Few Points About Project
The problem of morphing between two images is a very well addressed
problem in the graphics community. In last few years effort was also imparted
to extend the concept of 2D-image morphing in metamorphosis of 3D solids.
There are two distinct steps in morphing. The first one is the warping
of geometry and the second one is blending. Obtaining a quick and proper
warp of geometry is a major challenge for a good morphing. In this present
work an attempt has been made to use the implicit representation of geometry
to generate a warp. In recent years the research in the field of implicit
representation has got a momentum with the increase in popularity of R
function.
Here attempts have been made in two distinctly different ways to use
implicit representation for metamorphosis. These are described under following
headings.
-
Interpolation based.
-
Physical based.
What is an implicit representation?
-
Described by an algebraic function like f(x,y,z), where the zero of this
function describes the geometry.
-
With R-function implicit representation of all most any geometry can be
obtained.
Why implicit function?
-
Gives special type of metamorphosis. Which may be interesting.
-
Easy to do interpolation.
-
Easy to do morphing with physics.
Interpolation based:
If F(x,y) = 0 define initial geometry and G(x,y)=0 defines the final
one. The intermediate geometry is defined by
R(x,y) = t*F(x,y) + (x-t)*G(x,y)=0; where t is defined in the domain
[0,x]
-
Does not give desired result if one geometry does not totally overlap the
other.
-
This shortcoming is taken care of by properly scaling one function before
interpolation and then again applying reverse scaling to the result of
the interpolation.
-
Generation of disconnected domain near very thin section is a major drawback
of this method.
Physical based:
-
Use equation of a physical phenomenon to do metamorphosis.
-
In present work Laplace’s heat equation has been used.
-
The target or the source function is scaled in such a way so that the geometry
defined by one function is totally inside other. Heat equation is applied
to the annulus domain defined by these two functions.
-
Different but constant temperature is defined on the outer and the inner
boundary of the annulus domain.
-
This boundary value problem is solved with the specified temperature condition.
-
Inverse scaling is applied to the iso-thermal curves in the domain to obtain
the intermediate geometry.