Zhiqing Pan

Zhiqing Pan, Jiwei Jia, Lian Zhang

We propose second-order-in-time parametric finite element methods for surface diffusion of closed curves in two dimensions and closed surfaces in three dimensions. The construction is based on exact geometric variation identities along a quadratic temporal interpolation path. The induced area variation in 2D is evaluated exactly by Simpson's rule, while the induced volume variation in 3D is evaluated exactly by Boole's rule. The resulting fully discrete schemes preserve the enclosed area or volume exactly, without introducing an auxiliary Lagrange multiplier for the geometric constraint. They can be assembled on BGN-predicted auxiliary geometries and are therefore compatible with existing second-order BGN-type implementations. Numerical experiments demonstrate the expected second-order behavior, area/volume conservation, and good mesh quality for both curve and surface evolutions.

Yunkui Pang, Zhiqing Pan, Ruiyang Sun et al.

With the involvement of artificial intelligence (AI), sketches can be automatically generated under certain topics. Even though breakthroughs have been made in previous studies in this area, a relatively high proportion of the generated figures are too abstract to recognize, which illustrates that AIs fail to learn the general pattern of the target object when drawing. This paper posits that supervising the process of stroke generation can lead to a more accurate sketch interpretation. Based on that, a sketch generating system with an assistant convolutional neural network (CNN) predictor to suggest the shape of the next stroke is presented in this paper. In addition, a CNN-based discriminator is introduced to judge the recognizability of the end product. Since the base-line model is ineffective at generating multi-class sketches, we restrict the model to produce one category. Because the image of a cat is easy to identify, we consider cat sketches selected from the QuickDraw data set. This paper compares the proposed model with the original Sketch-RNN on 75K human-drawn cat sketches. The result indicates that our model produces sketches with higher quality than human's sketches.