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If you're ready to dive into the gory details, the answer to your problem
is in the following paper presented at Siggraph 2002 :
www.igd.fhg.de/~alexa/paper/matrix.pdf
You may also want to take a look at the Siggraph course "Visualizing
Quaternions" which could contain some information you haven't incorporated
into your quaternion interpolation method. In addition it has a "gentle"
introduction to geometric algebra which is really the basis for the first
mentioned paper.
ftp://ftp.cs.indiana.edu/pub/hanson/Siggraph01QuatCourse/quatvis1.pdf
ftp://ftp.cs.indiana.edu/pub/hanson/Siggraph01QuatCourse/quatvis2.pdf
ftp://ftp.cs.indiana.edu/pub/hanson/Siggraph01QuatCourse/quatvis3.pdf
ftp://ftp.cs.indiana.edu/pub/hanson/Siggraph01QuatCourse/quatvis4.pdf
Rasmus
On Thu, 27 Feb 2003, James Coburn wrote:
> Hello,
>
> Recently, I posted a question about interpolating with B-Splines. I
> am trying to interpolate complete motions and have adapted a quaternion
> interpolation method to account for the rotations while translations are
> interpolated using hermite curves. Each of my algorithms work correctly on
> their own. Combining both translations and rotations into one
> transformation results in numbers (visualized as animations) that seem to
> follow an unlikely path.
> Ideally we are looking for the path of lowest curvature (lowest
> energy) through all points. It seems that I am not combining the rotation
> and translation interpolations correctly. One possibility is that because
> the combination brings each position relatively close to the previous
> (applied rotations and translations individually makes the object move
> approximately 5 times as far when they are applied together) errors that
> could not be seen are now in such close proximity that they are visible.
>
> Does anyone have experience interpolating complete transforms,
> especially using quaternion math?
>
> Thank you for any help
>
> -James
>
> ------------------------------------------------------------------------------------------
> Brown University Orthopedic Research
> Dept of Engineering Rhode Island Hospital
> Providence, RI Providence, RI
>
> ---------------------------------------------------------------
> To unsubscribe send SIGNOFF BIOMCH-L to LISTSERV@nic.surfnet.nl
> For information and archives: http://isb.ri.ccf.org/biomch-l
> ---------------------------------------------------------------
>
--
-----------------------------------------------------------------------------
Rasmus.Tamstorf@disney.com "A problem worthy of attack,
Walt Disney Feature Animation proves its worth by hitting back" Kumbel
-----------------------------------------------------------------------------
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is in the following paper presented at Siggraph 2002 :
www.igd.fhg.de/~alexa/paper/matrix.pdf
You may also want to take a look at the Siggraph course "Visualizing
Quaternions" which could contain some information you haven't incorporated
into your quaternion interpolation method. In addition it has a "gentle"
introduction to geometric algebra which is really the basis for the first
mentioned paper.
ftp://ftp.cs.indiana.edu/pub/hanson/Siggraph01QuatCourse/quatvis1.pdf
ftp://ftp.cs.indiana.edu/pub/hanson/Siggraph01QuatCourse/quatvis2.pdf
ftp://ftp.cs.indiana.edu/pub/hanson/Siggraph01QuatCourse/quatvis3.pdf
ftp://ftp.cs.indiana.edu/pub/hanson/Siggraph01QuatCourse/quatvis4.pdf
Rasmus
On Thu, 27 Feb 2003, James Coburn wrote:
> Hello,
>
> Recently, I posted a question about interpolating with B-Splines. I
> am trying to interpolate complete motions and have adapted a quaternion
> interpolation method to account for the rotations while translations are
> interpolated using hermite curves. Each of my algorithms work correctly on
> their own. Combining both translations and rotations into one
> transformation results in numbers (visualized as animations) that seem to
> follow an unlikely path.
> Ideally we are looking for the path of lowest curvature (lowest
> energy) through all points. It seems that I am not combining the rotation
> and translation interpolations correctly. One possibility is that because
> the combination brings each position relatively close to the previous
> (applied rotations and translations individually makes the object move
> approximately 5 times as far when they are applied together) errors that
> could not be seen are now in such close proximity that they are visible.
>
> Does anyone have experience interpolating complete transforms,
> especially using quaternion math?
>
> Thank you for any help
>
> -James
>
> ------------------------------------------------------------------------------------------
> Brown University Orthopedic Research
> Dept of Engineering Rhode Island Hospital
> Providence, RI Providence, RI
>
> ---------------------------------------------------------------
> To unsubscribe send SIGNOFF BIOMCH-L to LISTSERV@nic.surfnet.nl
> For information and archives: http://isb.ri.ccf.org/biomch-l
> ---------------------------------------------------------------
>
--
-----------------------------------------------------------------------------
Rasmus.Tamstorf@disney.com "A problem worthy of attack,
Walt Disney Feature Animation proves its worth by hitting back" Kumbel
-----------------------------------------------------------------------------
---------------------------------------------------------------
To unsubscribe send SIGNOFF BIOMCH-L to LISTSERV@nic.surfnet.nl
For information and archives: http://isb.ri.ccf.org/biomch-l
---------------------------------------------------------------