The Visual Computer (1998) 14:1±17  Springer-Verlag 1998 1 Surface subdivision for generating super- quadrics M. Eugenia Montiel * , Alberto S. Aguado * , Ed Zaluska Electronics and Computer Science, University of Southampton, Highfield, Southampton SO17 1BJ, United Kingdom E-mail: memm93r@ecs.soton.ac.uk ejz@ecs.soton.ac.uk Superquadrics have been considered as important models for part-level description in computer graphics and computer vision. The description power of these models re- sides in their parameterised nature, which allows the definition of a wide variety of shapes, yet maintains a compact character- isation. We present a subdivision technique for modelling and displaying superquad- rics. The method defines the surface of a superquadric as a deformation of an ellip- soid. The linear arc-length parameterisat- ion obtained provides a regular distribution of the parameters along the surface. Fur- thermore, the definition simplifies compu- tations in scanning by avoiding the evalua- tion of rational exponents. We exploit the geometric properties of an ellipsoid during subdivision for additional simplification. Key words: Modelling of surfaces ± Sur- face subdivision ± Parametric surfaces ± Superquadrics ± Superellipses ± Rendering techniques ± Display algorithms ± Curve tracing ± Tessellation ± Reparameterisa- tion ± Deformations 1 Introduction The representation of surfaces in computer graph- ics and computer vision has been based mainly on three types of models: geometric models, local pointwise interpolation surfaces and global param- eterised models. Geometric models such as poly- hedra, spheres, cylinders and cones have been used widely for representing simple geometric parts of many objects. The simple geometry of these models makes it easy to describe objects and render of their surfaces, but the models pro- vide a limited variety of shapes. Local pointwise interpolation surfaces are the most common mod- els in computer graphics. These representations have mainly been defined with spline curves and have provided an extensive characterisation suit- able for free form modelling. Nevertheless, the complexity of their definition, given by their ex- tensive parameterisation, does not provide a com- pact characterisation generally applicable to part- level descriptions (Pentland 1986). Global param- eterised models have been proposed as intermedi- ate representations between global geometric primitives and pointwise interpolation surfaces. The definition of these models extends the de- scription power of simple geometric shapes. This provides a much more compact characterisation than pointwise interpolation techniques. Global parameterised models have been proven adequate for representing many components of natural ob- jects, as well as parts of industrial objects and sculptured surfaces (Barr 1984; Bloomenthal 1985; Chadwick et al. 1989; Semwal and Hallauer 1994; Soroka 1981). Due to their compact charac- terisation and description capabilities, these mod- els have played an important role for part-level representation in computer vision (Hanson 1988; Kumar et al. 1995; Marr and Nishihara 1978; Pentland 1986; Solina 1994; Solina and Bajcsy 1990). Superquadrics define an important family of global parameterised models. We obtain this family by extending the parameterisation of ellipsoids to in- clude rational exponents. Although this parame- terisation has been considered useful for shape rep- resentation, it does not provide a regular distribu- tion of the parameters along the surface, resulting in a bad behaviour near the asymptotes (Franklin and Barr 1981; Löffelmann and Gröller 1995). In this paper we present a novel approach to model- ling and displaying superquadrics that avoids diffi- culties caused by nonlinear arc-length parameteri- * Present address and correspondence to: A. Aguado INRIA Rhône-Alpes, ZIRST ± 655 avenue de lEu- rope, 38300 Montbonnot Saint-Martin, France E-mail: alberto.aguado@inrialpes.fr