Generation of a tree-like support structure for fused deposition modelling based on the L-system and an octree
Graphical abstract
Introduction
Fused deposition modelling (FDM) is one of the mainstream technologies for 3D printing. In general, the first step of the printing process is to melt the printing material at high temperature; then, the melted material is extruded on the printing tray layer by layer; finally, the 3D model is completed when it has cooled. Because every layer is extruded on the layer beneath it, the previous layer plays a role as the support structure of the current layer. The contour and area of every layer will change with increasing printing height. When the change is sufficiently violent, the support of the previous layer provided to the current layer will be insufficient. Usually, extra support structures are needed in this case, and these structures need to be discarded manually after printing. However, these extra support structures require extra printing materials and printing time. In addition, an unreasonable support structure may result in removal difficulty and could even damage the model when removed.
Many researchers have focused on improving the support structure of FDM. These studies can be divided into two parts: finding the required support areas and generating appropriate support structures for the required support areas. For the former, the typical methods were proposed by Allen and Dutta [1], who used the angle between the outwardly directed normal vectors of the triangular facets and the horizontal plane to find the required support areas, and Chalasani et al. [2], who adopted the model slicing method. In the latter work, two main branches were researched: internal supports that modify the inside of the object to balance material cost, print time and physical properties, and external supports that assist the fabrication process and are removed after completion [3].
Many methods have been proposed to generate internal supports during 3D printing. Wang et al. [4] presented an automatic solution to design a skin-frame structure that is designed by an optimization scheme. Zhang et al. [5] proposed a method for designing the internal support frame structure of 3D models based on their medial axis. Li et al. [6] proposed a density variable shape modelling method and utilized a pure mathematical 3D implicit function to generate a porous structure with a gradational interior. Wang et al. [7] built a self-supporting frame with a set of scale-adaptive parallelepiped grids to replace the solid interior of the printed model to reduce material consumption. Wu et al. [8] presented a novel method for generating application-specific infill structures on rhombic cells, in which an objective function can be improved by adaptively subdividing the rhombic grid to avoid additional support structures. Lee and Lee [9] used 3D block partitioning to divide a given object using arbitrary planes and merged the inner unit blocks into a combined block to minimize the inner support structure. Because the inner support structure usually cannot be removed, a support-free structure was also researched. Wang et al. [10] proposed a sparsity optimization framework with support-free constraints to reduce printing material. Wang et al. [11] presented a computational framework that can generate optimized hollow models to overcome the difficulty of fabricating voids inside a solid. Liu et al. [12] presented an edge contraction-based mesh simplification algorithm to optimize the position of the contracted edge for higher self-supportability. Lee et al. [13] proposed a novel approach for generating support-free interior hollowing for general 3D shapes using a Voronoi diagram of ellipses.
For some models that have mid-air or excessive overhang surfaces, external support structures are necessary as extra supports. Many researchers have conducted research on the generation of external supports. Huang et al. [14], [15] proposed a top-down approach for calculating the support slice layer by layer, where support structures are generated with sloping walls to reduce the volume of the support structure. Strano et al. [16] proposed an approach that used pure mathematical 3D implicit functions to design and generate cellular support structures. Dumas et al. [17] presented a technique that optimized a printable scaffolding composed of bridges and vertical pillars to support all points that were selected based on overhang and part stability. Qiu et al. [18] obtained the supporting points by Poisson disk sampling in the projected overhang area and used a cone scanning algorithm to detect the dependent points for each supporting point. Vanek et al. [19] introduced an approach that oriented the 3D model into a position with minimal area requiring support, and the areas were supported by a tree-like support structure that minimized the overall length. Schmidt and Umetani [20] presented a strategy for the top-down procedural generation of support structures, where struts are added to increase the print strength. Barnett and Gosselin [21] proposed the shell technique and the film technique, which were particularly suitable for weak support materials, and both techniques were demonstrated through the construction of parts using an experimental large-scale 3D foam printer. Hu et al. presented an orientation-driven shape optimizer to optimize the original model to achieve a more self-supported shape [22], and they extended their indirect computation to an approach in which the computation was directly based on the information of the input models [23]. Vaidya and Anand [24] presented a new approach using space-filling cellular structures in conjunction with Dijkstra's shortest path algorithm to generate optimized support structures. Song et al. [25] improved the L-system and proposed a support generation algorithm using its grammatical composition. Habib and Khoda [26] proposed a support architecture design methodology that clustered the required support points that were segmented into closed-convex regions and then generated self-supported slanting and pillar support structures based on these convex grains.
