# Questions tagged [surfaces]

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### Novel Approach to Normal Estimation in Surface Reconstruction

Not sure where to post this exactly but I am hoping to find out if my approach is in any way a novel method for estimating normals in a point cloud when performing surface reconstruction (in e.g. ball-...
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### A regular, connected, compact surface with curvature on $[0,1]$

today was my final differential geometry exam and there was a problem that I partially solved, but I have some doubts. The problem asked to prove that there exists a regular, connected, compact ...
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### When does the magnitude of the gradient equal the surface area of the $dxdy$ patch?

Given a surface $S$ in $\mathbb R^3$, what is the relationship between the gradient (when $S$ is defined as a level curve of function $F: \mathbb R^3 \to \mathbb R$) and surface area? I noticed such a ...
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### Can you explain to me the relationship between those two definitions of branched covering on surfaces?

I'm studying branched (or ramified) coverings between surfaces and the definition that was given in the book I'm reading is the following: "Lets consider two closed and connected surfaces $M$ and ...
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### Classification of good foliations of a pair of pants

The following is a proposition from FLP (Thurston's work on surfaces). Proposition 6.7 (Classification of good foliations of a pair of pants) The function $\mathcal{MF}_0(P^2)\to\Bbb R^3_+$, which to ...
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### Divergence theorem with normal component of a curl to a surface

Let $\mathbf{A}$ be a vector function in $\mathbf{R}^3$ and we want to find the normal and tangent components of $\nabla \times \mathbf{A}$ on a smooth and closed surface $\Gamma$. $\mathbf{n}$ is the ...
Let S be an oriented smooth surface containing a circle of radius 1 and a straight line, which intersect perpendicularly at a point $p\in S$. Show that if the Gauss curvature K of S satisfies K(p)=0, ...