# An Approach of Path Optimization Algorithm for 3D Concrete Printing Based on Graph Theory
## 1 Introduction
The new support generation method can significantly save more material. [PERSON] and [PERSON] [13] presented a novel approach to design and carry out trajectories over regular curved surfaces. Their course provides a unified methodology for surface fitting from 3D surface measurements and mapping a curve from 2D onto a 3D surface with minimal distortion. [PERSON] et al. [14] reconstructed CAD models from an original (GATech Buzz) sample with 2D image information. A CAD model for optimization and validation is adopted to sustain manufacturing reproduction based on system simulation feedback. To avoid collision with the produced path from the retraction path, their pick adaptive ring path generation and prediction in each planning iteration may also minimize material removal. [PERSON] et al. [15] focused on understanding how the nozzle path planning strategy and robot kinematics affect the geometry and porosity distribution in a 3D object and found that the nozzle path has an essential impact on the formation of under-built and over-built structures. The knowledge generated from this research can significantly influence the development of nozzle path planning strategies in AM, providing the means to produce improved near-net shapes with controlled porosity formation. [PERSON] et al. [16] proposed a load-dependent 3D printing path planning method for continuous fiber-reinforced plastics, which has been submitted[PERSON] By using the topological optimization methods, the load transmission paths were reordered and extracted. Then the developed stress vector tracing algorithm was used to generate the continuous load-dependent printing path of CFRPs from the extracted features, which contain geometry and stress vectors. The printing path planned by this method precisely follows the load transfer path of the part, which can provide higher mechanical properties. [PERSON] et al. [17] proposed a level-set-based optimization method to generate contour-parallel deposition paths for material extrusion-based additive manufacturing. The resulting contour path is smoothed using the level set from the input footprint; local optimization is then applied to smooth the points on the path by adaptively adjusting the position of the path. This deposition using the generated paths can effectively improve the manufacturing quality. [PERSON] et al. [18] introduced a methodology to compute advancing fields for material accumulation by always performing material deposition along the surfaces of convex hulls; therefore, the printing process is guaranteed to remain collision-free. The 3 Dprinting path is generated by their algorithm to fully fabricate models with large overhangs and high-genus topologies without any support structures. [PERSON] et al. 's method consists in the partition of a RC member into different concrete segments printed separately and assembling them into a unique element along with the steel reinforcement system [19]. The approach is expected to facilitate the production of free-form structurally optimized RC elements with the final aim of saving concrete material and, at the same time, fabricating lighter structures. [PERSON], [PERSON], and [PERSON] [20] developed a framework that creates a new polygonal mesh representation of the sparse infill domain of a layer-by-layer 3D printing job. It guarantees the existence of a single, continuous nozzle path covering each connected piece of the domain in every layer in this graphical model. Their algorithm produces a nozzle path that avoids material collisions and crossovers and can be printed in a continuous fashion, irrespective of the complex geometry or topology of the domain. Through multiple experiments, we found two crucial influencing factors of the nozzle running path on 3D concrete printing. They are: (1) When the nozzle runs a longer distance (idle stroke) in the non-printing area, the print time will be longer. (2) The nozzle head-up will produce a local accumulation effect, and when the print size is relatively small, the local cumulative effect is more obvious.