Stable Equilibrium Optimization for 3D Printed Objects

3D printing is increasingly popular, giving the public the ability to create objects. First of all, a 3D digital model is constructed by 3D modeling software, and then manufactured via 3D printer. Virtual environment with no physical rules makes the model stand with diverse gesture, but failed in the real world. We put forward the stable equilibrium optimization problem for 3D printed object for the first time. To solve this problem, we propose a stable equilibrium optimization algorithm based on the principle of the tumbler, which can make the object achieve stable equilibrium. Specifically, we voxelize the object iteratively from horizontal and vertical direction voxel by voxel until obtaining the best carving result, measured by an equation; for some exceptions, we continue to modify the bottom within an acceptable small range to achieve stable equilibrium. This novel heuristic carving strategy avoids possible problems such as suspension, self-intersection, etc. Modification of the bottom part within the small range also ensures that the shape of the object is basically unchanged. The feasibility of the proposed method is demonstrated by several examples of successful optimization. The limitation is that multiple material is not considered in this paper for the complexity of operation, which is to be explored in the future.