| 词汇 | principal-curvature |
| 释义 | BETA principal curvaturecollocation in Englishmeanings of principaland curvatureThese words are often used together. Click on the links below to explore the meanings. principal noun uk /ˈprɪn.sə.pəl/ us /ˈprɪn.sə.pəl/ US the person in charge of ... See more at principal curvature noun[ U or C ] uk /ˈkɜː.və.tʃər/ us /ˈkɝː.və.tʃɚ/ the state of being curved ... See more at curvature Examples of principal curvatureprincipal curvature The direction of the bisector of the straight lines indicates the zero principalcurvature direction. The transformation can be viewed as locally rotating the principalcurvature directions. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. If one bends a slice horizontally along a radius, non-zero principal curvatures are created along the bend, dictating that the other principalcurvature at these points must be zero. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. Points where the principal curvatures have the same sign, like a small fragment of an eggshell, are called synclastic points. As only the first step of this algorithm is used which is to calculate the principalcurvature images, the principal curvature is adopted as the name of this detector. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. This figure implies a monoclastic geometry for the folded surface, that is, the case where one of the principal curvatures equals zero and ratio of the principal curvatures is infinite. Although the curvature properties of all points on all surfaces obey equation (1), three classes of points can be distinguished on the basis of the signs of the principal curvatures. Mathematically, these two curvatures are called the principal curvatures, c1 and c2, and their meaning can be understood by the following thought experiment. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. The eigenvalues of the second fundamental form, represented in an orthonormal basis, are the principal curvatures of the surface. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. At such points the normal curvature in all directions are equal, hence, both principal curvatures are equal, and every tangent vector is a "principal direction". From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. Actually, any isoparametric submanifold is foliated by the holonomy tubes of a submanifold with constant principal curvatures i.e. a focal submanifold. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. The eigenvalues correspond to the principal curvatures of the surface and the eigenvectors are the corresponding principal directions. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. Together with the first fundamental form, it serves to define extrinsic invariants of the surface, its principal curvatures. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. The principal curvatures are the invariants of the pair consisting of the second and first fundamental forms. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. These examples are from corpora and from sources on the web. Any opinions in the examples do not represent the opinion of the Cambridge Dictionary editors or of Cambridge University Press or its licensors. |
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