Computational Assessment of Curvatures and Principal Directions of Implicit Surfaces from 3D Scalar Data

@inproceedings{Albin2016ComputationalAO,
  title={Computational Assessment of Curvatures and Principal Directions of Implicit Surfaces from 3D Scalar Data},
  author={Eric Albin and Ronnie Knikker and Shihe Xin and Christian Oliver Paschereit and Yves D’Angelo},
  booktitle={MMCS},
  year={2016}
}
An implicit method based on high-order differentiation to determine the mean, Gaussian and principal curvatures of implicit surfaces from a three-dimensional scalar field is presented and assessed. The method also determines normal vectors and principal directions. Compared to explicit methods, the implicit approach shows robustness and improved accuracy to measure curvatures of implicit surfaces. This is evaluated on simple cases where curvature is known in closed-form. The method is applied… 

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References

SHOWING 1-10 OF 40 REFERENCES

Estimating Gaussian curvatures from 3D meshes

TLDR
The proposed approach can handle vertices with the zero Gaussian curvature uniformly without localizing them as a separate process and the performance is further improved with the local Bezier curve approximation and subdivision.

Estimating Curvature on Triangular Meshes

TLDR
This paper has developed a suite of test cases for assessing both the detailed behavior of these methods, and the error statistics that occur for samples from a general mesh, and provides guidance in choosing an appropriate method for applications requiring curvature estimates.

Estimating the principal curvatures and the darboux frame from real 3-D range data

TLDR
It is shown that with current scanning technology and the algorithms presented here, reliable estimates of the principal curvatures and Darboux frame can be extracted from real data and used in a large variety of tasks.

A comparison of local surface geometry estimation methods

TLDR
The nonlinear quadric fitting method considered was found to perform the best but has the greatest computational cost while the facet based approach works as well as the other quadricfitting methods and has a much smaller computational cost.

Discrete Differential-Geometry Operators for Triangulated 2-Manifolds

TLDR
A unified and consistent set of flexible tools to approximate important geometric attributes, including normal vectors and curvatures on arbitrary triangle meshes, using averaging Voronoi cells and the mixed Finite-Element/Finite-Volume method is proposed.

A Level Set Formulation of Eulerian Interface Capturing Methods for Incompressible Fluid Flows

TLDR
Eulerian finite difference methods based on a level set formulation derived for incompressible, immiscible Navier?Stokes equations are proposed and are capable of computing interface singularities such as merging and reconnection.

A continuum method for modeling surface tension

Curvature formulas for implicit curves and surfaces