Excited to announce: In 2027 I'll join the UW Allen School (@UWCSE) in Seattle as tenure-track faculty in Computer Science! My group will advance core geometry processing + 3D AI for visual computing, science, & engineering. I'll be recruiting PhD students in the next cycle!

Tomorrow I'll speak at the FPTalks series on floating point and numerical analysis, about robust geometry for neural implicit surfaces (work w/ @_AlecJacobson). The other talks sound amazing, and I love this area! Check out this great organization. fptalks.org/talks/fptalks26.…

Have you dug deep into an evolving area of visual computing? Consider submitting to the 2027 EG STARs track! STARs are survey reports providing insight into the current state of the art and future directions. They're impactful and highly-cited! eg2027.isti.cnr.it/call-for-…

We give two variants of the algorithm, and show use cases for many problems like averaging values on surfaces, decaling, and stroke-aligned parameterization. It even works on point clouds!

Instead of the usual VxV scalar Laplacian, or a 2Vx2V vector Laplacian, we build a 3Vx3V homogenous "affine" Laplacian! This Laplacian allows new algorithms for simpler and more accurate computation of the logarithmic map, since it captures rotation and translation at once.

Previously in "The Vector Heat Method", we computed log maps with short-time heat flow, via a vector-valued Laplace matrix rotating between adjacent vertex tangent spaces. The big new idea is to rotate **and translate** vectors, by working homogenous coordinates.

Logarithmic maps are incredibly useful for algorithms on surfaces--they're local 2D coordinates centered at a given source. @yousufmsoliman and I found a better way to compute log maps w/ fast short-time heat flow in "The Affine Heat Method" presented @ SGP2025 today! 🧵

Huge shout out to the Bellairs Institute Workshop on Computer Animation, where this project began as a workshop collaboration! (12/12) - project: research.nvidia.com/labs/tor… - paper: nmwsharp.com/media/papers/ne… - code: github.com/nmwsharp/neural-p…

We even show a preliminary application as a data generator: if you have a _supervised_ physics learning setup, but no data, you can fit our subspace and use it to sample training data. (10/N)

Importantly, our low-dim subspace maps are a true 'dense' parameterization: every point in the subspace corresponds to a significant configuration. This makes many downstream tasks easy: for instance you can keyframe animate complex systems via a spline in the subspace! (9/N)

This formulation works out-of-the-box for systems far from the usual deformable bodies. Here, we model a rigid body kinematic mechanism with pin penalties at joints, parameterized by the entries of a transformation matrix. Subspace training finds the smooth motion! (8/N)