Geometry processing studies how to represent, analyse, and manipulate 3D shape on digital domains such as triangle meshes and point clouds. My work focuses on the Laplace–Beltrami operator on curved surfaces: its spectrum encodes intrinsic geometry and underpins applications from shape matching to physical simulation.
A central theme is to avoid prohibitively expensive linear algebra while preserving spectral fidelity — through subspace iteration, fast approximate eigen solvers, and locally supported bases for vector and tensor fields. These tools connect classical numerical analysis with interactive graphics and engineering workflows.
Subspace methods & Laplace–Beltrami eigenproblems
Computing many eigenpairs of the Laplace–Beltrami operator on high-resolution meshes is costly. Hierarchical subspace iteration targets this bottleneck by maintaining a multi-resolution hierarchy and iterating in progressively refined subspaces, so that low-frequency modes that matter for shape analysis emerge efficiently without assembling the full spectrum at once.
Related publications
Fast spectral approximation (FastSpectrum)
For applications that need approximate eigenfunctions quickly — for example interactive design or prototyping — we developed compact schemes that trade a controlled amount of accuracy for orders-of-magnitude speedups compared with direct solves, while remaining grounded in the continuous Laplace–Beltrami problem.
Related publications
Locally supported tangential vector, n-vector, and tensor fields
Direction fields and tensor quantities on surfaces appear in remeshing, quadrangulation, and non-photorealistic rendering. We construct fields with compact support so designers can edit regions locally without global recomputation, while preserving alignment and smoothness constraints where needed.
Related publications
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