Subdivision surfaces for CAD: integration through parameterization and local correction

The main roadblock that has limited the usage of subdivision surfaces in computer-aided design (CAD) systems is the lack of quality and precision that a model must achieve for being suitable in the engineering and manufacturing phases of design. The second roadblock concerns the integration into the modeling workflow, that, for engineering purposes, means providing a precise and controlled way of defining and editing models eventually composed of different geometric representations. This talk documents the experience in the context of a European project whose goal was the integration of subdivision surfaces in a CAD system. To this aim, a new CAD system paradigm with an extensible geometric kernel is introduced, where any new shape description can be integrated through the two successive steps of parameterization and evaluation, and a heterogeneous boundary representation is used to easily model different kinds of shapes. In this way, the newly introduced geometric description automatically inherits any pre-existing CAD tools, and it can interact in a natural way with the other geometric representations supported by the CAD system. To overcome the irregular behavior of subdivision surfaces in the neighborhood of extraordinary points, we locally modify the limit surface of the subdivision scheme so as to tune the analytic properties without affecting its geometric shape. Such correction is inspired by a polynomial blending approach, which generates multipatch surfaces evaluable at constant time at arbitrary parameter values. Some modeling examples will demonstrate the benefits of the proposed integration, and some tests will confirm the effectiveness of the proposed local correction method.