# The Morphing Space

Marc Alexa and Wolfgang Müller

Department of Computer Science, Interactive Graphics Systems Group

Darmstadt University of Technology, Rundeturmstr. 6, 64283 Darmstadt, Germany

{alexa|mueller}@gris.informatik.tu-darmstadt.de

## Abstract

Morphing is a well known technique to generate smooth transitions between two objects. We propose a more general understanding of morphing: First, we use morphing to describe objects as a composite of other objects. Second, we allow this description to incorporate more than two base objects. Given this concept a set of objects produced by morphing among multiple objects forms a mathematical space, which we call morphing space. We present a mathematical framework to discuss the properties of such spaces and their relation to the applied morphing algorithms for synthesizing the elements. We show that not only synthesis of objects but also analysis of objects is possible in a morphing space. Analysis results in the definition of an object in terms of the base objects of which it is comprised. Algorithms are proposed for both the synthesis and the analysis process.