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principal curvature

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At an umbilic all the sectional curvatures are equal; in particular the principal curvatures are equal.
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At flat umbilic points both principal curvatures are zero.
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Together with the first fundamental form, it serves to define extrinsic invariants of the surface, its principal curvatures.
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At parabolic points, one of the principal curvatures is zero.
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When a line of curvature has a local extremum of the same principal curvature then the curve has a ridge point.
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The mean curvature is an extrinsic measure of curvature equal to half the sum of the principal curvatures, k1 + k2/2.
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For most points on most surfaces, different sections will have different curvatures; the maximum and minimum values of these are called the principal curvatures.
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The mean curvature is the average of the two principal curvatures, which is constant because the two principal curvatures are constant at all points of the sphere.
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The Mean curvature is the average of the two principal curvatures. Steps:
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Gaussian curvature is the product of the two principal curvatures.
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Gaussian curvature The Gaussian curvature of a surface at a point is the product of the principal curvatures at that point.
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Configurations of lines of curvature near umbilics Lemon Monstar Star In these figures, the red curves are the lines of curvature for one family of principal directions, and the blue curves for the other.
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For most points on most surfaces, different sections will have different curvatures; the maximum and minimum values of these are called the principal curvatures .
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The lines of curvature or curvature lines are curves which are always tangent to a principal direction (they are integral curves for the principal direction fields).
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The mean curvature is the average of the two principal curvatures, which is constant because the two principal curvatures are constant at all points of the sphere. The sphere has constant mean curvature.
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If the principal bundle P is the frame bundle, or (more generally) if it has a solder form, then the connection is an example of an affine connection, and the curvature is not the only invariant, since the additional structure of the solder form θ, which is an equivariant Rn-valued 1-form on P, should be taken into account.
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The eigenvectors show the principal directions of the surface, including the directions of greatest and smallest curvature.
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This formula represents the equilibrium of forces, where n1 and n2 are the principal forces, 1/R1 and 1/R2 are curvatures in the directions of those forces and p is the external load if defined in the form-finding process.
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18 sinne gevind in 6 ms. Hulle kom uit baie bronne en word nie nagegaan nie.