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Results tagged with curves-and-surfaces
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user 31310
A surface is a generalization of a plane which needs not be flat, that is, the curvature is not necessarily zero. This is analogous to a curve generalizing a straight line
6
votes
Surface in 3D that realizes all pairs of principal curvatures
I had yesterday supplied an idea for the construction of such surface as an answer to Surface analog of clothoid: curvatures covering $\mathbb{R}$,
however I doubt, whether my construction really gene …
- 13.2k
7
votes
3
answers
675
views
Examples of complicated parametric Jordan curves
For test purposes I need parametric Jordan curves that are complicated in the sense of having many inflection points and ideally no symmetries.
When doing online search I always land at complex analys …
- 13.2k
2
votes
1
answer
83
views
"Slope Analogue" of Clothoids
It is well known, that the characterizing property of Clothoids is, that their curvature is proportional to length; that is also the reason, why they are used as design elements e.g. in road design.
…
- 13.2k
4
votes
1
answer
134
views
Name for Curves from Driving on Smooth Manifolds
Is there already name for the generalization of Clothoids to curves on smooth manifolds, i.e. where the curve's curvature depends linearly on the curve's length-parameter?
In the euclidean plane Cl …
- 13.2k
1
vote
Surface analog of clothoid: curvatures covering $\mathbb{R}$
when reading about the problem, I almost immediately had the idea to define a surface via the combination of two clothoids in a similar fashion as two circles are combined to define a torus:
The firs …
- 13.2k
3
votes
What is the analog of the "Fundamental Theorem of Space Curves," for surfaces, and beyond?
The fundamental equations you look for, are known as Gauss-Codazzi equations. I'm not an expert, but the Wiki article
http://en.wikipedia.org/wiki/Gauss%E2%80%93Codazzi_equations
gives an overview
- 13.2k
1
vote
1
answer
93
views
Smoothness Conditions for Planar "Mock-parametric" Spline Interpolation
By "mock-parametric" interpolating curves I understand a class of curves that connect a discrete sequence of points with a predefined degree of smoothness and, that correspond to a non-parametric func …
- 13.2k