# Tagged Questions

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**1**answer

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### Characterization of the medial axis of a surface

I would like to know if the following "characterization" of the medial axis of a surface is correct, and if so, how to prove it.
Let $S$ be a continuous, piecewise smooth, compact surface embedded in ...

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**1**answer

187 views

### Request for some references exploring the connections of Riemann surfaces with medical imaging

I'd like to know some references for a beginner who has basic background in Riemann surfaces and differential geometry, and would like to start learning/working on more applied areas, medical ...

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**1**answer

116 views

### Existence of Simple Closed Straightest Geodesics

There are at least three distinct simple closed quasigeodesics on convex polyhedra [Mat. Sb. (N.S.), 1949, 25(67) :2, 275–306 Quasi-geodesic lines on a convex surface Pogorelov].
Is the same true ...

**3**

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**1**answer

395 views

### Combinatorial geodesics

[There has been a flaw in my definition - as Sergei and Andreas pointed out. I hope I could fix it.]
I want to understand how the concepts of directions, straight (or shortest) lines, and geodesics ...

**6**

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**3**answers

337 views

### Herringbone partitions of regions and surfaces

Let $R \subset \mathbb{R}^2$ be a region of the plane bounded
by a Jordan curve. The boundary $\partial R$ could be a polygon,
or a smooth curve—there are variations depending upon boundary ...

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**2**answers

597 views

### Is there always a parallelogram cross-section of parallelepiped contained in the smallest box

Let $M$ be a centered parallelepiped, the intersection of $M$ and any plane $P$ that passes through the origin is a parallelogram or hexagon. Each parallelogram or hexagon has a cubic box that is the ...

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**2**answers

226 views

### Finding the Boundary Faces of the Zonohedron

A zonotope is a linear combination of m vectors with coefficients in [0,1]: $Z = \{ \sum \lambda_i v_i : 0 \leq \lambda _i \leq 1 \}$. The fancy way is to say it's the Minkowski sum of line segments ...