In this paper we propose a sketch-based interface for drawing and generating a realistic 3D human face with texture. The free form sketch-based interface allows a user to intuitively draw a portrait as in traditional pencil sketching way. Then, the user’s drawing is automatically reshaped to an accurate natural human facial shape with the guidance of a statistical description model, and an arti...

We study nonlinear control systems in the plane, affine with respect to control. We introduce two sets of feedback equivariants forming a phase portrait PP and a parameterized phase portrait PPP of the system. The phase portrait PP consists of an equilibrium set E, a critical set C (parameterized, for PPP), an optimality index, a canonical foliation and a drift direction. We show that under wea...

In this paper, different nonlinear dynamics analysis techniques are employed to unveil the rich nonlinear phenomena of the electromagnetic system. In particular, bifurcation diagrams, time responses, phase portraits, Poincare maps, power spectrum analysis, and the construction of basins of attraction are all powerful and effective tools for nonlinear dynamics problems. We also employ the method...