Shape Operator
A linear operator in differential geometry defined on the tangent plane of a surface that describes the rate of change of the normal vector along tangential directions; its eigenvalues are the principal curvatures, its trace corresponds to mean curvature and its determinant to Gaussian curvature, characterizing surface bending.
Timeline (last 90 days)
The key innovation of the NIEO method is to regularize the SDF with a shape operator energy functional defined on the SDF level set.
The eigenvalues of the shape operator are the principal curvatures, its trace corresponds to mean curvature, and its determinant corresponds to Gaussian curvature.
In the SDF framework, the shape operator can be computed analytically from the Hessian and gradient of the SDF.
All Facts (3)
The key innovation of the NIEO method is to regularize the SDF with a shape operator energy functional defined on the SDF level set.
50%UnverifiedThe eigenvalues of the shape operator are the principal curvatures, its trace corresponds to mean curvature, and its determinant corresponds to Gaussian curvature.
50%UnverifiedIn the SDF framework, the shape operator can be computed analytically from the Hessian and gradient of the SDF.
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