Quantifying the regularity of a 3D set of points on the surface of an ellipsoidal object

• Several natural and artificial structures, such as human skin and mammals cortices, exhibit a compound organization, with basic elements being distributed along a surface. The problem of quantifying the geometrical uniformity of this type of biological and physical compound structures is addressed in this work. This required the solution of several problems, including the detection, along the surface, of the borders of the compound system, defining the adjacency between the elements in the 3D space, and obtaining a reference of uniformity for calculating the polygonality. Specific approaches were devised and applied to address each of these difficulties, including connectivity criteria ensuring the adjacency to remain within the considered surface as well as the extension of the polygonality, originally suggested for 2D structures, to 3D compound systems. The potential of the so-obtained method is illustrated with respect to compound eyes of fungus gnats (small, forest dwelling flies), and interesting results are reported and discussed, including the fact that the uniformity tends to increase toward the center of the system, and the absence of correlation with two measurements traditionally used for characterizing this type of eyes.

Ämnesord

NATURVETENSKAP  -- Kemi -- Oorganisk kemi (hsv//swe)

NATURAL SCIENCES  -- Chemical Sciences -- Inorganic Chemistry (hsv//eng)

Nyckelord

3D Regularity

Compound structure

Ellipsoid hexagonal tilling

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art (ämneskategori)

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