Method for planning 3D printing path based on Fermat's spiral

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First Claim
1. A method of planning a 3D printing path for controlling a 3D printer to print an object, the method comprising:
 generating a plurality of isocontours for a given topological connected region, wherein adjacent isocontours of the plurality of isocontours have a set spacing therebetween;
constructing a spiral connected graph according to the plurality of isocontours;
generating a spiral connected tree according to the spiral connected graph;
generating the 3D printing path based on connecting a subset of the plurality of isocontours according to the spiral connected tree to form a connected Fermat spiral; and
smoothing the 3D printing path through a global optimization method based on a width of the printing path being consistent; and
controlling a path of a print head of the 3D printer according to the 3D printing path to print the object.
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Abstract
The present invention discloses a method of planning a 3D printing path based on Fermat'"'"'s spiral. The method comprises generating a plurality of isocontours for a given topological connected region, wherein adjacent isocontours of the plurality of isocontours have a set spacing therebetween. The method also comprises constructing a spiral connected graph according to the plurality of isocontours and generating a spiral connected tree according to the spiral connected graph. The method further comprises connecting a subset of the plurality of isocontours according to the spiral connected tree to form a connected Fermat spiral. The method additionally comprises smoothing the connected Fermat spiral through a global optimization method based on a width of the printing path being consistent.
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SYSTEMS AND METHODS FOR IMPROVED 3D PRINTING  
Patent #
US 20150266244A1
Filed 03/19/2015

Current Assignee
Autodesk Inc.

Sponsoring Entity
Autodesk Inc.

Deformable tree matching with tangentenhanced coherent point drift  
Patent #
US 9,305,352 B2
Filed 10/31/2013

Current Assignee
Siemens Corp.

Sponsoring Entity
Siemens Corp.

RADIAL LATTICE STRUCTURES FOR ADDITIVE MANUFACTURING  
Patent #
US 20160209820A1
Filed 01/15/2016

Current Assignee
Autodesk Inc.

Sponsoring Entity
Autodesk Inc.

