AffineTransform interpolation

[bob smith]

Is it generally possible to interpolate between two AffineTransform objects?

For instance, you may want to get the object that is midway between two AffineTransforms.

 

[Roedy Green]

For instance, you may want to get the object that is midway between two AffineTransforms.

I supposed you can create an Affine transform that uses the mean of
the parms of the two components. I think you would have to experiment.

 

[Knute Johnson]

Is it generally possible to interpolate between two AffineTransform objects?

For instance, you may want to get the object that is midway between two AffineTransforms.

It's been a long time since I've done any matrix math but I don't think
you can interpolate between transforms. Since a transform is a
multiplication does it even matter the order of transform if you do
multiples? You could rotate or translate half the distance.

I'm curious, what are you really trying to do?

 

[Jeff Higgins]

Is it generally possible to interpolate between two AffineTransform objects?

For instance, you may want to get the object that is midway between two AffineTransforms.

There was some discussion in "Linear Combination of Transformations",
Marc Alexa, 2002 available via Google Books. It was above my head
then and remains so now. David Eberly may have written some on the
subject. comp.graphics.algorithms has slowed to a crawl but some remain
to answer inquiries.

 

[Eric Sosman]

Is it generally possible to interpolate between two AffineTransform objects?

For instance, you may want to get the object that is midway between two AffineTransforms.

It's certainly possible to generate a transformation matrix
that is a weighted sum of two others:

[Mavg] = r * [Ma] + (1-r) * [Mb]

Alternatively, you could find a "geometric mean" as a matrix
whose square is the product of the two transformations:

[Mavg] * [Mavg] = [Ma] * [Mb]

(Note that the "matrix square root" is not unique. I don't know
how you'd decide which of many candidate root matrices to use, nor
how you might extend the idea to "weighted geometric means.")

Whether either of these satisfies your notion of "interpolate"
is something only you can determine.

 

[Lew]

For interpolation of transforms, the usual technique is to use quaternions.
They allow similar operations as matrix transforms, but are better-suited
to interpolation.

AFAIK, Java does not have built-in quaternion support, but it's just math.
If you can't find a third-party library for that, you can read up on it and
write your own without too much difficulty.

https://www.google.com/search?q=java+quaternion+library
seems to have some promising links.

 

[Knute Johnson]

Is it generally possible to interpolate between two AffineTransform objects?

For instance, you may want to get the object that is midway between two AffineTransforms.

Anybody remember the name of the programming language from the 70s that
had a bunch of built functions for things like matrix math? I think it
started with an A? School had a PDP 8 or 11 and it ran on that.

 

[Gene Wirchenko]

Anybody remember the name of the programming language from the 70s that
had a bunch of built functions for things like matrix math? I think it
started with an A? School had a PDP 8 or 11 and it ran on that.

BASIC?

HP 2000F BASIC had matrix functions. I only ever seriously used
it for array initialisation
MAT A=ZER
would zero array A. The matrix functions got dropped on any micro
BASICs I ever used.

Sincerely,

Gene Wirchenko

 

[Arne Vajhøj]

Anybody remember the name of the programming language from the 70s that
had a bunch of built functions for things like matrix math? I think it
started with an A? School had a PDP 8 or 11 and it ran on that.

APL?

Arne

 

[markspace]

Anybody remember the name of the programming language from the 70s that
had a bunch of built functions for things like matrix math? I think it
started with an A? School had a PDP 8 or 11 and it ran on that.

GraFORTH?

 

[Knute Johnson]

APL?

Arne

That's it Arne. It's been so long I just couldn't remember any more. I
wonder if it is still used?

 

[Arne Vajhøj]

That's it Arne. It's been so long I just couldn't remember any more. I
wonder if it is still used?

I think it is quite rare.

But it is still used.

I believe one of the more popular flavors/offspring is J:

http://www.jsoftware.com/

Arne

 

[Gene Wirchenko]

[snip]

APL was my first thought for language, but I had never heard of
it on the hardware you mentioned.

It used to be described as the ultimate write-only language. I remember
it being said that Ken Iverson wrote a GUI style text editor in 25 lines
of APL, but was unable to understand it six months later.

Yow! That makes INTERCAL and Brainfuck mere pikers.

[snip]

Sincerely,

Gene Wirchenko

 

[Arved Sandstrom]

It used to be described as the ultimate write-only language. I remember
it being said that Ken Iverson wrote a GUI style text editor in 25 lines
of APL, but was unable to understand it six months later.

... also by Iverson!

As far as J (or K for that matter) is concerned, it doesn't take but
some regular use of the language to master the symbols; the mnemonics
are pretty decent, and the extra operations created by combination with
.. and : relate quite well.

*Because* the language is so concise you typically have much less code
that you have to look at in order to figure out what's going on. Not
necessarily so with a pass of execution spread out over umpteen classes
and methods in Java or C#.

As wit any other language there is poor code written in J and good code
written in J. Good variable names, and choosing explicit or implicit
control structures as best suited, and in general not being too clever,
lead to readable and maintainable J code.

AHS