Subdivision surfaces integrated in a CAD system

• Perfect integration of subdivision surfaces in a CAD system.
• Interoperability of subdivision surfaces with other representations.
• B-rep representation of a subdivision solid and of hybrid NURBS/subdivision objects.
• Local correction of critical curvature and parameterization behavior.

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 workflows, that, for engineering purposes, means providing a precise and controlled way of defining and editing models possibly composed of different geometric representations. This paper 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 hybrid 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 a correction is inspired by the polynomial blending approach in Levin (2006) [1] and Zorin (2006)  [2], which we extend in some aspects and generalize to multipatch surfaces evaluable 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 patching method.