Geometric modeling without coordinates and indices (extended abstract)

Abstract

Summary form only given. We focus on dynamic geometric objects, which can be seen to develop over time. Examples include fractals, subdivision curves and surfaces, and models of growing biological structures. Coordinates and indices do not identify elements of these objects in a convenient, time-invariant way. For instance, the coordinates of a cell in a growing biological tissue may change over time, even though it materially is the same cell. Furthermore, if the cells are indexed, the indices may have to be updated following cell division in order to preserve consecutive numbering of the adjacent cells. Similarly, in the case of subdivision curves and surfaces, the existing points may change position over time, while the insertion of new points may require all points to be reindexed.