Nicholas Sharp @nmwsharp.bsky.social · Jul 2 Logarithmic maps are incredibly useful for algorithms on surfaces--they're local 2D coordinates centered at a given source. Yousuf Soliman and I found a better way to compute log maps w/ fast short-time heat flow in "The Affine Heat Method" presented @ SGP2025 today! 🧵
68 likes 2 replies
Replies
Nice work. One thing I was wondering on first reading, for the adaptive method what makes the diffused frame field special as opposed to any smooth frame field? What happens when you run it on just an arbitrary smooth frame field?
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.