Volume Parameterization for Design Automation of Customized Free-Form Products

This paper addresses the problem of volume parameterization that serves as the geometric kernel for design automation of customized free-form products. The purpose of volume parameterization is to establish a mapping between the spaces that are near to two reference free-form models, so that the shape of a product presented in free-form surfaces can be transferred from the space around one reference model to another reference model. The mapping is expected to keep the spatial relationship between the product model and reference models as much as possible. We separate the mapping into rigid body transformation and elastic warping. The rigid body transformation is determined by anchor points defined on the reference models using a least-squares fitting approach. The elastic warping function is more difficult to obtain, especially when the meshes of the reference objects are inconsistent. A three-stage approach is conducted. First, a coarse-level warping function is computed based on the anchor points. In the second phase, the topology consistency is maintained through a surface fitting process. Finally, the mapping of volume parameterization is established on the surface fitting result. Compared to previous methods, the approach presented here is more efficient. Also, benefitting from the separation of rigid body transformation and elastic warping, the transient shape of a transferred product does not give unexpected distortion. At the end of this paper, various industry applications of our approach in design automation are demonstrated. Note to Practitioners-The motivation of this research is to develop a geometric solution for the design automation of customized free-form objects, which can greatly improve the efficiency of design processes in various industries involving customized products (e.g., garment design, toy design, jewel design, shoe design, and glasses design, etc.). The products in the above industries are usually composed of a very complex geometry shape (represented by free-form surfaces), and is not driven by a parameter table but a reference object with free-form shapes (e.g., mannequin, toy, wrist, foot, and head models). After carefully designing a product around one particular reference model, it is desirable to have an automated tool for "grading" this product to other shape-changed reference objects while retaining the original spatial relationship between the product and reference models. This is called the design automation of a customized free-form object. Current commercial 3-D/2-D computer-aided design (CAD) systems, developed for the design automation of models with regular shape, cannot support the design automation in this manner. The approach in this paper develops efficient techniques for constraining and reconstructing a product represented by free-form surfaces around reference objects with different shapes, so that this design automation problem can be fundamentally solved. Although the approach has not been integrated into commercial CAD systems, the results based on our preliminary implementation are encouraging-the spatial relationship between reference models and the customized products is well preserved