Sentence examples for perpendicular vector from inspiring English sources
The three mutually perpendicular vector dipoles can be represented as the superposition of three mutually perpendicular tensile cracks (S4, Figure 1d).
An isotropic source is defined as three mutually perpendicular vector dipoles (S3, Figure 1c), of which the moment tensor is given as M = M 0 Iso 1 0 0 0 1 0 0 0 1, (7).
(a) A spherical source (S1), (b) a spherical crack source (S2), (c) an isotropic source (three mutually perpendicular vector dipoles) (S3), (d) an isotropic source (three mutually perpendicular tensile cracks) (S4), (e) an Eshelby spherical source with stress-free strain (S5), and (f) an Eshelby spherical source with strain-free stress (S6).
(a) A spherical source with purely outward radial expansion of Δs (S1), (b) a spherical crack source with outward and inward displacements (Δs and ds, respectively) along the spherical surface (S2), (c) an isotropic source with three mutually perpendicular vector dipoles (S3), and (d) a superposition of three mutually perpendicular tensile cracks (S4).
These representations include a spherical source with outward radial expansion (S1), a spherical crack source with outward and inward crack wall motions along the spherical surface (S2), an isotropic source represented by three mutually perpendicular vector dipoles (S3) or three mutually perpendicular tensile cracks (S4), and a spherical source undergoing a transformational expansion (S5).
From the cross product between the perpendicular vector of the hand plane and the perpendicular vector of the table plane, the spatial angle of the hand is estimated.
Such advanced features include normals (perpendicular vectors) as well as triangle-based and quadrangle-based geometric shapes.
Therefore, Apollonius' problem can be re-stated in Lie geometry as a problem of finding perpendicular vectors on the Lie quadric; specifically, the goal is to identify solution vectors Xsol that belong to the Lie quadric and are also orthogonal (perpendicular) to the vectors X1, X2 and X3 corresponding to the given circles.
: \left( X_{\mathrm{sol}}| X_{\mathrm{sol}} \right) = \left( X_{\mathrm{sol}}| X_{1} \right) = \left( X_{\mathrm{sol}}| X_{2} \right) = \left( X_{\mathrm{sol}}| X_{3} \right) = 0 The advantage of this re-statement is that one can exploit theorems from linear algebra on the maximum number of linearly independent, simultaneously perpendicular vectors.
Principal components analysis (PCA) was performed to identify the best linear fit to the data using a series of perpendicular vectors or principal components (PCs) [ 31].
In order to achieve real-time performance, we have proposed an optimization step which consists of forming plane clusters, based on the angle between their perpendicular vectors, and counting the inliers only for the planes that belong to the largest cluster.
