[tGarden-dev] Turk + O'Brien: hape Transformation Using Variational Implicit Functions

[Sha X. W. <xi...@mi...>]

For the record,

This work by colleagues here in GVU may be interesting for some 
pattern deformations in sound+image.  They recycled old calc of 
variations, etc.  reminded my of Morse theory, Pontrjagin
(http://www.math.harvard.edu/~elkies/M55b.99/pontrjagin.html) may be 
a source of music beh i don't know, ask yon or joel

anyway, turk & obrien's notion of influence shapes is quite 
suggestive.   i'd like to think of thrid player as an influence shape 
on mappings between two other players.... in some sense.

http://www.gvu.gatech.edu/people/faculty/greg.turk/morph/morph.html

Shape Transformation Using Variational Implicit Functions

       Greg Turk and James F. O'Brien
       Georgia Institute of Technology
       (To appear in SIGGRAPH 99)

Abstract

Traditionally, shape transformation using implicit functions is 
performed in two
distinct steps: 1) creating two implicit functions, and 2) 
interpolating between
these two functions. We present a new shape transformation method that
combines these two tasks into a single step. We create a transformation between
two N-dimensional objects by casting this as a scattered data interpolation
problem in N+1 dimensions. For the case of 2D shapes, we place all of our data
constraints within two planes, one for each shape. These planes are 
placed parallel
to one another in 3D. Zero-valued constraints specify the locations of shape
boundaries and positive-valued constraints are placed along the 
normal direction
in towards the center of the shape. We then invoke a variational interpolation
technique (the 3D generalization of thin-plate interpolation), and 
this yields a
single implicit function in 3D. Intermediate shapes are simply the zero-valued
contours of 2D slices through this 3D function. Shape transformation between 3D
shapes can be performed similarly by solving a 4D interpolation problem. To our
knowledge, ours is the first shape transformation method to unify the tasks of
implicit function creation and interpolation. The transformations 
produced by this
method appear smooth and natural, even between objects of differing topologies.
If desired, one or more additional shapes may be introduced that influence the
intermediate shapes in a sequence. Our method can also reconstruct 
surfaces from
multiple slices that are not restricted to being parallel to one another.


Don't get me wrong, I'm less interested in purely visual stuff, more 
on integrated pattern transformations.

Cheers,
Xin Wei