Summary

Read the paper. The shape difference operator is decided by the map between the two manifolds, the inner product spaces on the two manifolds. And the shape difference operator can be written as a matrix if we can find a basis of the inner product space.

Analysis

The theory of my project is clear. The most difficult part is to compute the basis of the inner product space and compute the difference matrix under some typical basis. I'm working on the implementing part of the method. After that, I can apply the shape difference analysis on k-Curve. The implementing of k-Curve is done.

Plan for completion

Continue on the implementing of functional map and shape difference operator. Then apply it on k-Curve. If the result is not good, I need to slightly modify the method to apply on the weight of rational polynomial curve.

References

[1] Yan, Z., Schiller, S., Wilensky, G., Carr, N. and Schaefer, S., 2017. k-curves: interpolation at local maximum curvature. ACM Transactions on Graphics (TOG), 36(4), p.129.

[2] Ovsjanikov, M., Ben-Chen, M., Solomon, J., Butscher, A. and Guibas, L., 2012. Functional maps: a flexible representation of maps between shapes. ACM Transactions on Graphics (TOG), 31(4), p.30.

[3] Rustamov, R.M., Ovsjanikov, M., Azencot, O., Ben-Chen, M., Chazal, F. and Guibas, L., 2013. Map-based exploration of intrinsic shape differences and variability. ACM Transactions on Graphics (TOG), 32(4), p.72.