Curvature Estimationl On triangle mesh
Updated 22 Oct 2018
If you use it for academic purposes please cite :
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
-FV -struct - Triangle mesh face vertex data structure (containing FV.face and
-toggleDerivatives - scalar 1 or 0 indicating whether or not to calculate curvature derivatives
-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
-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)
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.
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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