Neural networks based recognition of 3D freeform surface from 2D sketch

In this paper, the Back Propagation (BP) network and Radial Basis Function (RBF) neural network are employed to recognize and reconstruct 3D freeform surface from 2D freehand sketch. Some tests and comparison experiments have been made to evaluate the performance for the reconstruction of freeform surfaces of both networks using simulation data. The experimental results show that both BP and RBF based freeform surface reconstruction methods are feasible; and the RBF network performed better. The RBF average point error between the reconstructed 3D surface data and the desired 3D surface data is less than 0.05 over all our 75 test sample data

A convergent method for linear half-space kinetic equations

We give a unified proof for the well-posedness of a class of linear half-space equations with general incoming data and construct a Galerkin method to numerically resolve this type of equations in a systematic way. Our main strategy in both analysis and numerics includes three steps: adding damping terms to the original half-space equation, using an inf-sup argument and even-odd decomposition to establish the well-posedness of the damped equation, and then recovering solutions to the original half-space equation. The proposed numerical methods for the damped equation is shown to be quasi-optimal and the numerical error of approximations to the original equation is controlled by that of the damped equation. This efficient solution to the half-space problem is useful for kinetic-fluid coupling simulations