# Three Dimensional Distance Field Metamorphosis

## Daniel Cohen-Or, David Levin and Amira Solomovici

School of Mathematical Sciences, Tel-Aviv University, Ramat-Aviv 69978, Israel

# Abstract

Given two or more objects of general topology,
intermediate objects are constructed by a distance field
metamorphosis. In the presented method the interpolation
of the distance field is guided by a warp function which is
controlled by a set of corresponding anchor points.
Some rules for defining a smooth least-distorting warp function
are given. To reduce the distortion of the intermediate shapes,
the warp function is decomposed into a rigid rotational
part and an elastic part. The distance field
interpolation method is modified so that the interpolation is
done in correlation with the warp function.

The method provides the animator with a technique, which can be used
to create a set of models forming a smooth transition between pairs of
a given sequence of general keyframe models.
The advantage of the new approach is that it is capable of morphing between
objects having a different topological genus, with
most general object representations, and where no correspondence between the
geometric primitives of the models need be established.
The desired general correspondence is defined by an animator
in terms of a relatively small number of anchor points.

## Animations (in MPEG format)

__Address:__ Dept. of Computer
Science, School of Mathematical Sciences,

Tel-Aviv University,
Tel-Aviv 69978, Israel.

Phone: +972-3-640-7598

Fax: +972-3-640-9357

E-mail: {daniel | levin | amira}@math.tau.ac.il