10 Claims
 1. A method of planning a 3D printing path for controlling a 3D printer to print an object, the method comprising:
generating a plurality of isocontours for a given topological connected region, wherein adjacent isocontours of the plurality of isocontours have a set spacing therebetween; constructing a spiral connected graph according to the plurality of isocontours; generating a spiral connected tree according to the spiral connected graph; generating the 3D printing path based on connecting a subset of the plurality of isocontours according to the spiral connected tree to form a connected Fermat spiral; and smoothing the 3D printing path through a global optimization method based on a width of the printing path being consistent; and controlling a path of a print head of the 3D printer according to the 3D printing path to print the object.  View Dependent Claims (2, 3, 4, 5, 6, 7, 8, 9, 10)
1 Specification
The present Application is a continuation of PCT Application No. PCT/CN2016/084383 entitled “METHOD FOR PLANNING 3D PRINTING PATH BASED ON FERMAT'"'"'S SPIRAL” filed Jun. 1, 2016, which claims the priority benefit of Chinese Application No. 201610242579.1 entitled “METHOD FOR PLANNING 3D PRINTING PATH BASED ON FERMAT'"'"'S SPIRAL” filed Apr. 19, 2016, each of which is hereby expressly incorporated by reference herein in its entirety.
The present invention relates to threedimensional (3D) printing. Specifically, the present invention relates to a 3D printing path planning method.
3D printing is an emerging manufacturing technology of extruding a material layer by layer to manufacture physical objects based on digital models and is also referred to as additive manufacturing (AM). 3D printing, in which any complex 3D digital models can be input, is suitable for the manufacture of customizable products. In recent years, rapid development of 3D printing technologies has presented many opportunities and challenges to academia and related industries. 3D printing technologies are usually based on a discretestacking principle to manufacture the physical objects by extruding a material layer by layer. According to different printing materials and implementation processes, various 3D printing technologies can be divided into five types: (1) highenergy beam sintering and melting molding of a powder or filament material, e.g., selective laser sintering (SLS) and selective laser melting (SLM); (2) photocuring molding of liquid resin, e.g., stereo lithography appearance (SLA), digital light processing (DLP), etc.; (3) extrusion hot melt molding of wires, e.g., fused deposition modeling (FDM), etc.; (4) bonding or welding molding of sheets/boards/blocks, e.g., Laminated Object Manufacturing (LOM), etc.; and (5) liquid spray printing molding, e.g., three dimensional printing (3DP), etc.
A common 3D printing process includes threedimensional (3D) digital model generation, data format conversion, slice calculation, printing path planning and 3D printing. The 3D digital model generation is the basis of the entire 3D printing process, and a 3D digital model is generated generally using a variety of 3D modeling software (e.g., CAD software) or 3D scanning equipment. The 3D digital model is subjected to a data format conversion process and then transmitted. Currently, a common data format that is often used in 3D printing is the stereolithography (STL) file format. The slice calculation process is to “cut” the 3D model into slices. In order to materialize the slices generated in the slice calculation process, the path of a print head needs to be planned. The 3D printing material is converted into physical slices during the movement of the print head. Finally, a 3D printer prints (for example, extrudes material) according to the abovementioned slices and print head path control information, until a complete object is formed.
The path planning is a key step in the overall 3D model printing process. For any topological connected region, the existing path planning methods, such as a Zigzag method, may fill the region using multiple printing paths. Frequent onoff switching of the print head may severely affect the printing quality. On the other hand, the generated printing path may have many corners that are less than or close to 90 degrees, and sharp turns of the print head may seriously affect printing time and printing quality of the printed object.
In order to solve the above problems, an aspect of the present invention proposes a 3D printing path planning method based on a Fermat spiral, according to which any topological connected region is divided into multiple independent subregions by adopting a divideandrule method to fill Fermat spirals respectively, then the plurality of independent Fermat spirals are connected to generate a continuous printing path, and the printing path is smoothed by adopting a global optimization method under the constraint of keeping the width of the printing path consistent.
In order to achieve the above objective, the present invention adopts a method for planning a 3D printing path. The method is based on a Fermat spiral. The method comprises generating a plurality of isocontours for a given topological connected region, wherein adjacent isocontours of the plurality of isocontours have a set spacing therebetween. The method also comprises constructing a spiral connected graph according to the plurality of isocontours and generating a spiral connected tree according to the spiral connected graph. The method further comprises connecting a subset of the plurality of isocontours according to the spiral connected tree to form a connected Fermat spiral and smoothing the connected Fermat spiral through a global optimization method based on a width of the printing path being consistent.
