# Re: Discrete Curvature and Torsion for 3D-poly line

"Nodame Han" <tmeister@xxxxxxxxx> wrote in message <fu5pd4\$2b1
\$1@xxxxxxxxxxxxxxxxxx>...
Hi, I'm trying to calculate torsion and curvature of a 3D-
Curve, and then I'll compare different curves with each
other by using them.
Actually, it is composed of 3D-poly Lines connected to each
other by 3-d points (x,y,z). So, I don't think it's
necessary to calculate spline or interpolation (because
every curve is composed by same way).
It would be possible to get the profiles of torsion and
curvature by calculating kind of discrete version of them
at the turning points.

But I don't know how to...
Is there any good methods or reference?

Thanks.
-----------
As I see your problem, it will take a minimum of three neighboring points to
determine an approximate osculating plane, an approximate curvature
therein, and the binormal direction to it. At least one more point would be
required to determine the rate of change of this binormal to get an
approximate torsion. You will therefore need to estimate your curvature and
torsion using neighborhoods of at least four points and preferably many
more.

My octogenarian memory of the old differential geometry days is pretty hazy
by now, however. It would be better if you could find this problem already
worked out somewhere on the internet. Otherwise, I would have to put the
little grey cells through an awful lot of work.

Roger Stafford

.

## Relevant Pages

• Re: Discrete Curvature and Torsion for 3D-poly line
... appreciable amount of noise or inaccuracy. ... deteriorate again since it may cover too large a scope of curve variation. ... curvature and torsion in their exact form require differentiation with respect ...
(comp.soft-sys.matlab)
• Re: curvature and torsion on surfaces
... I think curvature and torsion ... In general, to find curvature and torsion, the best thing to do is ... which is the vector product of tangent times n, the normal, ie the unit ... An example of the former is curve of Viviani drawn on a sphere surface ...
(sci.math)
• Re: curvature and torsion on surfaces
... curvature or mean curvature. ... In general, to find curvature and torsion, the best thing to do is ... parametrise the curve by arc lengths. ... It is a curve with a single parameter "v". ...
(sci.math)
• Discrete Curvature and Torsion for 3D-poly line
... I'm trying to calculate torsion and curvature of a 3D- ... Curve, and then I'll compare different curves with each ...
(comp.soft-sys.matlab)
• Re: Fast maximum curvature calculation for a 3d bezier curve
... Its a cubic curve. ... Sometimes people use the term "curvature" to mean ... About the subdivision of the cubic curve using a test ...
(comp.graphics.algorithms)