Shape-from-intrinsic operator

Shape-from-Operator: Recovering Shapes from Intrinsic Operators

We formulate the problem of shape-from-operator (SfO), recovering an embedding of a mesh from intrinsic operators defined through the discrete metric (edge lengths). Particularly interesting instances of our SfO problem include: shape-from-Laplacian, allowing to transfer style between shapes; shape-from-difference operator, used to synthesize shape analogies; and shape-from-eigenvectors, allowi...

A Dirac Operator for Extrinsic Shape Analysis

The eigenfunctions and eigenvalues of the Laplace-Beltrami operator have proven to be a powerful tool for digital geometry processing, providing a description of geometry that is essentially independent of coordinates or the choice of discretization. However, since Laplace-Beltrami is purely intrinsic it struggles to capture important phenomena such as extrinsic bending, sharp edges, and fine s...

Steklov Geometry Processing: An Extrinsic Approach to Spectral Shape Analysis

We propose Steklov geometry processing, an extrinsic approach to spectral geometry processing and shape analysis. Intrinsic approaches, usually based on the Laplace–Beltrami operator, cannot capture the spatial embedding of a shape up to rigid motion, while many previous extrinsic methods lack theoretical justi cation. Instead, we propose a systematic approach by considering the Steklov eigenva...

Shape Operator of Slant Submanifolds in Kenmotsu Space Forms

Hypersurfaces of a Sasakian space form with recurrent shape operator

Let $(M^{2n},g)$ be a real hypersurface with recurrent shapeoperator and tangent to the structure vector field $xi$ of the Sasakian space form$widetilde{M}(c)$. We show that if the shape operator $A$ of $M$ isrecurrent then it is parallel. Moreover, we show that $M$is locally a product of two constant $phi-$sectional curvaturespaces.