  Polygonal modeling is a core task of content creation in Computer Graphics.
The complexity of modeling, in terms of the number and the order of operations
and time required to execute them makes it challenging to learn and execute.
Our goal is to automatically derive a polygonal modeling sequence for a given
target. Then, one can learn polygonal modeling by observing the resulting
sequence and also expedite the modeling process by starting from the
auto-generated result. As a starting point for building a system for 3D
modeling in the future, we tackle the 2D shape modeling problem and present
AutoPoly, a hybrid method that generates a polygonal mesh construction sequence
from a silhouette image. The key idea of our method is the use of the Monte
Carlo tree search (MCTS) algorithm and differentiable rendering to separately
predict sequential topological actions and geometric actions. Our hybrid method
can alter topology, whereas the recently proposed inverse shape estimation
methods using differentiable rendering can only handle a fixed topology. Our
novel reward function encourages MCTS to select topological actions that lead
to a simpler shape without self-intersection. We further designed two deep
learning-based methods to improve the expansion and simulation steps in the
MCTS search process: an $n$-step "future action prediction" network (nFAP-Net)
to generate candidates for potential topological actions, and a shape warping
network (WarpNet) to predict polygonal shapes given the predicted rendered
images and topological actions. We demonstrate the efficiency of our method on
2D polygonal shapes of multiple man-made object categories.
