Interactive Implicit Modelling Based on C1 Continuous Reconstruction of Regular Grids

Our goal is to provide a kernel to allow interactive and accurate modelling of volume objects. As a first step, we present a data structure for three-dimensional fields C continuous in the modelling space. Regular grids storing the field values discretely are combined with a triquadratic approximation filter to define volume objects. This association of a grid and an approximation/interpolation reconstruction allows the field to be defined by a C continuous real function and the surface to be directly visualised from its own equation. We show how accurate and high quality interactive visualisation is obtained during the modelling process, and we explain why the visualisation is faithful to the object definition. We also describe, as an example application of our data structure, how advanced Boolean operators realised with soft or free-form transitions are performed under the influence of an interactive modelling tool.