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 naturalQuote:> 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.

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

> 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.

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

A postscript version is downloadable from

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

Best regards,

andreas

> > 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

> A postscript version is downloadable from

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

> Best regards,

> andreas

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

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