An algorithmic approach to manifolds is presented, based on an object approach to the parametric plotting commands. The initial purpose was to blend geometric and symbolic aspects, so as to equip computer-assisted design (CAD) with symbolic capabilities. Nevertheless, this investigation aims more generally at providing a uniform treatment of analytic geometry and field analysis, in view of applications to physics, system modeling, and morphology.

After presenting the data structure, the core of this article describes a range of operators for manipulating manifolds. It stresses their potential use in shape design and scene description, in particular their ability to supersede several graphics packages. As such, the data type constitutes the foundation of a computational morphology. Then, various extensions are discussed: fields, mesh generation for finite element software, and the prospect of extending the vector analysis package, with emphasis on tensors and differential forms.