Firstly, based on the Cox-de Boor recursive formula, random degree NURBS curve generation algorithm is given. Then, this article discusses knot vector, the weight factor's influence on NURBS and presents the determination method of knot vector and weight factor. Secondly, NURBS curve inverse algorithm is studied and the focus is on cubic NURBS curve inverse algorithm, which is widely applied in engineering. Finally, based on C++ Builder development environment, the paper completes algorithm simulation and gives the specific application examples. Examples verify the efficiency and reliability of the algorithms, which has a high practical value in the CAD/CAM.

The advantage of the electromagnetic tomography is introduced briefly. Based on conjugate gradient algorithm, modified conjugate gradient algorithm for electromagnetic tomography (EMT) is proposed, which improves quality of reconstructed image and convergence speed efficiently. In the light of the lab electromagnetic tomography system, modified conjugate gradient for reconstructing images is verified. By evaluation of image error and the relevance, regularization, Landweber, conjugate gradient and modified conjugate gradient algorithms are compared. It can draw the conclusion that for different flow models, image error and the correlation using modified conjugate gradient algorithm is superior to the others in lab EMT system.