I am interested in theoretical and computational methods in geometry and their applications to problems in computer graphics and digital geometry processing.
My research focuses mainly on better understanding and representing shape and developing novel methods to preserve shape under large deformations.
In particular, I have published papers dealing with the following applications: interactive shape-and-image deformation, bounded distortion mappings, surface-and-volume parameterization, generalized barycentric coordinates, shape interpolation-and-animation, and computation of geodesics on manifolds. Three of my papers received the best paper award from the Eurographics Association, as well as my Ph.D. thesis. 13 papers of mine were published in ACM Transactions on Graphics which is the foremost journal in computer graphics and the top ranked journal among the 104 journals in the Computer Science: Software Engineering category.
My research heavily relies on various mathematical fields such as differential geometry and topology, complex and harmonic analysis, conformal geometry, and linear algebra. I am adapting mathematical concepts from the smooth to the discrete case, where computational methods can be applied to solve real-life problems.
A main challenge is to be able to design efficient and accurate numerical methods to solve the underlying optimization problems which are often nonconvex. My recent research efforts were to reduce such hard problems to convex or near-convex problems by applying a sophisticated change of variables or by decomposing the problem into smaller problems which are easier to solve.
In addition, I am enthusiastic about high efficiency general-purpose computations on parallel architectures, where many of my works utilize modern graphics processing units (GPU) to accelerate computations.