📝 Abstract:
Subdivision schemes are widely used in digital geometry processing, but they are typically optimized for geometric continuity rather than spectral properties. In this thesis, we investigate the problem of optimizing existing schemes, specifically the Butterfly subdivision, to preserve the spectrum of the cotangent Laplace-Beltrami operator. We implemented and evaluated several optimization strategies, including gradient descent, full optimization, binary optimization, and brute-force methods. We compare the behavior, computational performance, and limitations of each approach. We show that while achieving consistent preservation of the spectrum remains computationally challenging, this comparative study establishes practical baselines for future research in spectral mesh processing, specifically for subdivision and processes that comes after subdivision.