Proposed Protocol For Measuring Curvaturementioning

confidence: 99%

Plant-pollinator specialization: Origin and measurement of curvature

Boehm

Jankowski

Cronk

2021

Preprint

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A feature of biodiversity is the abundance of curves displayed by organs and organisms. Curvature is a widespread, convergent trait that has important ecological and evolutionary implications. In pollination ecology, the curvature of flowers and pollinator mouthparts (e.g. hummingbird bills) along the dorsiventral plane has been associated with specialization, competition, and species co-existence. Six methods have historically been used to measure curvature in pollination systems; we provide a solution to this inconsistency by defining curvature using well-established concepts from differential geometry. Intuitively, curvature is the degree to which a line is not straight, but more formally, it is the rate at which the tangent of a curve changes direction with respect to arc length. Here, we establish a protocol wherein a line is fitted against landmarks placed on an image of a curved organ or organism, then curvature is computed at many points along the fitted line and the sum taken. The protocol is demonstrated by studying the development of nectar spur curvature in the flowering plant genus Epimedium (Berberidaceae). By clarifying the definition of curvature, our aim is to make the language of comparative morphology more precise and broadly applicable to capture other curved structures in nature.

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Section: A Proposed Protocol For Measuring Curvaturementioning

confidence: 99%

Plant-pollinator specialization: Origin and measurement of curvature

Boehm

Jankowski

Cronk

2021

Preprint

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“…Although angle functions have been used previously for shape analysis, see e.g. [103], Zahn and Roskies provided a formal treatment by focusing on the shapes of planar closed curves. Note that in representing a curve β by its angle function θ, one has already removed the effect of translations of β.…”

Section: Curves With Fixed Parameterizationsmentioning

confidence: 99%