## Curvature Estimationl On triangle mesh

version 1.2.1.0 (8.87 KB) by
Computes curvature and curvature derivative tensors in each vertex of a triangle meshes

Updated 22 Oct 2018

1. "Estimating Curvatures and Their Derivatives on Triangle Meshes" by Szymon Rusinkiewicz (2004)
2. Y. Ben Shabat, A. Fischer, "Design of Adaptive Porous Micro-structures using curvature analysis for Additive Manufacturing" the 25th CIRP Design conference. 2015, Haifa, Israel.
This code was implemented according to .

GetCurvatures computes the curvature tensor and the principal curvatures at
%each vertex of a mesh given in a face vertex data structure
%INPUT:
-FV -struct - Triangle mesh face vertex data structure (containing FV.face and
FV.Vertices)
-toggleDerivatives - scalar 1 or 0 indicating whether or not to calculate curvature derivatives
%OUTPUT:
-PrincipalCurvatures - 2XN matrix (where N is the number of vertices containing the principal curvatures k1 and k2 at each vertex
-PrincipalDir1 - NX3 matrix containing the direction of the k1 principal
curvature.
-PrincipalDir2 - NX3 matrix containing the direction of the k2 principal curvature.
-FaceCMatrix - 4XM matrix (where M is the number of faces) containing the 4
%coefficients of the curvature tensr of each face
VertexCMatrix- 4XN matrix (where M is the number of faces) containing the 4 coefficients of the curvature tensor of each tensor.
-Cmagnitude - NX1 matrix containing the square sum of the curvature tensor coefficients at each vertex (invariant scalar indicating the change of curvature)

### Cite As

Rusinkiewicz, S. “Estimating Curvatures and Their Derivatives on Triangle Meshes.” Proceedings. 2nd International Symposium on 3D Data Processing, Visualization and Transmission, 2004. 3DPVT 2004., IEEE, doi:10.1109/tdpvt.2004.1335277.

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Shabat, Yizhak Ben, and Anath Fischer. “Design of Porous Micro-Structures Using Curvature Analysis for Additive-Manufacturing.” Procedia CIRP, vol. 36, Elsevier BV, 2015, pp. 279–84, doi:10.1016/j.procir.2015.01.057.

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##### MATLAB Release Compatibility
Created with R2012b
Compatible with any release
##### Platform Compatibility
Windows macOS Linux