## contour interpolation question

### contour interpolation question

I have two pieces of cross section,each cross section is consist of 2
dimensional points ,but the numbers of the two cross section is different,I
want to find a smooth interpolation between these two cross section, can
anybody give somen inspiration? thanks!
I have find some reference concering Shape Interpolation,Shape Morphing and
so on,but to my understand these reference all deal with the problem that
the cross section have same point number,maybe i did not understand tyhese
reference correctly.

### contour interpolation question

Quote:> I have two pieces of cross section,each cross section is consist of 2
> dimensional points ,but the numbers of the two cross section is
different,I
> want to find a smooth interpolation between these two cross section, can
> anybody give somen inspiration? thanks!
> I have find some reference concering Shape Interpolation,Shape Morphing
and
> so on,but to my understand these reference all deal with the problem that
> the cross section have same point number,maybe i did not understand tyhese
> reference correctly.

Interpolate each set of points with a curve, perhaps natural
cubic splines will do.  Once you have curve representations,
the algorithm I have successfully used for a natural interpolation
between two curves is contained in the document
http://www.magic-software.com/Documentation/MedialBasedMorphing.pdf
The idea is to have a one-to-one correspondence between
curve points by using "normalized arc length" p in [0,1] for
each curve (p = s/L where L is the total curve length and s
is the arc length parameter).  Once you have this, you can
average the curvatures of the curve, then integrate this to
obtain the interpolated curve.  An example I use to show the
power of this method is to take two spirals, wound in opposite
directions.  The interpolated curves show one spiral unwinding
to a line segment, then winding itself into the form of the other.

--
Dave Eberly

http://www.magic-software.com
http://www.wild-magic.com

### contour interpolation question

> I have two pieces of cross section,each cross section is consist of 2
> dimensional points ,but the numbers of the two cross section is different,I
> want to find a smooth interpolation between these two cross section, can
> anybody give somen inspiration? thanks!
> I have find some reference concering Shape Interpolation,Shape Morphing and
> so on,but to my understand these reference all deal with the problem that
> the cross section have same point number,maybe i did not understand tyhese
> reference correctly.

Hello,

You might take a look at: G. Barequet and M. Sharir, Piecewise-linear interpolation
between polygonal slices,  Computer Vision and Image Understanding
(CVIU), vol. 63 (2), pp. 251-272, March 1996

http://www.cs.technion.ac.il/~barequet/papers.html

Best regards,

andreas

### contour interpolation question

> > I have two pieces of cross section,each cross section is consist of 2
> > dimensional points ,but the numbers of the two cross section is different,I
> > want to find a smooth interpolation between these two cross section, can
> > anybody give somen inspiration? thanks!
> > I have find some reference concering Shape Interpolation,Shape Morphing and
> > so on,but to my understand these reference all deal with the problem that
> > the cross section have same point number,maybe i did not understand tyhese
> > reference correctly.
> Hello,

> You might take a look at: G. Barequet and M. Sharir, Piecewise-linear   interpolation
> between polygonal slices,  Computer Vision and Image Understanding
> (CVIU), vol. 63 (2), pp. 251-272, March 1996
> http://www.cs.technion.ac.il/~barequet/papers.html

> Best regards,
> andreas

The interpolation of polylines or closed contours is fairly simple by
Fourier Series.
Noisy data can be smoothed by ignoring higher harmonics.
Different numbers of samples are handled easily.
Tutorial on demand.

Best regards --Gernot Hoffmann