In this paper, the generation of external support structures for fused deposition modelling is studied, and a new tree-like support structure generation method based on L-systems and octrees is presented to obtain stable support structures quickly with few materials that can be removed easily. This paper is organized as follows. In Section 2, the principle of the 3D L-system is explained regarding the generation of the 3D tree-like support structure. In Section 3, an algorithm based on the octree data structure is proposed for quickly obtaining the intersections of tree-like rays and the 3D model. The whole process of designing the tree-like support structure is indicated in Section 4, which includes the method for determining the number of support structures in each required support area, the root nodes, the initial step size, the number of iterations and the diameter of each branch of each tree, as well as the pruning operation for eliminating redundant branches. The case studies are presented in Section 5, in which the support structures of several models obtained using our method are exhibited and printed using a real 3D printer. In Section 6, the method proposed in this paper is compared with similar research, and the limitations of the method are discussed. In the final section, some conclusions are presented.
Section snippets
Design of a tree-like structure based on the L-system
The L-system is an abbreviation for the Lindenmayer system, which is a mathematical model of cell interactions during growth, as proposed by the Hungarian biologist Lindenmayer in 1968 [27]. L-systems, which are widely used in the simulation of plant growth processes, are actually string rewriting systems that define different basic characters, such as drawing a line segment, rotating the current direction to another direction and increasing or decreasing the step size. Graphics can be
Intersection algorithm based on an octree data structure
An octree is a data structure commonly used to describe 3D space. It is an improvement of the method used to represent shape and volume by using a 3D voxel array and is also an extension of the quad-tree method in 3D space. Each child node of the octree represents the volume element of a spatial cube, and each node contains eight sub-nodes, which together represent the volume of the parent node.
The support structure generation algorithm of our work uses this method to obtain the intersection
Design of the support structure for fused deposition modelling
The branch structure can be generated by extending the L-system into 3D space. To use this branch structure as a support structure for the STL model, we must know how many branch structures of this type are needed for each required support area. The initial growth point TreeStartPoint of each branch structure, the number num of iterations, the initial step size length and the diameter dia of each branch must also be determined. After the initial support structure is generated, the top branches
Simulation
The method proposed in this paper is implemented in the development platform of Microsoft Visual Studio 2015 software using the C++ language, and the model is displayed by OpenGL. Generally, the CAD model is first imported into the ASCII STL model. Then, the model can be automatically added to the support structure when it is imported into the tree-like support generation software, and the original model and the support structure will be merged into a new STL model. Fig. 7 shows the support
Discussion
As a simulation method of plant growth processes, L-systems are commonly used to generate very complex trees and flowers in computer graphics. An octree, as a tree data structure describing 3D space that is used for scene management in 3D space, can improve the efficiency of scene modelling and the speed of path searching. The pruning algorithm is often used to subtract some subtrees or leaf nodes from the decision tree model and use its root node as a new leaf node to simplify the model. This
Conclusions
In this paper, a support structure generation method based on the L-system and an octree is proposed for fused deposition modelling. The method utilizes the L-system to generate a bottom-up tree support structure and achieves fast intersection through an octree data structure. At the same time, a pruning algorithm considering the topological relationship of the support trees is proposed to remove excess branches. This method includes three parts. The first part uses the L-system grammatical
Acknowledgements
This research was supported by the National Science and Technology Major Project of China (2014ZX04001051) and the Experimental Technology Research Funding Project of Huazhong University of Science and Technology (2015-9).
References (27)
- et al.
Cost-effective printing of 3D objects with skin-frame structures
ACM Trans. Graph.
(2013) - et al.
Medial axis tree-an internal supporting structure for 3D printing
Comput. Aided Geom. Des.
(2015) - et al.
Cost-effective printing of 3D objects with self-supporting property
Visual. Comput.
(2018) - et al.
Self-supporting rhombic infill structures for additive manufacturing
Comput. Aided Des.
(2016) - et al.
Support-free frame structures
Comput. Graph.
(2017) - et al.
Support-free hollowing
IEEE Trans. Vis. Comput. Graph.
(2017) - et al.
Generating sparse self-supporting wireframe models for 3D printing using mesh simplification
Graph. Models
(2018) - et al.
Support-free hollowing for 3D printing via Voronoi diagram of ellipses
Comput. Aided Des.
(2018) - et al.
Slice data based support generation algorithm for fused deposition modeling
Tsinghua Sci. Technol.
(2009) - et al.
Weak support material techniques for alternative additive manufacturing materials
Addit. Manuf.
(2015)
Support slimming for single material based additive manufacturing
Comput. Aided Des.
Optimum support structure generation for additive manufacturing using unit cell structures and support removal constraint
Procedia Manuf.
Grain-based support architecture design for additive manufacturing
Procedia Manuf.
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