Skip to main content
We gratefully acknowledge support from the Simons Foundation, member institutions, and all contributors. Donate
arXiv logo
Cornell University Logo

Mathematics > Algebraic Geometry

arXiv:0912.2986 (math)
[Submitted on 15 Dec 2009 (v1), last revised 18 Jan 2011 (this version, v3)]

Title:On the convex hull of a space curve

Authors:Kristian Ranestad, Bernd Sturmfels
View PDF
Abstract:The boundary of the convex hull of a compact algebraic curve in real 3-space defines a real algebraic surface. For general curves, that boundary surface is reducible, consisting of tritangent planes and a scroll of stationary bisecants. We express the degree of this surface in terms of the degree, genus and singularities of the curve. We present algorithms for computing their defining polynomials, and we exhibit a wide range of examples.
Comments: 19 pages, 4 figures, minor changes
Subjects: Algebraic Geometry (math.AG); Computational Geometry (cs.CG)
Cite as: arXiv:0912.2986 [math.AG]
  (or arXiv:0912.2986v3 [math.AG] for this version)
  https://doi.org/10.48550/arXiv.0912.2986

Submission history

From: Bernd Sturmfels [view email]
[v1] Tue, 15 Dec 2009 20:21:51 UTC (802 KB)
[v2] Mon, 8 Feb 2010 07:20:56 UTC (803 KB)
[v3] Tue, 18 Jan 2011 20:01:56 UTC (803 KB)
Full-text links:

Access Paper:

view license
Current browse context:
math.AG
< prev   |   next >
new | recent | 2009-12
Change to browse by:
cs
cs.CG
math

References & Citations

2 blog links

(what is this?)
export BibTeX citation

Bookmark

BibSonomy logo Reddit logo

Bibliographic and Citation Tools

Bibliographic Explorer (What is the Explorer?)
Connected Papers (What is Connected Papers?)
Litmaps (What is Litmaps?)
scite Smart Citations (What are Smart Citations?)

Code, Data and Media Associated with this Article

alphaXiv (What is alphaXiv?)
CatalyzeX Code Finder for Papers (What is CatalyzeX?)
DagsHub (What is DagsHub?)
Gotit.pub (What is GotitPub?)
Hugging Face (What is Huggingface?)
Papers with Code (What is Papers with Code?)
ScienceCast (What is ScienceCast?)

Demos

Replicate (What is Replicate?)
Hugging Face Spaces (What is Spaces?)
TXYZ.AI (What is TXYZ.AI?)

Recommenders and Search Tools

Influence Flower (What are Influence Flowers?)
CORE Recommender (What is CORE?)

arXivLabs: experimental projects with community collaborators

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.

Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)