In some aspects, each generated isocontour of the plurality of isocontours is expressed by a combination of (1) a distance from the respective isocontour to a boundary of the given topological connected region and (2) an index among the plurality of isocontours with the distance.
In some aspects, constructing a spiral connected graph according to the plurality of isocontours and generating a spiral connected tree according to the spiral connected graph comprises constructing a weighted spiral connected graph according to the plurality of isocontours and selecting a minimum spanning tree (MST) generated from the spiral connected graph as the spiral connected tree.
In some aspects, in constructing the weighted spiral connected graph according to the plurality of isocontours, each isocontour of the plurality of isocontours corresponds to one node in the spiral connected graph, and, if a connected edge of an isocontour of the plurality of isocontours relative to an adjacent isocontour of the plurality of isocontours is nonempty, the spiral connected graph has an edge connecting the nodes of the isocontour and the adjacent isocontour, wherein a weight value of the edge is the length of the connected edge.
In some aspects, connecting a subset of the plurality of isocontours according to the spiral connected tree to form a connected Fermat spiral comprises decomposing the spiral connected tree into multiple independent Fermat spiral subtrees and trunk nodes, connecting isocontours that correspond to the Fermat spiral subtrees to generate a sub Fermat spiral, connecting the sub Fermat spiral with isocontours that correspond to the trunk nodes associated with the sub Fermat spiral, and connecting the isocontours corresponding to the trunk nodes.
In some aspects, in decomposing the spiral connected tree into multiple independent Fermat spiral subtrees and trunk nodes, in the spiral connected tree, first nodes of which degrees are less than or equal to two degrees are defined as type I nodes, second nodes of which degrees are greater than two degrees are defined as type II nodes, and connected type I nodes are connected into different Fermat spiral subtrees.
In some aspects, connecting isocontours that correspond to the Fermat spiral subtrees to generate a sub Fermat spiral comprises connecting the isocontours that correspond to the Fermat spiral subtrees to generate a sub spiral and generating a corresponding sub Fermat spiral from the sub spiral.
In some aspects, connecting the isocontours that correspond to the Fermat spiral subtrees to generate a sub spiral comprises selecting an enterpoint on an outermost isocontour corresponding to the Fermat spiral subtrees, starting from the enterpoint, connecting two adjacent isocontours into a continuous line, and connecting all the isocontours that correspond to the Fermat spiral subtrees into the sub spiral.
In some aspects, smoothing the connected Fermat spiral through a global optimization method based on a width of the printing path being consistent comprises dynamically selecting sample points based on a curvature of each position of the connected Fermat spiral, constructing a global optimization function, setting penalties for penalty terms of a magnitude of perturbations on the sample points, a degree of smoothness, and a degree of spacing maintenance, and calculating an optimal solution of the global optimization function through an iterative GaussianNewton optimization method.
In some aspects, in dynamically selecting sample points based on the curvature of each position of the connected Fermat spiral, more sample points are selected at a first position having a larger curvature than at a second position having a smaller curvature than the first position.
Embodiments of the present invention have the following beneficial effects:
(1) A continuous printing path can be generated for any topological connected region, and the print head does not need any onoff switching operation in the printing process, which is beneficial to improving the printing quality;
(2) Compared with the conventional Zigzag method, the proposed path planning method for generating the continuous printing path reduces the number of corners that are less than or close to 90 degrees, and is beneficial to reducing the printing time;
(3) The present invention can be directly used for a fused deposition modeling (FDM) printer, is beneficial to improving the object printing quality of the FDM printer and reducing the required printing time, and has an effect of promoting the development of the FDM printer;
(4) The present invention can be transformed according to the basic knowledge in the art to be applied to SLS, SLM, SLA, DLP, LOM and other types of printers, thus being widely applicable;
(5) The present invention is particularly suitable for applications in the fields of bioprinting, printing of metal materials for aerospace and the like, which require high internal quality of printed objects, and is beneficial to improving the internal printing quality;
(6) In the present invention, a print head path having both characteristics of continuousness and smoothness is generated based on a Fermat spiral for any topological connected region, thereby significantly improving the printing quality and reducing the printing time.
The present invention will be further illustrated below in conjunction with the accompanying drawings and embodiments.
As shown in
