Second Phase of the Honda Grant:

Title :: Constrained Scaling of Trimmed, Multi-Patch NURBS Surfaces

PI : Dr. Fuhua (Frank) Cheng
Co-PI : Dr. Caiming Zhang, Dr. Pifu Zhang

Goal :

To Provide the design industry with the capability of globally or locally

modifying (scaling) an existing model (such as a vehicle) in length, heigth,

or width without affecting certain significant features (trimming curves) on

the original model and, consequently, avoiding expensive re-desiogn process.

Current Achievement :

Two techniques have been developed by our research group for the second

phase. They are the attach-and-deform based approach and the fix-and-

stretch based approach. The first result was published in the ASME DTM


  "Constrained Shape Scaling of Trimmed NURBS Surfaces"
   (with P.  Zhang and C. Zhang), Proc. 1999 ASME Design
   Theory and Methodology Conference (ASME DTM-99),
   September 12-15, 1999, Las Vegas, NV.

The second result will appear in the Computer-Aided Design journal:

  "Constrained Shape Scaling of Trimmed NURBS Surfaces using
   Fix-and-Stretch Approach" (with P. Zhang and C. Zhang), to
   appear in Computer-Aided Design.

A brief description and analysis of these techniques are given below.

First technique : the attach-and-deform based approach

The new surface is formed by scaling the given (multi-patch) NURBS surface according to the scaling requirement first. The (original) features are then attached to the scaled NURBS surface at appropriate locations. Because of the difference between the curvature of the scaled surface and the original features, a deformation of the scaled surface is needed to guarantee complete attachment of the features to the scaled surface. The deformation process of the scaled surface should not change the boundary curves of the scaled surface (to avoid violating boundary condition with adjacent surfaces). It should also reflect the shape and curvature distribution of the scaled surface. This is achieved by minimizing a shape-preserving objective function which covers all the factors in the deformation process such as bending, stretching and spring effects. The resulting surface maintains a NURBS representation and, hence, is compatible with most of the current data-exchange standards. This process can be illustrated as follows :