IJPAM: Volume 11, No. 1 (2004)

AN INTRODUCTION TO AN ANALYTICAL
WAY TO COMPUTE THE VOLUME OF BLOBS

Dominique Faudot$^1$, Gilles Gesquière$^2$, Lionel Garnier$^3$
$^{1,2,3}$LE2I, Informatique
Université de Bourgogne
BP 47870, 21078 Dijon Cedex, FRANCE
$^1$e-mail: faudot@u-bourgogne.fr
$^2$e-mail: gesquiere@u-bourgogne.fr
$^3$e-mail: garnier@u-bourgogne.fr


Abstract.Using implicit surfaces is of interest in the field of interactive modelling. A first interest lies in automatic changes of topology. Volumic representation of objects is another interest. However, modelling non-compressible material with implicit surfaces remains difficult. The volume of implicit objects changes with the position of their centres. We can compute volume using numerical method, but these kinds of methods bring a quick but inaccurate result. In this paper, we propose an analytical method to obtain exact results. We present this method for two blobs. Afterward, we prove we can extend this method to several blobs.

Received: March 3, 2003

AMS Subject Classification: 28A75, 51M25

Key Words and Phrases: implicit surface, volume computation, analytical method

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2004
Volume: 11
Issue: 1