In step (1), each isocontour generated is expressed by c_{i,j}, wherein i indicates the distance d(∂R)=(i−0.5)w from the corresponding isocontour to the boundary of the given topological connected region, and j is an index among all isocontours with the distance i. The connected edge of the isocontour c_{i,j }relative to the c_{i+1,j′} is defined as: O_{i,j,j′}={pϵC_{i,j}d(p,c_{i+1,j′})<d(p,c_{i+1,k}), k≠j′}.
In step (2), the specific method of generating a spiral connected tree according to the isocontours includes (21) constructing a weighted spiral connected graph, G, according to the isocontours and (22) selecting a minimum spanning tree generated from the spiral connected graph as the spiral connected tree T, as shown in
In step (21), each isocontour corresponds to one node in the spiral connected graph, and if the connected edge O_{i,j,j′} of the isocontour c_{i,j }relative to the c_{i+1,j′} is nonempty, the spiral connected graph has an edge connecting the nodes c_{i,j }and c_{i+1,j′}, wherein the weight value of the edge is the length of the connected edge O_{i,j,j′}.
In step (3), the specific method of connecting the isocontours to generate a connected Fermat spiral includes (31) decomposing the spiral connected tree into multiple independent Fermat spiral subtrees and trunk nodes;
The specific method of connecting the isocontours to generate a connected Fermat spiral further includes (32) connecting the isocontours corresponding to the Fermat spiral subtrees to generate a sub Fermat spiral, as shown in
In step (32), the specific method of connecting the isocontours corresponding to the Fermat spiral subtrees to generate a sub Fermat spiral includes (321) connecting the isocontours corresponding to the Fermat spiral subtrees to generate a sub spiral. As shown in
In step (32), the specific method of connecting the isocontours corresponding to the Fermat spiral subtrees to generate a sub Fermat spiral also includes (322) generating a corresponding sub Fermat spiral from the sub spiral. As shown in
As shown in
In step (33), the sub Fermat spiral is connected with the isocontours corresponding to the trunk nodes associated with the sub Fermat spiral. As shown in
In step (34), the isocontours corresponding to the two trunk nodes are connected as shown in
In step (4), the specific method of smoothing the generated connected Fermat spiral includes (41) dynamically selecting sample points based on the curvature of each position of the connected Fermat spiral, with the purpose that more sample points are selected at the position having a larger curvature, and fewer sample points are selected at the position having a smaller curvature, wherein the selected sample points are p_{1}^{0}, . . . , p_{N}^{0}. The specific method of smoothing the generated connected Fermat spiral also includes (42) performing local position perturbations on the sample points under the constraint that the width of the printing path is kept consistent to achieve the objective of smoothing the generated path and constructing a global optimization function, including three penalty terms for punishment with respect to the magnitude of the perturbations on the sample points, the degree of smoothness and the degree of spacing maintenance.
An equation f_{regu}=Σ_{i=1}^{N}p_{i}p_{i}^{0}^{2 }the penalty term for the magnitude of the perturbations on the sample points, wherein p_{1}, . . . , P_{N }are the sample points, and p_{i}p_{i}^{0} is the length of the edge. The penalty term for the degree of smoothness is expressed as: f_{smooth}=Σ_{i=1}^{N2}∥(1−u_{i})p_{i}+u_{i}p_{i+2}−p_{i+1}∥^{2}, wherein u_{i}=u_{i}=p_{i+1}^{0}p_{i}^{0}/(p_{i+1}^{0}p_{i}^{0}+p_{i+2}^{0}p_{i+1}^{0}).
For each point p_{i}, there are two cases of its closest points on the adjacent paths. In the first case, such a closest point is a point on the edge of the adjacent path, as shown in
As shown in
0≤t_{i,j}≤1. ε={(p_{i},p_{j},p_{j+1})} is defined. The closest fixed point p_{j }solved in the first case certainly satisfies 0≤t_{i,j}≤1, and then V={p_{i},p_{j}}. The penalty term that defines the degree of spacing maintenance is: f_{space}=Σ_{(p}_{i}_{,p}_{j}_{,p}_{j+1}_{)ϵε}(p_{i}f_{ij}−d)^{2}+Σ_{(p}_{i}_{,p}_{j}_{)ϵv}(p_{i}p_{j}−d)^{2}. In summary, the global optimization objective function is:
α is a parameter that controls the degree of smoothness, and β is a parameter that controls the degree of spacing maintenance, generally, α=200, and β=1.0.
The specific method of smoothing the generated connected Fermat spiral also includes (43) calculating an optimal solution of the optimization function through an iterative GaussNewton optimization method.
The abovementioned global optimization objective function contains both a discrete component (ε, V) and a continuous component (f_{requ}), and the patent adopts iterative optimization thereof in sequence. When a fixed point is fixed, the discrete component ε, V is calculated. When the discrete component ε, V is fixed, the global optimization objective function is solved using the GaussNewton method.
The entire optimization process is usually completed only by 48 iterations.
Although the specific embodiments of the present invention are described above in combination with the accompanying drawings, the protection scope of the present invention is not limited thereto. It should be understood by those skilled in the art that various modifications or variations that could be made by those skilled in the art based on the technical solution of the present invention without any creative effort shall fall into the protection scope of the present invention.