Gradient‐based shell generation and deformation

Shell becomes popular in a variety of modeling techniques for representing small‐scale features and increasing visual complexity. Current shell generation algorithms do not measure the volume distortion for geometric texture mapping. And when the object deforms, it is very challenging for existing algorithms to wrap the space inside the shell without large artifacts. We propose an approach to these problems by minimizing the difference between the deformation gradient of the space in the shell and the rotation component of it. Because the shell space is warped as rigid as possible, small features embedded in the shell can be preserved well. Furthermore, our algorithm can achieve shell‐like object deformation. We introduce a novel hierarchical dimension reduction method to solve the involved nonlinear optimization problem efficiently. Finally, several examples are presented to demonstrate the usefulness of our algorithm. Copyright © 2007 John Wiley & Sons, Ltd.