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The orientations of the crystals in the bicrystal as well as the reference single crystals have been chosen such that an approximate plane strain condition is achieved.
The segmentation is similar to a previous method for approximate plane segmentation for organized point clouds [25].
From this figure, it is seen that the distribution of control points are in an approximate plane.
And in the cases that the common points are distributed in a rigid or approximate plane, the sign ± in Eq. (36) is properly chosen so that det(R) = + 1 is satisfied.
The above case is the ideal one, but in the case that the common points are distributed in an approximate plane, although {d}_3ge {d}_2>{d}_1>mathbf{0}, (38 and the order of magnitude of d i for i = 1, 2, 3 differs greatly from each other.
For the Procrustes algorithm, due to utilization of the singular value decomposition technique, the computed rotation matrix always satisfies the constraint condition R T R = I 3; however, in the cases that the common points are distributed in a rigid or approximate plane, this situation that det(R) = − 1 rather than det(R) = + 1 usually happens.
Similar(51)
This simplified irradiation pattern and experimental set-up were designed to approximate plane-strain conditions and was chosen for proof of concept.
We also mention that in [66] (resp. [101]) CGO approximate solutions are concentrated near planes (resp. spheres) and provided some local results related to the local DN map.
This paper presents a procedure to find an approximate symmetry plane from a point cloud for the reverse engineering of a symmetric object.
To generate a CAD model satisfying the original aesthetic and functional design, it is essential to extract approximate symmetry planes.
Since the focus is located at the axis of the cylinder, the focal volume approximates a plane detection area at a distance of about the length of the radius [ 16].
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com