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Mechanics Preliminaries
Published in J. N. Reddy, Theories and Analyses of Beams and Axisymmetric Circular Plates, 2022
force per unit mass, and a is the acceleration. Since the total vector area of a closed surface is zero, we have Δsn^−Δs1e^1−Δs2e^2−Δs3e^3=0.
Theory of Strain
Published in Prasun Kumar Nayak, Mijanur Rahaman Seikh, Continuum Mechanics, 2022
Prasun Kumar Nayak, Mijanur Rahaman Seikh
Similar expressions are obtained for the vector area da1 and da2 by replacing the index 3 by 1 and 2, respectively as da1=J∂X1∂xmdA1im;da2=J∂X2∂xmdA2ir
Fiber-reinforced tissues: directional averaging
Published in Benjamin Loret, Fernando M. F. Simões, Biomechanical Aspects of Soft Tissues, 2017
Benjamin Loret, Fernando M. F. Simões
The differential vector area and differential area result as, () dS→=∂m∂θ^∂m∂ϕdθdϕ=msinθdθdϕ,dS≡|dS→|=sinθdθdϕ,
Applying computational geometry to designing an occlusal splint
Published in Computer Methods in Biomechanics and Biomedical Engineering: Imaging & Visualization, 2020
Agnieszka Anna Tomaka, Leszek Luchowski, Dariusz Pojda, Krzysztof Skabek, Michał Tarnawski
The boundary can be divided into loops surrounding holes or isles and chains joining different special points (Figure 7). The orientation of the edge boundaries allows us to classify loops as either holes or isles (Algorithm 4). The sign of the dot product of the vector area of the loop and the mean normal vector of the adjacent faces classifies the loop. Seen from as the reference direction, the isle is circumscribed anticlockwise, and the hole is circumscribed clockwise (Figure 8(b,c)).
FiberNet: auto-detection of multi-fibers in microscopic image using instance segmentation
Published in The Journal of The Textile Institute, 2023
Chen et al. (2017) proposed a new scheme based on concave point matching to realize the segmentation of overlapping fibers in complex scenarios where multiple fibers stick to each other or cross. By integrating the geometric properties of the concave point, the triangular vector area approach was utilized to discover the concave point of the picture contour and assess whether the concave point matches the goal concave point. Connecting matching concave spots in a picture results in fiber segmentation.